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in Factorization by (56.3k points)

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

 p2 + 6p – 16

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We have,

p2 + 6p – 16

Coefficient of p2 is unity. So, we add and subtract square of half of coefficient of p.

p2 + 6p – 16 = p2 + 6p + 32 – 32 – 16 (Adding and subtracting 32)

= (p + 3)2 – 52 (Completing the square)

By using the formula (a2 – b2) = (a+b) (a-b)

= (p + 3 + 5) (p + 3 – 5)

= (p + 8) (p – 2)

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