- c.
6 x^2 + 11x– 2 = 6x^2 – x+ 12x– 2 = (6x^2 – x) +
(12x– 2) = x(6x– 1) + 2(6x– 1) = (x+ 2)(6x– 1)
- b.
12 x^2 – 37x– 10 = 12x^2 + 3x– 40x– 10 = 3x(4x
- – 10(4x+ 1) = (3x– 10)(4x+ 1)
- c.
7 x^2 – 12x+ 5 = 7x^2 – 5x– 7x+ 5 = x(7x– 5) –
(7x– 5) = (7x– 5)(x– 1)
- a.
9 – 7x– 2x^2 = 9 + 2x– 9x– 2x^2 = 1(9 + 2x) –
x(9 + 2x) = (9 + 2x)(1 – x)
- c.
2 x^3 + 6x^2 + 4x= 2x(x^2 + 3x+ 2) =
2 x(x^2 + x+ 2x+ 2)
= 2 x(x(x+ 1) + 2(x+ 1) = 2x(x+ 2)(x+ 1)
- c.
–4x^5 + 24x^4 – 20x^3 = –4x^3 (x^2 – 6x+ 5) =
–4x^3 (x^2 – x– 5x+ 5)
= –4x^3 (x(x– 1) – 5(x–1)) = –4x^3 (x– 5)(x–1)
- b.
–27x^4 + 27x^3 – 6x^2 = –3x^2 (9x^2 – 9x+ 2) =
–3x^2 (9x^2 – 6x– 3x+ 2)
= –3x^2 [(9x^2 –6x) – (3x– 2)] = –3x^2 [3x(3x– 2)
- (3x– 2)] = –3x^2 (3x– 1)(3x– 2)
- b.
x^2 (x+ 1) – 5x(x+ 1) + 6(x+ 1) = (x+ 1)(x^2 –
5 x+ 6) = (x+ 1)(x^2 – 2x– 3x+ 6)
= (x+ 1)[x(x– 2) – 3(x– 2)] = (x+ 1)(x– 3)
(x– 2)
- a.
2 x^2 (x^2 – 4) – x(x^2 – 4) + (4 – x^2 ) = 2x^2 (x^2 – 4) –
x(x^2 – 4) – (x^2 – 4) = (x^2 – 4)[2x^2 – x– 1]
= (x^2 – 4)[2x^2 – 2x+ x– 1] = (x^2 – 4)[2x(x– 1)
+ (x–1)] = (x^2 – 4)(2x+ 1)(x– 1)
= (x– 2)(x+ 2)(2x+ 1)(x– 1)
428. b.
27(x– 3) + 6x(x– 3) – x^2 (x– 3) = (x– 3)(27 +
6 x– x^2 ) = (x– 3)(27 + 6x+ x^2 )
= –(x– 3)(x^2 – 6x– 27) = –(x– 3)(x^2 – 9x+ 3x
- = –(x– 3)(x(x– 9) + 3(x– 9))
= –(x– 3)(x+ 3)(x– 9)
- c.
(x^2 + 4x+ 3)x^2 + (x^2 + 4x+ 3)3x+ 2(x^2 + 4x+
3) = (x^2 + 4x+ 3)[x^2 + 3x+ 2]
= (x^2 + 3x+ x+ 3)[x^2 + x+ 2x+ 2] = (x(x+
3) + (x+ 3))[x(x+ 1) + 2(x+ 1)]
= ((x+ 1)(x+ 3))[(x+ 2)(x+ 1)] = (x+ 1)^2 (x
+ 2)(x+ 3)
- a.
18(x^2 + 6x+ 8) – 2x^2 (x^2 + 6x+ 8) = (x^2 + 6x+
8)[18 – 2x^2 ] = (x^2 + 6x+ 8)[2(9 – x^2 )]
= (x^2 + 4x+ 2x+ 8)[2(3^2 – x^2 )] = (x(x+ 4)
+2(x+ 4))[2(3 – x)(3 + x)]
= 2(x+ 2)(x+ 4)(3 – x)(3 + x)
- a.
2 x^2 (16 + x^4 ) + 3x(16 + x^4 ) = (16 + x^4 ) = (16 +
x^4 )[2x^2 + 3x+ 1]
= (16 + x^4 )[2x^2 + 2x+ x+ 1] = (16 + x^4 )[2x(x
+ 1) + (x+ 1)] = (16 + x^4 )(2x+ 1)(x+ 1)
- a.
6 x^2 (1 – x^4 ) + 13x(1 – x^4 ) + 6(1 – x^4 ) = (1 – x^4 )
[6x^2 + 13x+ 6] = (1 – x^4 )[6x^2 + 4x+ 9x+ 6]
= (1^2 – (x^2 )^2 )[2x(3x+ 2) + 3(3x+ 2)] =
(1 – x^2 )(1 + x^2 )(2x+ 3)(3x+ 2)
= (1 – x)(1 + x)(1 + x^2 )(2x+ 3)(3x+ 2)
ANSWERS & EXPLANATIONS–
