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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Factor the polynomial.a4 - 2a2 - 48
Factor the polynomial.m4 - 3m2 - 10
Factor the polynomial.(5x - 2)3 - 8
Factor the polynomial.(3x + 4)3 - 1
Factor the polynomial.(x - 4)3 + 64
Factor the polynomial.(a + 1)3 + 27
Factor the polynomial.4(5x + 7)2 + 12(5x + 7) + 9
Factor the polynomial.9(a - 4)2 + 30(a - 4) + 25
Factor the polynomial.6(4z - 3)2 + 7(4z - 3) - 3
Factor the polynomial.7(3k - 1)2 + 26(3k - 1) - 8
Factor the polynomial.125 - (4a - b)3
Factor the polynomial.27 - (m + 2n)3
Factor the polynomial.(b + 3)3 - 27
Factor the polynomial.(r + 6)3 - 216
Factor the polynomial.27z9 + 64y12
Factor the polynomial.27y9 + 125z6
Factor the polynomial.8m3 - 27n3
Factor the polynomial.125x3 - 27
Factor the polynomial.27 - r3
Factor the polynomial.8 - a3
Factor the polynomial.9m2 - n2 - 2n - 1
Factor the polynomial.y2 - x2 + 12x - 36
Factor the polynomial.m2 + 10m + 25 - n4
Factor the polynomial.x2 - 8x + 16 - y2
Factor the polynomial.m4 - 1296
Factor the polynomial.p4 - 625
Factor the polynomial.(p - 2q)2 - 100
Factor each polynomial.(a + b)2 - 16
Factor the polynomial.36z2 - 81y4
Factor the polynomial.25s4 - 9t2
Factor the polynomial.y4 - 81
Factor the polynomial.x4 - 16
Factor each polynomial.16q2 - 25
Factor the polynomial.9a2 - 16
Factor the trinomial, if possible.(2p + q)2 - 10(2p + q) + 25
Factor the trinomial, if possible.(a - 3b)2 - 6(a - 3b) + 9
Factor the trinomial, if possible.9m2n2 + 12mn + 4
Factor the trinomial, if possible.4x2y2 + 28xy + 49
Factor the trinomial, if possible.20p2 - 100pq + 125q2
Factor the trinomial, if possible.32a2 + 48ab + 18b2
Factor the trinomial, if possible.16p2 - 40p + 25
Factor the trinomial, if possible.9m2 - 12m + 4
Factor the trinomial, if possible.18x5 + 15x4z - 75x3z2
Factor the trinomial, if possible.24a4 + 10a3b - 4a2b2
Factor the trinomial, if possible.30a2 + am - m2
Factor the trinomial, if possible.12x2 - xy - y2
Factor each trinomial, if possible.12s2 + 11st - 5t2
Factor the trinomial, if possible.5a2 - 7ab - 6b2
Factor the trinomial, if possible.14m2 + 11mr - 15r2
Factor the trinomial, if possible.6k2 + 5kp - 6p2
Factor the trinomial, if possible.36x3 + 18x2 - 4x
Factor the trinomial, if possible.12a3 + 10a2 - 42a
Factor the trinomial, if possible.9x2 + 4x - 2
Factor the trinomial, if possible.15p2 + 24p + 8
Factor the trinomial, if possible.9y2 - 18y + 8
Factor the trinomial, if possible.3m2 + 14m + 8
Factor the trinomial, if possible.8h2 - 2h - 21
Factor the trinomial, if possible.6a2 - 11a + 4
Factor the polynomial by grouping.20z2 - 8x + 5pz2 - 2px
Factor the polynomial by grouping.p2q2 - 10 - 2q2 + 5p2
Factor the polynomial by grouping.4x6 + 36 - x6y - 9y
Factor the polynomial by grouping.2m4 + 6 - am4 - 3a
Factor the polynomial by grouping.10ab - 6b + 35a - 21
Factor the polynomial by grouping.6st + 9t - 10s - 15
Kurt factored 16a2 - 40a - 6a + 15 by grouping and obtained (8a - 3)(2a - 5). Callie factored the same polynomial and gave an answer of (3 - 8a)(5 - 2a). Which answer is correct?
When directed to completely factor the polynomial 4x2y5 - 8xy3, a student wrote 2xy3(2xy2 - 4). When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer.
