DIVIDING POLYNOMIALS BY TRINOMIALS

Consider two polynomials f(x) and g(x), if we divide f(x) by g(x), we have to follow the given instruction.

Problem 1 :

(5x⁶ – 16x⁵ – 11x⁴ + 22x³ + 14x² – 4x + 9) ÷ (x² - 4x + 2)

Solution :

Let f(x) = 5x⁶ – 16x⁵ – 11x⁴ + 22x³ + 14x² – 4x + 9

and

g(x) = x² - 4x + 2

Step 1 :

Divide 5x⁶ by x², so 5x⁶/x² ==> 5x⁴

Put 5x⁴ at the top. Now, multiply 5x⁴ by (x² - 4x + 2)

5x⁴ (x² - 4x + 2) = 5x⁶ - 20x⁵ + 10x⁴

Write 5x⁶ - 20x⁵ + 10x⁴ below the given polynomial and then subtract.

Step 2 :

After subtraction, we will have a polynomial, take the first term from inside.

Here 4x⁵ should be divided by x²

4x⁵/x² ==> 4x³

Now, multiply 4x³ by (x² - 4x + 2)

 4x³ (x² - 4x + 2) = 4x⁵ - 16x⁴ + 8x³

Subtract this polynomial from the previous one.

Repeat the process until, we receive degree of the remainder be lesser than to degree of dividend.

Note :

If the order of the given polynomial is rearranged, then write it in the correct order and start division.

IF any term is missing replace it by 0 and then divide.