Factor by Grouping Solver

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.

 

Factor by Grouping Solver - Using the AC method:

 

Steps to factoring using trinomials ac method:

Different steps to solve factoring using trinomials ac method are,

  • Given trinomials
  • Given trinomials is in the standard form ax2 + bx + c.
  • Multiply the coefficients a and c in the expression.
  • Different ways to get the product of ac, we multiply two integers.
  • If we add a and c then we get the result as equals to b means choose that way.
  • Factor the expression by grouping
  • Solve the terms.

 

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Example 1:

Factor the given trinomials expression by using ac method.

5x2 + 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.

           Factor by grouping solver for trinomial AC method

          Given trinomial expression

          5x2 + 20 + 29x

          Given trinomials is in the standard form ax2 + bx + c = 0.

          5x2 + 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+ 25x + 4x + 20 = 0

          Group the first two terms and last two terms together

          (5x+ 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

Factor by grouping solver - using different monomial:

 

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 ax2 + 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.