Question

p²-7P-18 polynomial elements​

Answer 1

Answer:

p^2. - 7p -18

p^2. -9p + 2p - 18

p(p-9) +2(p-9)

(p+2)(p-9)

p=9,-2

Answer 2

Answer:

$\Large\boxed{(p+2)(p-9)}$

Step-by-step explanation:

GIVEN:

p²-7p-18 (by using with foil method formula and exponent rule.)

SOLUTIONS:

$\mathsf{FOIL \quad METHOD \quad FORMULA}$

$\displaystyle \mathsf{(A+B)(C+D)=AC+AD+BC+BD}$

A=P

B=2

C=P

D=(-9)

$\Rightarrow \displaystyle \mathsf{PP+P(-9)+2P+2(-9)}}$

Change positive sign to negative sign.

$\displaystyle \mathsf{+(-Y)=-Y}$

$\displaystyle \mathsf{PP-9P+2P-2\times9}}$

Solve.

$\displaystyle \mathsf{PP-9P+2P-2\times9}}=\boxed{P^2-7P-18}}$

$\mathsf{Factors \quad of \quad p^2-7p-18}$

$\mathsf{DISTRIBUTIVE \quad PROPERTY}$

$\mathsf{A(B+C)=AB+AC}$

$\displaystyle \mathsf{p^2+2p+(-9p-18)}$

Factor it out by p.

$\mathsf{p^2=pp}$

$\mathsf{pp+2p}}$

Common term of p.

$\displaystyle \mathsf{p(p+2)}$

Factor it out by -9.

$\displaystyle \mathsf{-9p-18}$

$\displaystyle \mathsf{2\times9=18}$

Common term of -9.

$\displaystyle \mathsf{=-9(p+2)}$

Rewrite the whole problem down.

$\displaystyle (p+2)-9(p+2)$

Solve.

Common term of p+2.

$\longrightarrow\Large\boxed{\mathsf{(p+2)(p-9)}}$

Hence, the polynomial elements of p²-7p-18 is (p+2)(p-9).