Question

By actual division, find the quotient and the remainder when $35x+7x^2+24$ is divided by $x+4$.

Answer 1

Given,

• Here, we are asked to find the quotient and remainder when
• $p\left(x\right)=35x+7x^2+24$ is divided by $g\left(x\right)=x+4$.
• The first step is to arrange the polynomial expression p(x) in the descending order of degree.

$p\left(x\right)=7x^2+35x+24$

• Now, for the first term of the quotient, divide the first term of the dividend by the first term of the divisor. And,
• We will multiply this term of the quotient by the divisor to get the product.
• And, subtract the product of the divisor and the quotient from the dividend.
• Therefore, on dividing p(x) by g (x) , we get,

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• Consider the remainder obtained as the
• new dividend and repeat steps 2 to 3 until the degree of the remainder is less than the degree of the divisor. So,

• Hence, 7x +7 is the quotient and the remainder is -4 here.