Question

Find the factored form of a polynomial $p$($x$) which has a simple zero at $x=-3$ and a double zero at $x=\frac{5}{4}$

• A. $p\left(x\right)=2(x+3)(5x-4)$
• B. $p\left(x\right)=(x+3)(5x-4{)}^2$
• C. $p\left(x\right)=2(x+3)(4x-5)$
• D. $p\left(x\right)=(x+3)(4x-5{)}^2$

Answer 1

The correct option is D $p\left(x\right)=(x+3)(4x-5{)}^2$

The polynomial has a simple zero at $x=-3$, which corresponds to a factor of $(x+3)$.

The double zero and $x=\frac{5}{4}$ results from a repeated (squared) factor, means factor is ($4x-5{)}^2$ so you can eliminate A and C.

To choose between B and (D),

clearly choice (D) is correct