Mentally factor the trinomial $x ^ { 2 } - 10 x + 16$
A) $( x + 4 ) ( x + 4 )$
B) $( x - 4 ) ( x - 4 )$
C) $( x + 2 ) ( x - 8 )$
D) $( x - 2 ) ( x - 8 )$
E) $( x + 2 ) ( x + 8 )$

Question

Quizplus · Accepted Answer

To mentally factor the trinomial, we need to look for two numbers that multiply to give the constant term (16) and add to give the coefficient of the middle term (-10). Those numbers are -2 and -8. So we can rewrite the trinomial as:

$x^2 - 10x + 16 = x^2 - 2x - 8x + 16$

Now we can factor by grouping:

$(x^2 - 2x) - (8x - 16) = x(x - 2) - 8(x - 2) = (x - 2)(x - 8)$

Therefore, the factorization is $(x-2)(x-8)$, which corresponds to answer choice D.

Mentally Factor the Trinomial x2−10x+16x ^ { 2 } - 10 x + 16x2−10x+16

Mentally Factor the Trinomial $x ^ { 2 } - 10 x + 16$