Factoring Expressions
In this page we are going to discuss about factoring expressions concept . In mathematics, Polynomial expression is one important topic in algebra. Factoring polynomial expression is defined as the process of solving the given polynomials expression by using the concepts of factoring. Using the greatest common factor, the given polynomial expression can be factorized. Let us solve some example problems for factoring polynomial expression.
Different steps to solve polynomials expression,
- Given polynomial expression
- Polynomial expression is arranged in the order of powers and then it is in the standard form of ax2 + bx + c = 0
- Factor the polynomial expression
- Simplify the factored terms
Example 1:
Factor the given polynomial expression m2 - 21m + 110 = 0
Solution:
Given polynomial expression
m2 - 21m + 110= 0
It can be already arranged in the form an order of powers
m2 - 21m + 110 = 0
Given polynomial expression in the standard form ax2 + bx + c = 0
m2 - 21m + 110 = 0
Factor the polynomial expression
m2 - 21m + 110 = 0
m2 - 10m – 11m + 110 = 0
m(m - 10) - 11 (m - 10) = 0
(m - 10) (m - 11) = 0
Solve the factors for the expression
m - 11 = 0 (or) m – 10 = 0
m = 11 and 10
Solution:
x = 10 and 11.
Example 2:
Factor the given polynomial expression m2 + 34m + 64 = 0
Solution:
Given polynomial expression
m2 + 34m + 64 = 0
It can be already arranged in the form an order of powers
m2 + 34m + 64 = 0
Given polynomial expression in the standard form ax2 + bx + c = 0
m2 + 34m + 64 = 0
Factor the polynomial expression
m2 + 34m + 64 = 0
m2 + 32m + 2m + 64 = 0
m(m + 32) + 2(m + 32) = 0
(m + 32) (m + 2) = 0
Solve the factors for the expression
m + 32 = 0 and m + 2= 0
m = - 32 and m = - 2
Solution:
x = - 32 and - 2.
Example 3:
Factor the given polynomial expression x2 – 2x - 35 = 0
Solution:
Given polynomial expression
x2 - 2x - 35 = 0
It can be already arranged in the form an order of powers
x2 - 2x - 35 = 0
Given polynomial expression in the standard form ax2 + bx + c = 0
x2 - 2x - 35 = 0
Factor the given expression
x2 - 2x - 35 = 0
x2 + 5x - 7x - 35 = 0
x(x + 5) - 7(x + 5) = 0
(x + 5) (x - 7) = 0
Solve the factors for the expression
x + 5 = 0 and x - 7 = 0
x = - 5 and x = 7
Solution:
x = - 5 and x = 7.
