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Questions and Answers of College Algebra

Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (fg)(2)
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (fh) (-1)
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (1)(yf)
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (gh) (-2)
Simplify each expression. Assume that all variables represent nonzero real numbers.35 • 3-6
Simplify each expression. Assume that all variables represent nonzero real numbers.44 • 4-6
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (gh)(-3)
Simplify each expression. Assume that all variables represent nonzero real numbers.a-3a2a-4
Simplify each expression. Assume that all variables represent nonzero real numbers.k-5k-3k4
Simplify each expression. Assume that all variables represent nonzero real numbers.(5-3)-2
Simplify each expression. Assume that all variables represent nonzero real numbers.(4-4)-2
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (fg)(-2)
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (fg)(0)
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (fh) (0)
Simplify each expression. Assume that all variables represent nonzero real numbers.(x-4)3
Simplify each expression. Assume that all variables represent nonzero real numbers. (K2)-3k4
Simplify each expression. Assume that all variables represent nonzero real numbers.(x-3)6
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (7-) (81)
Simplify each expression. Assume that all variables represent nonzero real numbers. sxt-(ex)
Let ƒ(x) = x2 - 9, g(x) = 2x, and h(x) = x - 3. Find each of the following. (fg 3
Consider the figure.What is the length of each side of the blue square in terms of a and b? a b b
Simplify each expression. Assume that all variables represent nonzero real numbers. z(+)zt
Simplify each expression. Assume that all variables represent nonzero real numbers. -2m-¹(m³) ²
Consider the figure.What is the formula for the area of a square? Use the formula to write an expression, in the form of a product, for the area of the blue square. a b b
Simplify each expression. Assume that all variables represent nonzero real numbers. (5a-¹)4(a²)-3
Consider the figure.Each green rectangle has an area of________ . Therefore, the total area in green is represented by the polynomial__________. a b b
Simplify each expression. Assume that all variables represent nonzero real numbers. (3p-4)²(p³)-1
Consider the figure.The yellow square has an area of________ . a b b
Simplify each expression. Assume that all variables represent nonzero real numbers. (2-4x³)-1
Simplify each expression. Assume that all variables represent nonzero real numbers. -4a³b²-3 12ab-4
Choose the letter of the correct response. Which choice is an example of a polynomial in factored form? A. 3x²y³ + 6x²(2x + y) C. (-2+ 3x) (5y² + 4y + 3) B. 5(x + y)2 10(x + y)³ D. (3x + 4)
Factor out the greatest common factor. 8s + 16t
Factor out the greatest common factor. 35p + 70q
Consider the figure.The area of the entire colored region is represented by__________ , because each side of the entire colored region has length _______. a b b
Consider the figure.(a) What must be true about the expressions for the area of the blue square found in Exercises 124 and 128?(b) Write an equation based on the answer in part (a).Data from in
Simplify each expression. Assume that all variables represent nonzero real numbers. (3pq)q² 6p²q4
Simplify each expression. Assume that all variables represent nonzero real numbers. 1-(fm) 9m³
Simplify each expression. Assume that all variables represent nonzero real numbers. 996-D a³b-4
Consider the figure.Draw a figure and give a similar proof for (a + b)2 = a2 + 2ab + b2. a b b
Simplify each expression. Assume that all variables represent nonzero real numbers. (-8xy)y3 4x5y4
Simplify each expression. Assume that all variables represent nonzero real numbers. 5p4 &. (z_d)
Simplify each expression. Assume that all variables represent nonzero real numbers. 2(-m-¹)-4 9(m-³)²
Simplify each expression. Assume that all variables represent nonzero real numbers. 4a³(a-¹)3 (a-²)-² -2
Simplify each expression. Assume that all variables represent nonzero real numbers. 12k-²(k-³)-4 6k5
Simplify each expression. Assume that all variables represent nonzero real numbers. (3rs)-2 32x²5-4
Simplify each expression. Assume that all variables represent nonzero real numbers. 2P . q². 3 304 -4 q -1
