Factor the trinomial by grouping, if possible. $10 x ^ { 2 } - 9 x - 9$
A) $( 3 x + 5 ) ( 3 x - 2 )$
B) $( 5 x + 3 ) ( 2 x - 3 )$
C) $( 5 x - 3 ) ( 2 x - 3 )$
D) $( 5 x + 3 ) ( 2 x + 3 )$
E)The trinomial is prime.

Question

Quizplus · Accepted Answer

To factor by grouping, we need to find two numbers whose product is $10\cdot(-9)=-90$ and whose sum is $-9$. We can see that $-15$ and $6$ satisfy these conditions. So we rewrite the trinomial as $10x^2-15x+6x-9$. Then we group the first two terms and the last two terms: $(10x^2-15x)+(6x-9)$. We can factor $5x$ out of the first group and $3$ out of the second group: $5x(2x-3)+3(2x-3)$. We can see that $(2x-3)$ is a common factor, so we can write the expression as $(2x-3)(5x+3)$.

Factor the Trinomial by Grouping, If Possible 10x2−9x−910 x ^ { 2 } - 9 x - 910x2−9x−9

Factor the Trinomial by Grouping, If Possible $10 x ^ { 2 } - 9 x - 9$