Question

Which of the binomials below is a factor of this trinomial?

x^2+3x-10

a)x^3+5
b)x-5
c)x+2
d)x+5



x^2+4x-32

a)x+4
b)x^2+8
c)x-4
d)x-8



x^2+6x+8

a)x^2+4
b)x+4
c)x-4
d)x+8


x^2+7x-60

a)x-12
b)x^2-5
c)x+12
d)x+5

x^2+19x+84

a)x-7
b)x^2+12
c)x+84
d)x+7

Answer 1

x^2 + 3x - 10 = x^2 - 2x + 5x - 10 = (x^2 - 2x) + (5x - 10) = x(x - 2) + 5(x - 2) = (x + 5)(x - 2)
Therefore, x + 5 is a factor of x^2 + 3x - 10

x^2 + 4x - 32 = x^2 - 4x + 8x - 32 = (x^2 - 4x) + (8x - 32) = x(x - 4) + 8(x - 4) = (x + 8)(x - 4)
Therefore, x - 4 is a factor of x^2 + 4x - 32