In mathematics, factoring is an interesting topic in algebra. Given polynomial expression can be factored by using the grouping method. The given polynomial expression can be factored by different methods that are trinomials by ac method and group the polynomials more than two groups. Let us solve some example problems in factor by grouping.
Steps to factoring using trinomials ac method:
Different steps to solve factoring using trinomials ac method are,
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Example 1:
Factor the given trinomials expression by using ac method.
5x^{2} + 20 + 29x
Solution:
The given expression has three coefficients a, b and c that can be enters into the solver like in this. If we enter the calculate option it will show the steps like below in the solver. Solution to the expression is displayed as follows.
Given trinomial expression
5x^{2} + 20 + 29x
Given trinomials is in the standard form ax^{2} + bx + c = 0.
5x^{2} + 29x + 20 = 0
Here a = 5, b = 29 and c = 20
Multiply the coefficients a and c in the expression.
5 × 20 = 100
Different ways to get the product of ac, we multiply two integers.
1 × 100 = 100
2 × 50 = 100
4 × 25 = 100
5 × 20 = 100
10 × 10 = 100
If we add a and c then we get the result as equals to b means choose that way.
1 + 100 = 101 ≠ 29
2 + 50 = 52 ≠ 29
4 + 25 = 29 = 29
Factor the expression
5x^{2 }+ 25x + 4x + 20 = 0
Group the first two terms and last two terms together
(5x^{2 }+ 25x)+ (4x + 20) = 0
5x (x + 5) + 4 (x + 5) = 0
(5x + 4) (x + 5) = 0
Solve the terms.
5x + 4 = 0 (or) x + 5 = 0
x = - `4/5` (or) -5
Solution:
x = -`4/5` (or) -5
Step 1:
Given polynomial expression.
Step 2:
Find the common monomial factors in the expression. The expression does not have the common terms means, using factor by grouping method
Step 3:
For more than two groups of terms can be factor by grouping method.
Step 4:
Simplify the grouping terms.
Step 5:
Solution
Example 1:
Factoring the polynomial expression 500xy + 600xb – 160ya – 320ab by using factor by group.
Solution:
Step 1:
Given polynomial expression 500xy + 600xb – 160ya – 320ab
Step 2:
Given expression in the standard form ax^{2} + bx + c = 0.
500xy + 600xb – 160ya – 320ab = 0
Step 3:
Groups the terms
500xy + 600xb – 160ya – 320ab = 0
(500xy + 600xb) – (160ya – 320ab) = 0
Step 4:
Find the greatest common factor for the expression.
100x (5y – 6b) – 160a (y – 2b) = 0
(100x – 160a) (5y – 6b) (y – 2b) = 0
Step 5:
Solution:
(100x – 160a) (5y – 6b) (y – 2b) = 0.