Factorize each of the following quadratic polynomials by using the method of completing the square:

Question:

Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p − 16

Solution:

$\mathrm{p}^{2}+6 \mathrm{p}-16$

$=\mathrm{p}^{2}+6 \mathrm{p}+\left(\frac{6}{2}\right)^{2}-\left(\frac{6}{2}\right)^{2}-16 \quad\left[\right.$ Adding and subtracting $\left(\frac{6}{2}\right)^{2}$, that is, $\left.3^{2}\right]$

$=\mathrm{p}^{2}+6 \mathrm{p}+3^{2}-9-16$

$=(\mathrm{p}+3)^{2}-25 \quad[$ Completing the square $]$

$=(\mathrm{p}+3)^{2}-5^{2}$

$=[(\mathrm{p}+3)-5][(\mathrm{p}+3)+5]$

$=(\mathrm{p}+3-5)(\mathrm{p}+3+5)$

$=(\mathrm{p}-2)(\mathrm{p}+8)$

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now