Question

what side lengths should be used to model a rectangle with an area of $x^2 + 3x - 10$ square units?\
\bigcirc $x - 5$ and $x + 2$\
\bigcirc $x - 2$ and $x + 5$\
\bigcirc $x$ and $x + 3$\
\bigcirc $x + 3$ and $x - 10$

Explanation:

Step1: Identify trinomial structure

We need to factor $x^2 + 3x - 10$, which follows $x^2+bx+c$.

Step2: Find pair of factors

Find two numbers that multiply to $-10$ and add to $3$. The numbers are $5$ and $-2$, since $5\times(-2)=-10$ and $5+(-2)=3$.

Step3: Write factored form

Substitute the numbers into the factored form $(x+m)(x+n)$:
$(x+5)(x-2)$

Answer:

x - 2 and x + 5