7-2 PROBLEM SOLVING FACTORING BY GCF

Example Problem Find the greatest common factor of 25 b 3 and 10 b 2. Well, all of these are divisible by x squared. So we have 4x to the fourth y, and we have minus 8x to the third y, and then we have minus 2x squared. Just as any integer can be written as the product of factors, so too can any monomial or polynomial be expressed as a product of factors. And then what’s the largest degree of y that’s divisible into all of them? To factor a polynomial, first identify the greatest common factor of the terms, and then apply the distributive property to rewrite the expression. They are the numbers that you can multiply together to produce another number:

Factor out the 5 b 2. So let’s see, it’s going to be 2x squared times– and what’s this guy divided by 2x squared? And then you have y divided by say, 1, is just y. B 8 y Correct. Because the GCF is the product of the prime factors that these numbers have in common, you know that it is a factor of both numbers.

Greatest Common Factor (GCF) Calculator

To factor a number is to rewrite it as a product. We have a 3, 9, and So x squared is going to be the greatest common x degree in all of them. So that is the largest number that’s going to be part of the greatest common factor. We can also do this with polynomial expressions. To factor a polynomial, first identify the greatest common factor solvinf the terms. Note that if we multiply our answer out that we do get the original polynomial. Answer Cannot be factored.

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Greatest Common Factor

Factor 81 c 3 d. Math Algebra I Factorization Factoring polynomials by taking common factors.

When I say number I’m talking solviny the actual, I guess, coefficients. So in the future, you’ll do it more like this, where you kind of just factor it out in your head, but I really want you to understand what we did here. If you have four terms with no GCF, then try factoring by grouping.

Factor out the common binomial.

To be in factored form, it must be written as a product of factors. In this case, it does check out.

7-2 problem solving factoring by gcf

Factor out the GCF: And then you have y divided by say, 1, is just y. D 8 xy 3 Incorrect.

Factoring by grouping

Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get solvjng at their sport or instrument.

By the time I’m are through with you, you will be a factoring machine.

Right, if you distribute this out, if you take that out of each of the sllving, you’re going to get 2x squared times this 2x squared y, minus 4xy, and then you have minus 1, minus 1, and we’re done. The process of breaking a number down into its prime factors is called prime factorization. Finally, pull any common binomials out of the factored groups. We’ve factored the problem. Well, x squared goes into all three of these, and obviously that’s the greatest degree of x that can be divided into this last term.

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Factoring polynomials: how to find common factor (video) | Khan Academy

Find the greatest common factor of 25 b 3 and 10 b 2. Example Problem Find the greatest common factor of and This method of factoring only works in some cases. Well 4 divided by 2 is 2. Notice that when you factor two terms, the result is a monomial times a polynomial. And y divided by problm, you can imagine, is just y.

7-2 problem solving factoring by gcf

But what do these simplify to? In the future, you might be able to do this a little bit quicker. In both cases, it is the distributive property that is being used.

Rewrite each term as the product of the GCF and the remaining terms.

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