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Understanding the Remainder and Factor Theorems with Synthetic Division

This lesson explores the Remainder and Factor Theorems in polynomials. Learn how to use synthetic division to check if a polynomial has a specific factor, and understand the conditions that apply when the remainder is zero. The Factor Theorem states that a polynomial ( f(x) ) has a factor ( (x - c) ) if ( f(c) = 0 ). Through examples, we will determine if given binomials are factors of polynomials and find remainders when not, while also identifying the zeros of various functions.

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Understanding the Remainder and Factor Theorems with Synthetic Division

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  1. 9.8 Day 1 – Remainder and Factor Theorems

  2. Use synthetic division to divide by: 1. 2.

  3. Note: When using synthetic division if you have a remainder of zero, then is a factor of the polynomial! • Factor Theorem: A polynomial has a factor if and only if .

  4. Use the Factor Theorem to decide whether the binomial given in the form is a factor of the polynomial given as . If it is not, give the remainder when is divided by . 3.

  5. Use the Factor Theorem to decide whether the binomial given in the form is a factor of the polynomial given as . If it is not, give the remainder when is divided by . 4.

  6. Use the Factor Theorem to decide whether the binomial given in the form is a factor of the polynomial given as . If it is not, give the remainder when is divided by . 5.

  7. 6. Factor given that

  8. 7. Factor given that

  9. 8. One zero of is . Find the other zeros of the function.

  10. 9. One zero of is . Find the other zeros of the function.

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