Factor out the greatest common factor from the polynomial.5(a + 3)3 - 2(a + 3) + (a + 3)2
Factor out the greatest common factor from the polynomial.2(m - 1) - 3(m - 1)2 + 2(m - 1)3
Factor out the greatest common factor from the polynomial.(4z - 5)(3z - 2) - (3z - 9)(3z - 2)
Factor out the greatest common factor from the polynomial.(5r - 6)(r + 3) - (2r - 1)(r + 3)
Factor out the greatest common factor from the polynomial.6x(a + b) - 4y(a + b)
Factor out the greatest common factor from the polynomial.2(a + b) + 4m(a + b)
Factor out the greatest common factor from the polynomial.28r4s2 + 7r3s - 35r4s3
Factor out the greatest common factor from each polynomial.4k2m3 + 8k4m3 - 12k2m4
Factor out the greatest common factor from each polynomial.-3z5w2 - 18z3w4
Factor out the greatest common factor from each polynomial.-4p3q4 - 2p2q5
Factor out the greatest common factor from each polynomial.5h2j + hj
Factor out the greatest common factor from each polynomial.xy - 5xy2
Factor out the greatest common factor from the polynomial.9z4 + 81z
Factor out the greatest common factor from each polynomial.8k3 + 24k
Factor out the greatest common factor from each polynomial.15r - 27
Factor out the greatest common factor from each polynomial.12m + 60
Work each problem.Which of the following is the correct factorization of x3 + 8?A. (x + 2)3 B. (x + 2)(x2 + 2x + 4)C. (x + 2)(x2 - 2x + 4) D. (x + 2)(x2 - 4x + 4)
Which of the following is the correct complete factorization of x4 - 1?A. (x2 - 1)(x2 + 1) B. (x2 + 1)(x + 1)(x - 1)C. (x2 - 1)2D. (x - 1)2(x + 1)2
Work each problem.Which of the following is the correct factorization of 6x2 + x - 12?A. (3x + 4)(2x + 3) B. (3x - 4)(2x - 3)C. (3x + 4)(2x - 3) D. (3x - 4)(2x + 3)
Work each problem.Match each polynomial in Column I with its factored form in Column II.I....................................................................II(a) 8x3 - 27.................................A. (3 - 2x)(9 + 6x + 4x2)(b) 8x3 + 27................................B. (2x - 3)(4x2 + 6x +
Work each problem.Match each polynomial in Column I with its factored form in Column II.I................................................................................II(a) x2 + 10xy + 25y2................................A. (x + 5y)(x - 5y)(b) x2 - 10xy + 25y2................................B. (x
Fill in the blank(s) to correctly complete each sentence.There is no factoring pattern for a in the real number system. In particular, x2 + y2 does not factor as (x + y)2, for real numbers x and y.
Fill in the blank(s) to correctly complete each sentence.When a polynomial has more than three terms, it can sometimes be factored using_________ .
Fill in the blank(s) to correctly complete each sentence.Factoring is the opposite of _________ .
Fill in the blank(s) to correctly complete each sentence.A polynomial is factored completely when it is written as a product of ______ .
Fill in the blank(s) to correctly complete each sentence.The process of finding polynomials whose product equals a given polynomial is called ___________.
The special products can be used to perform selected multiplications. On the left, we use (x + y)(x - y) = x2 - y2. On the right, (x - y)2 = x2 - 2xy + y2.Use special products to evaluate each expression.63 × 57 472 = (50 – 3)² 51 x 49 = (50 + 1)(50 – 1) = 502 – 12 = 502 – 2(50)(3) + 32 =
The special products can be used to perform selected multiplications. On the left, we use (x + y)(x - y) = x2 - y2. On the right, (x - y)2 = x2 - 2xy + y2.Use special products to evaluate each expression.99 × 101 472 = (50 – 3)² 51 x 49 = (50 + 1)(50 – 1) = 502 – 12 = 502 – 2(50)(3) + 32
Perform the operation mentally. 154 54
Perform the operation mentally. 4.25 2.15
Perform the operation mentally.(242)(0.52)
Perform the operation mentally.(0.253)(4003)
The graph shows the number of farms in the United States for selected years since 1950. We can use the formula Number of farms = 0.001259x2 - 5.039x + 5044 to get a good approximation of the number of farms for these years by substituting the year for x and evaluating the polynomial. For example,
The graph shows the number of farms in the United States for selected years since 1950. We can use the formula Number of farms = 0.001259x2 - 5.039x + 5044 to get a good approximation of the number of farms for these years by substituting the year for x and evaluating the polynomial. For example,
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