Question

Factor the expression:
$r^2+19rs+90s^2$

• A. $\left(r+3s\right)\left(r+30s\right)$
• B. $\left(r+3\right)\left(r+30s^2\right)$
• C. $\left(r+10s\right)\left(r+9s\right)$
• D. $\left(r+10\right)\left(r+9s^2\right)$

Answer 1

The correct option is C

$\left(r+10s\right)\left(r+9s\right)$

Step-1: Explanation for correct option:

Option (C) :

Factoring by grouping method and simplified as follows:

$\begin{array}{rcl}{r}^2+19rs+90s^2& =& r^2+10rs+9rs+90s^2\\ & \Rightarrow & r^2+19rs+90s^2=r\left(r+10s\right)+9s\left(r+10s\right)\\ \therefore r^2+19rs+90s^2& =& \left(r+10s\right)\left(r+9s\right)\end{array}$

So, the factor is $\left(r+10s\right)\left(r+9s\right)$.

Therefore, the option $\left(C\right)$ is correct.

Step-2: Explanation for incorrect options:

Since the missing value determined above is not equivalent to the value mentioned in option $\left(A\right)$, option $\left(B\right)$, and option $\left(D\right)$.

Therefore, option $\left(A\right)$, option $\left(B\right)$, and option $\left(D\right)$ are incorrect options.

Hence, option $\left(C\right)$ is the correct answer.