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mathematics
precalculus

Questions and Answers of Precalculus

Solve the equation. x2 = 9x
Solve the equation. w(4 – w2) = 8 – w3
Solve the equation. z(z2 + 1) = 3 + z2
Solve the equation. (x + 2) (x – 2) = (x – 3)2
Solve the equation. (x + 7)(x – 1) = (x + 1)2
Solve the equation. 4 y 2y
Solve the equation. 4 3 y y
Solve the equation. 0.9t = 1 + t
Solve the equation. 0.9t = 0.4 + 0.1t
Solve the equation. -x = 5 2.
Solve the equation. 3 4 4 |1
Solve the equation. 5 - (2x - 1) = 10
Solve the equation. 8x - (2x + 1) = 3x - 10
Solve the equation. 3(2 - x) = 2x - 1
Solve the equation. 2(3 + 2x) = 3(x - 4)
Solve the equation. 3 - 2x = 2 - x
Solve the equation. 6 - x = 2x + 9
Solve the equation. 2/3 x = 9/2
Solve the equation. 5 x- 12 1/3
Solve the equation. 3x + 4 = -8
The following expressions are called continued fractions: Each simplifies to an expression of the form Trace the successive values of a, b, and c as you “continue” the fraction. Can you
An electrical circuit contains three resistors connected in parallel. If the resistance of each is R1 ,R2 and R3 ohms, respectively, their combined resistance R is given by the
The focal length of a lens with an index of refraction n is Where R1 and R2 are the radii of curvature of the front and back surfaces of the lens. Express as a rational expression. Evaluate the
Expressions that occur in calculus are given. Reduce each expression to lowest terms. |(x² + 9) · 2 – (2x – 5)· 2x (x² + 9)?
Expressions that occur in calculus are given. Reduce each expression to lowest terms. (х2 + 1):3 — (3х + 4):2х (x² + 1)² (3x + 4):2х
Expressions that occur in calculus are given. Reduce each expression to lowest terms. (2x – 5)· 3x² – x³. 2 (2x – 5)2
Expressions that occur in calculus are given. Reduce each expression to lowest terms. (3х + 1):2х — 2-3 (3х + 1)2
Expressions that occur in calculus are given. Reduce each expression to lowest terms. x•2x - (x² – 4)• 1 (x² – 4)²
Expressions that occur in calculus are given. Reduce each expression to lowest terms. (x² + 1) • 1 х - 2х (x² + 1)² 2 + 1)²
Expressions that occur in calculus are given. Reduce each expression to lowest terms. |(4x + 1) •5 – (5x – 2) · 4 (5x – 2)²
Expressions that occur in calculus are given. Reduce each expression to lowest terms. (2х + 3) :3 — (3х — 5):2 (3х — 5)?
Perform the indicated operation and simplify the result. Leave your answer in factored form. 2х + 5 х х — 3 х x2 (х + 1)? х — 3 х+ 3
Perform the indicated operation and simplify the result. Leave your answer in factored form. х — 2 х х + 2 х+1 2х — 3 х х +1 х
Perform the indicated operation and simplify the result. Leave your answer in factored form. 4 + 3 x2
Perform the indicated operation and simplify the result. Leave your answer in factored form. х х
Perform the indicated operation and simplify the result. Leave your answer in factored form. 2 6. |(x + 2)²(x – 1) (x + 2)(x – 1)²
Perform the indicated operation and simplify the result. Leave your answer in factored form. 3 (х — 1)°(х + 1) (х — 1)(х + 1).
Perform the indicated operation and simplify the result. Leave your answer in factored form. х — 4 Зх x2 — 2х + 1 х — 1
Perform the indicated operation and simplify the result. Leave your answer in factored form. x² – 4 x + x – 6 4
Perform the indicated operation and simplify the result. Leave your answer in factored form. x + 1 x + 5x – 24
Perform the indicated operation and simplify the result. Leave your answer in factored form. x² - 2x – 24 x² – 7x + 6
Perform the indicated operation and simplify the result. Leave your answer in factored form. х — 1 х x² + 1
Perform the indicated operation and simplify the result. Leave your answer in factored form. х х2 — 4 х
Perform the indicated operation and simplify the result. Leave your answer in factored form. 9. Зx2 2х — 1 2х — 1 2x
Perform the indicated operation and simplify the result. Leave your answer in factored form. х? 2x 4 2х — 3 3
Perform the indicated operation and simplify the result. Leave your answer in factored form. 3 + x 3 — х x - 9 9x
Perform the indicated operation and simplify the result. Leave your answer in factored form. х 4 + x 4x x² – 16
Perform the indicated operation and simplify the result. Leave your answer in factored form. х — 2 4х х2 — 4х + 4 12х
Perform the indicated operation and simplify the result. Leave your answer in factored form. 8х x? – 1 10х х+1
Perform the indicated operation and simplify the result. Leave your answer in factored form. x' + 1 12 x? + x 4x – 2
Perform the indicated operation and simplify the result. Leave your answer in factored form. 4x2 x³ - 64 x² – 16 2x
