Question

if ( p(-4) = 0 ), which of the following statements is true about ( p(x) )?
( p(0) = -4 )
( x + 4 ) is a factor of ( p(x) )
( p(x) = 0 ), has four negative roots
( 4 ) is a root of ( p(x) = 0 )

Explanation:

Step1: Recall Factor Theorem

The Factor Theorem states that for a polynomial $P(x)$, if $P(c)=0$, then $(x-c)$ is a factor of $P(x)$.

Step2: Apply given condition

We know $P(-4)=0$. Substitute $c=-4$ into the Factor Theorem:
$(x - (-4)) = x+4$ is a factor of $P(x)$.

Step3: Eliminate other options

• $P(0)=-4$: No info about $P(0)$ is given.
• $P(x)=0$ has four negative roots: No info about root count/sign.
• $4$ is a root: A root $c$ means $P(c)=0$, but $P(4)

eq0$ is not confirmed.

Answer:

B. x+4 is a factor of P(x)