Question

By actual division, find the quotient and the remainder when $3x+2^2+1$ is divided by $x+2$.

Answer 1

Given,

• Here, we are asked to find the quotient and remainder when

• $p\left(x\right)=3x+2x^2+1$ is divided by $g\left(x\right)=x+2$.

• The first step is to arrange the polynomial expression p(x) in the descending order of degree.

$p\left(x\right)=2x^2+3x+1$ .

• 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,

• 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, 2x -1 is the quotient and the remainder is 3 here.