Zeros and remainders of polynomials worksheet
Write the value you substitute. For a divisor of the form x − a, evaluate the polynomial at a.
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Worked example · Find the remainder on division by x + 2
For p(x) = x² + 3x + 1, find the remainder when dividing by x + 2.
Write x + 2 as x − (−2) and substitute −2.
Evaluate p(−2) = 4 − 6 + 1 = −1. That is the remainder.
Practice questions
- Find the zero of p(x) = 2x − 6.
- For p(x) = x² − 5x + 6, check whether 2 is a zero.
- Find the remainder when x² + 2x − 3 is divided by x − 2.
- Find the remainder when x³ − 2x + 4 is divided by x + 1.
- Is x − 3 a factor of x² − 4x + 3?
- Find k if x + 2 is a factor of x² + kx − 6.