Question

By actual division, find the quotient and the remainder when $-13a-14a^2+12$ is divided by $2a+3.$

Answer 1

Given,

• Here, we are asked to find the quotient and remainder when
• $p\left(a\right)=-13a-14a^2+12$ is divided by $g\left(a\right)=2a+3.$
• The first step is to arrange the polynomial expression p(x) in the descending order of degree.

$p\left(a\right)=-14a^2-13a+12.$

• Now, for the first term of the quotient, divide the first term of the dividend by the first term of the divisor.
• 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(a) by g (a) , 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, 7a + 4 is the quotient and the remainder is 0 here.