Question

Which of the following are the common zeros of the polynomials $(x^2-16)(x+9)$ and $(x^2-81)(x+4)$ ?

• A. $-4$
• B. $4$
• C. $-9$
• D. $9$

Answer 1

Answer: (A), (C)

$-9$

Let the given polynomials be
$P\left(x\right)=(x^2-16)(x+9)$ and $Q\left(x\right)=(x^2-81)(x+4)$

Simplifying
$P\left(x\right)=(x^2-16)(x+9)$
$=(x-4)(x+4)(x+9)$
and
$Q\left(x\right)=(x^2-81)(x+4)$
$=(x-9)(x+9)(x+4)$

Common factors in $P\left(x\right)$ and $Q\left(x\right)$ are $(x+4)$ and $(x+9)$
$\Rightarrow$ Common zeros are $-4,-9$