Perform the indicated operation and simplify the result. Leave your answer in factored form. x? 3 х 2х бх + 10
Perform the indicated operation and simplify the result. Leave your answer in factored form. Зх + 6 х х? — 4 5x
Reduce each rational expression to lowest terms. Зу? — у — 2 Зу? + 5у + 2
Reduce each rational expression to lowest terms. y? – 25 2y – 8y – 10
Reduce each rational expression to lowest terms. x? + 4x + 4 x² - 4
Reduce each rational expression to lowest terms. .2 24x? 12x2 - бх
Reduce each rational expression to lowest terms. 15.x + 24x Зx2
Reduce each rational expression to lowest terms. х — 2х Зх — 6
Reduce each rational expression to lowest terms. 4x + 8x 12x + 24
Reduce each rational expression to lowest terms. Зх + 9 .2 x – 9
True or False.The LCM 2x3 + 6x2 and 6x4 + 4x3 is 4x3(x + 1).
True False. The rational expression 2x3 - 4x / x - 2 is reduced to lowest terms.
LCM is an abbreviation for _______.
When the numerator and denominator of a rational expression contain no common factors (except 1 and ), the rational expression is in________.
Find the sum of a, b, c, and d if . x - 2x + 3x + 5 x + 2 ax? + bx + c +
Use synthetic division to determine whether is a factor of the given polynomial. 3x4 + x3 – 3x + 1; x + 1/3
Use synthetic division to determine whether is a factor of the given polynomial. 2x4 – x3 + 2x – 1; x – ½
Use synthetic division to determine whether is a factor of the given polynomial. x6 – 16x4 + x2– 16; x + 4
Use synthetic division to determine whether is a factor of the given polynomial. 4x6 – 64x4 + x2 – 15; x + 4
Use synthetic division to determine whether is a factor of the given polynomial. 2x6 – 18x4 + x2 – 9; x+ 3
Use synthetic division to determine whether is a factor of the given polynomial. 3x6 + 82x3 + 27; x + 3
Use synthetic division to determine whether is a factor of the given polynomial. 4x4 – 15x2 – 4; x – 2
Use synthetic division to determine whether is a factor of the given polynomial. 3x4 – 6x3 – 5x + 10; x – 2
Use synthetic division to determine whether is a factor of the given polynomial. -4x3 + 5x2 + 8; x + 3
Use synthetic division to determine whether is a factor of the given polynomial.4x3 – 3x2 – 8x + 4; x – 2
Use synthetic division to find the quotient and remainder when: x5 + 1 is divided by x + 1
Use synthetic division to find the quotient and remainder when: x5 – 1 is divided by x – 1
Use synthetic division to find the quotient and remainder when: 0.1x2 -0.2 is divided by x + 2.1
Use synthetic division to find the quotient and remainder when: 0.1x3 + 0.2x is divided by x + 1.1
Use synthetic division to find the quotient and remainder when: x5 + 5x3 – 10 is divided by x + 1
Use synthetic division to find the quotient and remainder when: 4x6 – 3x4 + x2 + 5 is divided by x – 1
Use synthetic division to find the quotient and remainder when: x4 + x2 + 2 is divided by x – 2
Use synthetic division to find the quotient and remainder when: x5 – 4x3 + x is divided by x + 3
Use synthetic division to find the quotient and remainder when: -4x3 + 2x2 – x + 1 is divided by x + 2
Use synthetic division to find the quotient and remainder when: 3x3 + 2x2 – x + 3 is divided by x - 3
Use synthetic division to find the quotient and remainder when: x3 + 2x2 – 3x + 1 is divided by x + 1
Use synthetic division to find the quotient and remainder when: x3 – x2 + 2x + 4 is divided by x - 2
True or False. -2)5 3 2 -10 14 -32 16 -31 -7 5x + 3x2 + 2x + 1 x + 2 -31 5x? – 7x + 16 + x + 2
True or False.In using synthetic division, the divisor is always a polynomial of degree 1, whose leading coefficient is 1.
To divide 2x3 – 5x + 1 by x + 1 by using synthetic division, the first step is to write_______.
To check division, the expression that is being divided, the dividend, should equal the product of the_________ and the______ plus the_______.
Give a careful statement about the degree of the sum of two polynomials of the same degree.
Explain why the degree of the sum of two polynomials of different degrees equals the larger of their degrees.
Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.
Show that x3 + x + 1 is prime.
Show that x2 + 4 is prime.
Expressions that occur in calculus are given. Factor completely each expression. 3(4x + 5)2 •4(5x +1)2 + (4x + 5)3 • 2x(5x + 1) •5
Expressions that occur in calculus are given. Factor completely each expression. 2(3x – 5) •3(2x + 1)3 + (3x – 5)2 •3(2x + 1)2 •2
Expressions that occur in calculus are given. Factor completely each expression. 3x2(3x + 4)2 + x3 •2(3x + 4) •3

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