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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Factor the given expressions completely.25x2 + 45x − 10
Factor the given expressions completely.27L6 + 216L3
Factor the given expressions completely.2s2 + 13s + 11
Factor the given expressions completely.12pq2 − 8pq − 28pq3
Factor the given expressions completely.a3s 5 − 8000a3s2
Factor the given expressions completely.5 − 12y + 7y2
Factor the given expressions completely.27a2b − 24ab − 9a
Factor the given expressions completely.(a + b)3 + 64
Factor the given expressions completely.3z2 − 19z + 6
Factor the given expressions completely.2a2 − 2b2 + 4c2 − 6d2
Factor the given expressions completely.125 + (2x + y)3
Factor the given expressions completely.10R4 − 6R2 − 4
Factor the given expressions completely.5a + 10ax − 5ay − 20az
Factor the given expressions completely.64 − x6
Factor the given expressions completely.2t2 + 7t − 15
Factor the given expressions completely.x2 − 9
Factor the given expressions completely.2a6 − 54b6
Factor the given expressions completely.20 − 20n + 3n2
Factor the given expressions completely.r2 − 25
Factor the given expressions completely.x6 − 2x3 + 1
Factor the given expressions completely.3t2 − 7tu + 4u2
Factor the given expressions completely.100 − 4A2
Factor the given expressions completely.n6 + 4n3 + 4
Factor the given expressions completely.3x2 + xy − 14y2
Factor the given expressions completely.49 − Z4
Factor the given expressions completely. Each is from the technical area indicated.32x − 4x4 (rocket trajectory)
Factor the given expressions completely.6x2 + x − 5
Factor the given expressions completely.36a4 + 1
Factor the given expressions completely. Each is from the technical area indicated.kT3 − kT03 (thermodynamics)
Factor the given expressions completely.2z2 + 13z − 5
Factor the given expressions completely.324z2 + 4
Factor the given expressions completely. Each is from the technical area indicated.D4 − d3D (machine design)
Factor the given expressions completely. Each is from the technical area indicated.(molecular interaction) 12 6 (²) ¹² − (²) º r
Factor the given expressions completely.9x2 + 7xy − 2y2
Factor the given expressions completely.162s2 − 50t2
Factor the given expressions completely. Each is from the technical area indicated.(h + 2t)3 − h3 (container design)
Factor the given expressions completely.4r2 + 11rs − 3s2
Factor the given expressions completely.36s2 − 121t4
Factor the given expressions completely. Each is from the technical area indicated.QH4 + Q4H (thermodynamics)
Factor the given expressions completely.12m2 + 60m + 75
Factor the given expressions completely.144n2 − 169p4
Factor the given expressions completely.48q2 + 72q + 27
Factor the given expressions completely.36a2b2 + 169c2
Perform the indicated operations.Using multiplication, verify the identitya3 + b3 = (a + b)(a2 − ab + b2) .
Factor the given expressions completely.8x2 − 24x + 18
Factor the given expressions completely.(x + y)2 − 9
Using multiplication, verify the identitya3 − b3 = (a − b)(a2 + ab + b2).
Factor the given expressions completely.3a2c2 − 6ac + 3
Factor the given expressions completely.(a − b)2 − 1
Factor x6− y6 as the difference of cubes.
Factor the given expressions completely.8 − 2x2
Factor the given expressions completely.9t2 − 15t + 4
Factor x 6 − y6 as the difference of squares. Then explain how the result of Exercise 39 can be shown to be the same as the result in this exercise.Data from Exercises 39Factor x6− y6 as the
Factor the given expressions completely.6t4 + t2 − 12
Factor the given expressions completely.5a4 − 125a2
By factoring (n3 + 1), explain why this expression represents a number that is not prime if n is an integer greater than one.
Factor the given expressions completely.8b6 + 31b3 − 4
Factor the given expressions completely.300x2 − 2700z2
A certain wind turbine produces a power of 1200v3 (in watts) where v is the wind speed. Find an expression, in factored form, for the difference in power for the wind speeds v1 and v2.
Factor the given expressions completely.12n4 + 8n2 − 15
Factor the given expressions completely.28x2 − 700y2
Factor the given expressions completely.4p2 − 25pq + 6q2
Factor the given expressions completely.2(I − 3)2 − 8
Factor the given expressions completely.12x2 + 4xy − 5y2
Factor the given expressions completely.a(x + 2)2 − ay2
Factor the given expressions completely.12x2 + 47xy − 4y2
Factor the given expressions completely.x4 − 16
Factor the given expressions completely.8r2 − 14rs − 9s2
Factor the given expressions completely.81 − y4
Factor the given expressions completely.12 − 14x + 2x2
Factor the given expressions completely.x10 − x2
Factor the given expressions completely.6y2 − 33y − 18
Factor the given expressions completely.2x4 − 8y4
Factor the given expressions completely.4x5 + 14x3 − 8x
Solve for the indicated variable.2a − b = ab + 3, for a
Factor the given expressions completely.12B2 + 22BH − 4H2
Solve for the indicated variable.n(x + 1) = 5 − x, for x
Solve for the indicated variable.3 − 2s = 2(3 − st), for s
Factor the given expressions completely.ax3 + 4a2x2 − 12a3x
Factor the given expressions completely.15x2 − 39x3 + 18x4
Solve for the indicated variable.k(2 − y) = y(2k − 1), for y
Solve for the indicated variable.(x + 2k)(x − 2) = x2 + 3x − 4k, for k
Factor the given expressions by grouping as illustrated in Example 10.3x − 3y + bx − byData from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms,
Factor the given expressions by grouping as illustrated in Example 10.am + an + cn + cmData from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms, but
Factor the given expressions by grouping as illustrated in Example 10.2y − y2 − 6y4 + 12y3Data from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four
Factor the given expressions completely.4x2n + 13xn − 12
Solve for the indicated variable.(2x − 3k)(x + 1) = 2x2 − x − 3, for k
Factor the given expressions by grouping as illustrated in Example 10.a2 + ax − ab − bxData from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms,
Factor the given expressions completely.12B2n + 19BnH − 10H2
Factor the given expressions by grouping as illustrated in Example 10.S3 − 5S2 − S + 5Data from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms,
Factor the given expressions completely. Each is from the technical area indicated.16t2 − 80t + 64 (projectile motion)
Factor the given expressions completely. Each is from the technical area indicated.9x2 − 33Lx + 30L2 (civil engineering)
Factor the given expressions by grouping as illustrated in Example 10.x3 + 3x2 − 4x − 12Data from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms,
Factor the given expressions by grouping as illustrated in Example 10.x2 − y2 + x − yData from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms, but
Factor the given expressions completely. Each is from the technical area indicated.d4 − 10d2 + 16 (magnetic field)
Factor the given expressions by grouping as illustrated in Example 10.4p2 − q2 + 2p + qData from Example 10Factor: 2x − 2y + ax − ay.We see that there is no common factor to all four terms, but
Factor the given expressions completely. Each is from the technical area indicated.3e2 + 18e − 1560 (fuel efficiency)
Evaluate the given expressions by using factoring. The results may be checked with a calculator. 89 88 7
Factor the given expressions completely. Each is from the technical area indicated.3Q2 + Q − 30 (fire science)
Factor the given expressions completely. Each is from the technical area indicated.bT2 − 40bT + 400b (thermodynamics)

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