Factoring by Grouping – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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How do you factor a quadratic equation written in the standard form of ax² + bx + c when the a value is greater than 1? You can use a trick.

First, find factors of ac that sum to b. You may want to make a list. Next, write two new terms using the factors, and then group the four terms into binomials making sure when you factor out the greatest common factor, the second binomial is the same.

Let’s use an example: 2x² + 13x +15. Since ac is equal to 30, determine the factors of 30 that sum to the value of b which is 13. The factors are 3 and 10. Now modify the original equation to include the new terms 10x and 3x. The modified equation is 2x² + 10x + 3x + 15. Next, use parentheses to group: (2x² + 10)x + (3x +15). Factor out the GCF: 2x(x + 5) + 3(x + 5), and then write as a binomial pair: (2x + 3) (x + 5). Check your work by foiling.

As you continue to work with polynomials, you will notice there are a limited number of types of equations and if you learn to recognize the formats, factoring and solving becomes much easier. To see more examples of factoring of polynomials by grouping, watch this video.

Understand the relationship between zeros and factors of polynomials.


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Exercises in this Practice Problem
Explain how to factor the given quadratic polynomial by grouping.
Factor the polynomial $15x^2+9x-6$.
Indicate the coefficients of the quadratic polynomials.
Factor the given polynomial.
Complete the following table of factors and sums.
Consider the appropriate factorization.