Factor.
-$15 z ^ { 2 } + 4 z - 4$
A) $( 15 z + 2 ) ( z - 2 )$
B) Prime
C) $( 3 z + 2 ) ( 5 z - 2 )$
D) $( 3 z - 2 ) ( 5 z + 2 )$

Question

Quizplus · Accepted Answer

This is a quadratic trinomial that cannot be factored easily using the AC method or by grouping. Therefore, we need to use the quadratic formula or complete the square to find the roots of the equation. However, we notice that the coefficient of the squared term (15) and the constant term (-4) have factors (3 and 5) in common. Therefore, we can try factoring out the greatest common factor (GCF) of the three terms, which is 1, and see if that helps us to factor the trinomial. That gives us:

$15 z ^ { 2 } + 4 z - 4 = [15 z ^ { 2 } / 1] + [4 z / 1] + [-4 / 1]$

$= 3z(5z+2)-2(5z+2)$

$= (3z-2)(5z+2)$

Therefore, the factored form of the given trinomial is (3z-2)(5z+2), which is choice (C).

Factor - 15z2+4z−415 z ^ { 2 } + 4 z - 415z2+4z−4

Factor
- $15 z ^ { 2 } + 4 z - 4$