Simplify each expression. Assume that all variables represent nonzero real numbers. (-y-4)² 6(y-5)-1
Simplify each expression. Assume that all variables represent nonzero real numbers. (2k) ²m-5 (km) -3
Simplify each expression. Assume that all variables represent nonzero real numbers. 523-3/8a-1-3 152-2 2a²
Simplify each expression. Assume that all variables represent nonzero real numbers. 8x6y3 x4y-4 -2
Simplify each expression. Assume that all variables represent nonzero real numbers. 2²y4(y-3) -1 25y-2
Simplify each expression. Assume that all variables represent nonzero real numbers. 3-¹m² (m²)-1 3²m-2
Simplify each expression. Assume that all variables represent nonzero real numbers. 5m4n-3-2 m=5n²
Simplify each expression. Assume that all variables represent nonzero real numbers. -3x4,6 15x6y7, -3
Simplify each expression. Assume that all variables represent nonzero real numbers. (2k) ²k³ k-lk-5 (5k-2)-3
Choose the letter of the correct response. Which choice is the correct completely factored form of 8 + 24r? A. 8(3r) B. -8 (-3r) C. 8(1 + 3r) D. 4(2 +6r)
Simplify each expression. Assume that all variables represent nonzero real numbers. (2m²p³)²(4m²p)-² (-3mp4)-¹(2m³p4)3
Simplify each expression. Assume that all variables represent nonzero real numbers. (-5y³24)2(2y25)-2 10(y4z) ³(3y³z2)-1
A student factored the following polynomial as shown.The teacher did not give the student full credit. Give the correct answer. 4x²y5 - 8xy³ = 2xy³(2xy² - 4)
A student factored the following polynomial as shown.The teacher did not give the student full credit. Give the correct answer. 2tw² 16t+5w² - 40 = (2tw² = 2t (w²8) + 5(w² - 8) 16t) + (5w² - 40)
Find the greatest common factor for each list of terms. 6m(r + t)2, 3p(r + t) 4
Find the greatest common factor for each list of terms. 7z²(m + n)4, 9z³(m + n)5
Find the greatest common factor for each list of terms.9m3, 3m2, 15m
Find the greatest common factor for each list of terms.4a2, 6a, 2a3
Find the greatest common factor for each list of terms.16xy3, 24x2y2, 8x2y
Find the greatest common factor for each list of terms.10m2n2, 25mn3, 50m2n
Factor out the greatest common factor. 15r - 45
Factor out the greatest common factor. 4 + 20 z
Factor out the greatest common factor. 9 + 27x
Factor out the greatest common factor. 8y - 15
Factor out the greatest common factor. 7x - 40
Factor out the greatest common factor. -4p3q4 - 2p2q5
Factor out the greatest common factor. 16z2n6 + 64zn7 - 32z3n3
Factor out the greatest common factor. -3z5w2 - 18z3w4
Factor out the greatest common factor.6k3 - 36k4 - 48k5
Factor out the greatest common factor.7x3 + 35x4 - 14x5
Factor out the greatest common factor. (m − 4) (m + 2) + (m − 4) (m + 3) - -
Factor out the greatest common factor. 10t5 - 2t3 - 4t4
Factor out the greatest common factor. (OI + 2) (S-2) + (L + ²) (S-2)
Factor out the greatest common factor. 6p3 - 3p2 - 9p4
Factor out the greatest common factor. 15a2c3 - 25ac2 + 5ac
Factor out the greatest common factor. 15y3z3 - 27y2z4 + 3yz3
Factor out the greatest common factor. 5r3s5 + 10r2s2 - 15r4s2
Factor out the greatest common factor. 14a3b2 + 7a2b - 21a5b3 + 42ab4
Factor out the greatest common factor. 12km3 - 24k3m2 + 36k2m4 - 60k4m3
Factor out the greatest common factor. (3x + 2)(x −4) − (3x + 2)(x+8)
Factor out the greatest common factor. 4(3x)² – (3 − x)³ + 3(3 − x) -
Factor out the greatest common factor. (2z - 1)(z + 6) - (2z - 1)(z-5)
Factor out the greatest common factor. 5(2-x)² - 2(2-x) ³
Factor out the greatest common factor. 15(2z + 1)³ + 10(2z + 1)² - 25(2z + 1)
Factor out the greatest common factor. 6(a + 2b)² − 4(a + 2b)³ + 12(a + 2b)4
Factor out the greatest common factor. z(xs) (x - c)z
Factor out the greatest common factor. 5(m + p)³ - 10(m + p)² - 15(m + p)4
Factor out the greatest common factor. 2(ts) + 4(ts)² – (ts)³
Factor out the greatest common factor. −9a²(p + q) − 3a³(p+q)² + 6a(p+q)³
Factor each polynomial in two ways. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient.-r3 + 3r2 + 5r
Factor each polynomial in two ways. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient.-t4 + 8t3 - 12t
Factor each polynomial in two ways. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient.-12s5 + 48s4
Factor each polynomial in two ways. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient.-16y4 + 64y3
Factor each polynomial in two ways. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient.-2x5 + 6x3 + 4x2

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