Factor the expression completely. $22 r ^ { 2 } - 13 r s - 30 s ^ { 2 }$
A) $\quad ( 2 r - 3 s ) ( 11 r + 10 s )$
B) $\quad ( 3 r - 2 s ) ( 11 r + 10 s )$
C) $\quad ( 2 r + 3 s ) ( 11 r - 10 s )$
D) $\quad ( 2 r - 3 s ) ( 10 r + 11 s )$

Question

Quizplus · Accepted Answer

We can factorize the expression by using the AC method. The product of 22 and -30 is -660, and the factors of -660 whose sum is -13 are -33 and 20. We then split the middle term -13rs into -33rs + 20rs and group the terms:
\begin{align*} 22 r ^ { 2 } - 13 r s - 30 s ^ { 2 }&= 22 r ^ { 2 } - 33 r s + 20 r s - 30 s ^ { 2 } \ &= 11 r ( 2 r - 3 s ) + 10 s ( 2 r - 3 s ) \ &= ( 2 r - 3 s ) ( 11 r + 10 s ) \end{align*}
Therefore, the answer is choice A.

Factor the Expression Completely 22r2−13rs−30s222 r ^ { 2 } - 13 r s - 30 s ^ { 2 }22r2−13rs−30s2

Factor the Expression Completely $22 r ^ { 2 } - 13 r s - 30 s ^ { 2 }$