Representing a polynomial as a product

2020-11-30T13:38:36+02:00

Simplifying polynomials often requires you to divide the polynomial into factors. When dividing a polynomial into factors, the polynomial is written as the product of two or more polynomials. Expressing a polynomial as a product is an excellent aid in solving certain types of quadratic equations. In this case, the solutions can be found as solutions to familiar first-order equations.

If each polynomial term has the same factor, it can be distinguished as a common factor using the following distributive property:

[[$$ ab + ac = a (b + c) $$]]

Dividing a polynomial into its factors is the inverse of removing brackets from an expression.

[[$ {\color {green} {\text {–––––– removing brackets ––––}} \color {green} \rightarrow} \\ {\color {red}3}(2x + 1) = {\color {red}3} \cdot 2x + {\color {red}3} \cdot 1 = 6x +3 \\ {\color {blue} \leftarrow \color {blue}{\text {–––––– dividing into factors ––––}}} \\ $]]

Example 1

Divide the binomial [[$ x ^ 3 + x ^ 2 $]] into factors.

Example 2

Divide the trinomial [[$ 4a ^ 3b ^ 2 + 6a ^ 2b - 2b $]] into factors.

4. Representing a polynomial as a product

Representing a polynomial as a product

Example 1

Example 2

Exercises