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Cycle 3 - Lesson 2 – The Factor Theorem 1.

What are the zeros (x-intercepts) of the function f ( x)  2 x  1x  2x  3 ?

2.

Expand the function to get to standard form:

f ( x)  2 x  1x  2x  3

3.

Choose one of the zeros (x-intercepts) and substitute that value into the function in standard form.

4.

What is the value of the function (the y-value) when you substitute one of the zeros (x-intercepts)?

The FACTOR theorem

For integer values of a and b with a ≠ 0, The factor theorem states that x – b is a _____________ of a polynomial P(x) if and only if ___________ = 0. Similarly, ____________ is a factor of P(x) if and only if

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Check if it is factor 3 2 Determine if x – 3 and x + 2 are factors of f ( x)  x  x  14 x  24

Finding the zeros Find the factors and zeros of this function by checking values with the Factor theorem.

f(x) =

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A better way to fully factor polynomial functions…LONG DIVISION! Instead of guessing and checking to find all of the zeros, once we have found one factor, we can use long division to determine the remaining factors. Example: Fully factor this cubic function then draw a sketch. Step 1: Find one of the factors using the Factor theorem

Step 2: Perform long division

Step 3: Factor the remaining polynomial

Step 4: Set each factor = 0 to determine the zeros.

f ( x)  x 3  2 x 2  5 x  6

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Cycle 3 – Lesson 2 – Factor Theorem – Practice Questions

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