Question

Completely factor the trinomial, if possible. 7p^2+16p+4

Answer 1

SOLUTION

Write out the expression

$7p^2+16p+4$

Step1; Multiply the first and the last term

$\begin{gathered} 7p^2\times4=28p^2 \\ \text{second term=16p} \end{gathered}$

Step2: Obtain the factors of that completely replace the product and the second term above

$\begin{gathered} 28p^2=14p\times2p \\ 16p=14p+2p \end{gathered}$

Step3: Replace the second term with the factors you obtained above

$\begin{gathered} 7p^2+16p+4 \\ 7p^2+2p+14p+4 \end{gathered}$

Step4: Break the expression into groups

$\mleft(7p^2+2p\mright)+\mleft(14p+4\mright)$

Step5: Factor the expression in paranthesis

$\begin{gathered} (7p^2+2p)+(14p+4) \\ p(7p+2)+2(7p+2) \\ (7p+2)(p+2) \end{gathered}$

Hence

The complete factor of the trinomial is (7p+2)(p+2)