Question

Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder. $p\left(x\right)=x^4-5x+6$, $g\left(x\right)=2-x^2$.

Answer 1

Step 1: Divide the highest degree term of the dividend by the highest degree term of the divisor.

• $x^4$ is the highest term in dividend and $-x^2$ is the highest term in divisor and we will divide $x^4$ by $-x^2$, we get the first term of the quotient as $-x^2$

Step 2: Multiply the quotient with the divisor..

• The product is $x^4-2x^2$

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

• we get $2x^2-5x+6$ after subtraction
• Repeat the steps till the remainder is zero or deg r(x) < deg g(x).
• So, the quotient is $-x^2-2$
  And the remainder is $-5x+10$.