Lesson 38

Dividing polynomials using long division

division

□Polynomial long division is a similar process to integer long division.

divisor

quotient

dividend

divide

□ (12x3 - 6x2 + 5x + 4) by 3x

□ 4x2 -2x + 1□ 3x 12x3 - 6x2 + 5x + 4□ subtract 12x3

□ 0 - 6x2 +5x + 4□ subtract - 6x2

□ 0 + 5x + 4□ subtract 3x□ 2x + 4 □ answer 4x2 - 2x + 1 + 2x+4□ 3x

divide

□(32x4 - 104x3 + 56x2 + 11x + 4) by 8x

Dividing a polynomial by a polynomial

□Divide:

□(x4 + 2x3 - 13x2 - 38x -24) by ( x+4)

□(3x4 + 11x3 - 55x2 + 113x + 79) by (x +7)

Dividing a polynomial by a polynomial with missing

terms□Divide:□(4x4 - x3 - 11x - 484) by (x2 + 11)□ Even though there are missing terms, include a

place for them and divide as usual.

□(4x4 -x3 + 0x2 -11x -484) by(x2 + 0x + 11)

□(4x4 + 8x3 -55x2 + 24x) by (x2 + 3)

Testing if one polynomial is a factor of another

□Is (x+2) a factor of 2x3 -x2 -7x +6□Divide - if remainder is 0, then it is a

factor.

□Is (x+3) a factor of 6x3 -6x2 -6x + 6?□Is (x+5) a factor of 8x3 +37x2 -11x +

20?□Is (x+6) a factor of 4x3 +35x2 +73x

+150?