Question

Find the quotient and remainder obtained when $p\left(x\right)=10x+6x^2-24$ is divided by $g\left(x\right)=2x+6.$

Answer 1

• Here, we are asked to find the quotient and remainder when
• p(x)=10x+6x2-24 is divided by g(x) = 2x+6.
• Let’s divide the polynomials step by step.

Step 1:

• The first step is to arrange the polynomial expression p(x) in the descending order of degree. I.e write down the problem in the division format.

$p\left(x\right)=6x^2+10x-24$

Step 2: Find the quotient of the first term of the dividend by the first term of the divisor.

• Now, for the first term of the quotient, divide the first term of the dividend by the first term of the divisor.
• When we divide $6x^2$ by $2x$, we get $3x$.

On multiplying $3x$ with $2x+6$ we obtain $6x²+18x.$

• This product should be subtracted from the dividend 6x²+10x-24 which results in the remainder -8x-24

Step 3: Subtract the product of the divisor and the quotient from the dividend.

• Now, we will subtract this product from the dividend, and bring down the next term (if any).
• The difference and the brought down term will form the new dividend.
• If the degree of remainder > degree of the divisor, consider the remainder as the new dividend.

Here
-8x-24 will be our new dividend.

Step 4: Consider the remainder obtained as the new dividend and repeat the above steps until the degree of the remainder is less than the degree of the divisor.

• So, we have to find the next term of the quotient.
• What do we get if -8x is divided by 2x ?
• Exactly, we will get 4.
• So, the next term of our quotient is 4.
• When we multiply 4 with the divisor, we get -8x-24.
• The next step is to subtract -8x-24 from -8x-24.