Question

find quotient and remainder when x²+10x+25 is divided by x+3 also verify division algorithm.​

Answer 1

Answer:

View the attachment for the division.

Verification of division algorithm:

p(x) = q(x) x d(x) + r(x)

where p(x) is the dividend, q(x) is the quotient, d(x) is the divisor and r(x) is the remainder.

On substitution,

x² + 10x + 25 = (x + 7)(x + 3) + 4

x² + 10x + 25 = x² + 3x +7x + 21 + 4

x² + 10x + 25 = x² + 10x + 25

Hence, verified.

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