Dividing Polynomials

Divisor

Dividend

Quotient

24667

Divide

Dividing PolynomialsLong division

1) Write as a long division problem. 2) Focusing on the front term, figure out what you need to

multiply by to get the first term of the polynomial3) Write that on top of the “house” and multiply it through to

the divisor4) Subtract the resulting expression5) Repeat the process until you get to the end of the dividend6) If there is a remainder, write that as a fraction.

𝑥2+3 𝑥−8𝑥+2

You Try:

1) 2)

Dividing Polynomialssynthetic division

This can ONLY be done when divisor is x ± c1) Write the OPPOSITE of the divisor’s constant on the outside of a

vertical line |2) Write the COEFFICIENTS of the dividend next to that (keep the

signs)3) Drop the first dividend number, multiply that by the divisor number

and place under the next coefficient 4) Add the two numbers and write the result under that, repeat the

process of multiplying and adding until you get to the end of the polynomial

5) Write the results as the quotient, the last value is the remainder.

𝑥2+3 𝑥−4𝑥+2

You Try:

1) 2)

Remainder Theorem: For a given a polynomial, p(x), the remainder when dividing by x – a [a is a constant] will be equal to p(a). [the value of the polynomial when you substitute a in for x]

Also, x – a is a FACTOR of p(x) if f(a) = 0 [remainder is zero]

Example: Determine if x + 2 is a FACTOR of 2x2 – 3x + 5.