Question

Dividing p(x) = x^2 + 12x + 36 by
x + 5), the remainder is​

Answer 1

Refer to the above attachment for the answer

Q = x+7

R = 1

Answer 2

The remainder when p(x) = x² + 12x + 36  divided by x + 5 is 1

Given:

p(x) = x² + 12x + 36  divided by  x + 5

To find:

The remainder when p(x) is divided by x + 5

Solution:

By the Remainder theorem  

when a polynomial f(x) is divided by a linear polynomial (x - a), then the remainder of f(x) will be equal to p(a)

Given p(x) = x^2 + 12x + 36 divided by x + 5

Find remainder of p(x) as given below

take x + 5 = 0 ⇒ x = -5

Now substitute x = - 5 in p(x)

⇒ p(-5) = (-5)² + 12(-5) + 36

= 25 - 60 + 36

= 1

The remainder when p(x) = x² + 12x + 36  divided by x + 5 is 1

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