need help factoring these polynomials please?

Question

factor
A)x^2+13x+12
B)x^2-2x-8
C)2x^2-10x+12
D)3x^3+12x^2-15x

Answer 1

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note: it won't be able to factor cubics (like problem d)

Answer 2

A) x^2 + 13x + 12 =
x^2 + 13x + (13/2)^2 - (13/2)^2 + 12 =
(x + 13/2)^2 - (169 - 48)/4 =
( x + 13/2)^2 - 121/4 =
(x + 13/2 - 11/2)(x + 13/2 + 11/2) =
(x + 1)(x + 12)

B) x^2 - 2x - 8 =
x^2 - 2x + 1 - 1 - 8 =
(x - 1)^2 - 9 =
(x - 1 - 3)(x - 1 + 3) =
(x - 4)(x + 2)

C) 2x^2 - 10x + 12 =
2 (x^2 - 5x + 6) =
2(x^2 - 5x + (5/2)^2 - (5/2)^2 + 6) =
2((x - 5/2)^2 - (25 - 24)/4) =
2((x - 5/2)^2 - 1/4) =
2 (x - 5/2 - 1/2)(x - 5/2 + 1/4) =
2 (x - 3)(x - 1)

D) 3x^3 + 12x^2 - 15x =
3x (x^2 + 4x - 5) =
3x ( x^2 + 4x + 4 - 4 - 5) =
3x ((x + 2)^2 - 9) =
3x (x + 2 - 3)(x + 2 + 3) =
3x (x-1)(x+5)

Answer 3

A) x^2+13x+12
= (x+12)(x+1)

B) x^2-2x-8
= (x+2)(x-4)

C) 2x^2-10x+12
= 2(x^2 - 5x + 6)
= 2(x-3)(x-2)

D) 3x^3+12x^2-15x
= 3x(x^2 + 4x - 5)
= 3x(x+5)(x-1)

Answer 4

A. x^2+13x+12=(x+1)(x+12) =0 x=-1or -12
B. x^2-2x-8= (x+2)(x-4)=0 x=-2 or 4
C. 2x^2-10x+12 = (2x-6)(x-2)=0 x=3 or 2
D.3x^3+12x^2-15x=x(3x^2+4x-15)=0
x(3x-5)(x+3) x=0, 5/3 or -3

Answer 5

1.x^2 +13x +12
= x^2 +12x +x + 12
= x(x+12) + (x+12)
=(x+12)(x+1)
2.x^2 - 2x - 8
= x^2 - 4x + 2x - 8
= x(x-4) + 2(x-4)
= (x+2)(x-4)
3.2x^2 - 10x + 12
= 2x^2 - 6x - 4x + 12
= 2x(x-6) - 4(x-3)
= 2(x-2)(x-3)
4.3x^3 + 12x^2 -15x
= 3x(x^2 + 4x - 5)
= 3x(x^2 - 5x + x - 5)
= 3x(x-5)(x+1)

Answer 6

A) (X+12)(x+1)
B) (x-4)(x+2)
C) 2(x-3)(x-2)
D) 3x(x+5)(x-1)