If a binomial (x – a) is a factor of a polynomial f(x), then
If a binomial (x – a) is a factor of a polynomial f(x), then
the remainder when dividing f(x) by (x – a) will be _______.
3 Simple Steps for Factoring a Polynomial Function (when given one factor)
1. _________________________________
2. _________________________________
3. _________________________________
Application – Finding the Lengths of a Box – Follow the same steps!!!
?
?
x – 4
Example: Consider the function [pic]. Given that two of its factors are (x – 3) and (2x + 1), find the remaining factors.
Given a polynomial and one (or more) of its factors, find the remaining factors of the polynomial.
1. x3 + 3x2 – 6x – 8; x – 2
2. x3 + 7x2 + 7x – 15; x – 1
3. x3 - 9x2 + 27x – 27; x – 3
4. 3x3 - 4x2 - 17x + 6; x + 2
5. 18x3 + 9x2 - 2x - 1; 2x + 1
6. [pic]; [pic] & [pic]
7. The volume of water in a rectangular swimming pool can be modeled by the polynomial 2x3 - 9x2 + 7x + 6. If the depth of the pool is given by the polynomial 2x + 1, what polynomials express the length and width of the pool?
8. Mrs. Holst is building a rectangular bird box. The volume can be modeled by the function 4x3 - 12x2 - x + 3. If the height of the box is given by x – 3, find the length and width of the base of the box.
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Given: f(x) = x3 + 6x2 – x – 30 show that
(x + 3) is a factor. Then find all the other factors.
Given: f(x) = 2x4 - x3 – 18x2 +9x show that (x +3) and (2x-1) are factors. Then find all the factors.
V = x3 + 3x2 – 36x + 32 what are the missing lengths of the sides?
YOU DO: Given a polynomial show that the factor given is a factor and then find the remaining factors of the polynomial.
1. [pic] 2. [pic]
3. [pic]are factors. 4. Given the volume of a rectangular prism is
[pic]and the length of one side is [pic]. Find the lengths of the other two sides.
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