![]() ![]() On the back side is the answer key for your partner. 30 7 5x 15x² 10x -1 -3x -2 Solution: 15x2 + 7x – 2 (3x + 2)(5x - 1)ġ2 You Try 2x2 +3x –9 6x2 + x – 2 4x2 + 9x + 2ġ3 Partner Activity! On the front side of your Factoring Practice are your questions. Check answer: (x-5)(3x+2) 3x2 -13x -10=(x-5)(3x+2)Ħ Solve the x-box way Example: Factor 3x2 -13x -10 x -5 (3)(-10)= -30 3xįACTOR the x-box way ax2 + bx + c GCF GCF Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum GCFĨ Examples Factor using the x-box method. To remember the special moment, Adventure Mike snaps some photos.1 Factoring Quadratics using X-Box method and Factor by Groupingģ Homework! Score out of 26 Divide by 2.6Ĥ X- Marks the Spot Product a∙c factors factors Sum bĮxample: Factor 3x2 -13x -10 -13x= -15x +2x 1. Let’s fast forward, the treehouse is finally finished. If his girlfriend wants a bigger treehouse, it won’t be a problem because he can just adjust the size of the sides. The polynomial is factored!Īdventure Mike has the measurements for the two sides of the treehouse. Last step, combine the two GCFs, to create a new binomial. Also, be especially careful you don't make a sign error. This is a little tricky because you have to group the terms so that, when you factor out the GCF, the remaining binomial is the same for each. Write two new terms using the factors of 'ac' that sum to 'b', and multiplied by 'x'.ĭoes this format look familiar? Remember the highlighted terms - from the example problem? Now to group, use parentheses to group the four terms into two binomials. Now, watch carefully while I do some mathemagic. 6 and 15 are factors of -90 and sum to 9. Hmm can you find the pair of factors that also sum to 9? That's right. So since 'ac' = -90, here's a list of some of the factors of -90 – let's take a look. We need to find the factors of 'ac' that sum to 'b'. Okay, so how do you get from the standard form to the factored form when 'a' is not equal to 1? There's a little trick to doing this. After combining these like terms, the result is a trinomial in standard, quadratic form with 'a' equal to a number other than 1. ![]() To help you understand factoring by grouping, pay attention to the terms that are highlighted. Working backwards, first, use the FOIL method to multiply the two binomials.īefore combining like terms, we have 3x² + 6x – x – 2. To put this method into perspective, we'll start at the end result, with the factors. To show him how to factor by grouping, let’s use another problem as an example. To figure out the measurements for the sides of the treehouse, how can Mike factor this expression? Multiplying Binomials This looks familiar, doesn’t it? This expression is in the standard form of a quadratic polynomial, ax²+bx+c, but notice it's a trinomial and 'a' is equal to a number other than 1. Let’s take a look at the expression he wrote, 15x²+9x-6. So, to save time, rather than measuring and calculating everything all over again, he can use grouping to factor polynomials. Oh jeez, his girlfriend just remembered – she wants a balcony, so she and Mike can watch the sunset. Using a snake as a measuring stick, Mike figured out the polynomial expression to represent the total area. Understand the relationship between zeros and factors of polynomials.Īdventure Mike and his girlfriend plan to build a treehouse. To see more examples of factoring of polynomials by grouping, watch this video. ![]() Check your work by foiling.Īs 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. Factor out the GCF: 2x(x + 5) + 3(x + 5), and then write as a binomial pair: (2x + 3) (x + 5). Next, use parentheses to group: (2x² + 10)x + (3x +15). The modified equation is 2x² + 10x + 3x + 15. Now modify the original equation to include the new terms 10x and 3x. Since ac is equal to 30, determine the factors of 30 that sum to the value of b which is 13. ![]() 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. 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.įirst, find factors of ac that sum to b. ![]()
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