### 7-2 PROBLEM SOLVING FACTORING BY GCF

Factor out the like factor, 5, from the second group. Factor out the GCF of a polynomial. In the next two tutorials we will add on other types of factoring. And then finally, 2x squared is the same thing as if we factor out 2x squared– so we have that negative sign out front– if we factor out 2x squared, it’s the same thing as 2x squared, times 2x squared, over 2x squared. 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. The two groups 7 x x — 3 and 5 x — 1 do not have any common factors, so this polynomial cannot be factored any further. Factoring is very helpful in simplifying and solving equations using polynomials. Similarly, you could say that 8x to the third y– I’ll put the negative out front– is the same thing as 2x squared, our greatest common factor, times 8x to the third y, over 2x squared. You correctly identified 5 b as a factor of one pair, leaving 2 a and 1, and 4 as the factor of the other pair, also leaving 2 a and 1. You can check this by doing the multiplication. Find the greatest common factor of 81 c 3 d and 45 c 2 d 2. So you can factor out a 5 and rewrite the polynomial as a 5 8 a — 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.

Factor out a GCF from each separate binomial. Find the greatest common factor of 25 b 3 and 10 b 2. Math works just like anything else, if you want to get good at it, then you need to practice it.

## Factoring polynomials: common factor

Factor out the like factor, xfrom the first group. Note that this is not in factored form because of the minus sign we have before the 7 in the problem. There fctoring no magic. But what do these simplify to? So x squared is going to be the greatest common x degree in all of them.

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# Factoring by grouping (article) | Khan Academy

So to factor this, we need to figure out what the greatest common factor of each of these terms are. Example Problem Find the greatest common factor of 25 b 3 and 10 b 2. 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.

So that is the largest number that’s going to be part of the greatest common factor. And then what’s the largest degree of y that’s divisible into all of them? Priblem then what’s the greatest, I guess, factor, what’s the greatest degree of x that’s divisible into all three of these?

When factoring a four-term polynomial using grouping, find the common factor of pairs of terms rather vy the whole polynomial. And to figure that something else we can literally undistribute the 2x squared, say this is the same thing, or even before we undistribute the 2x squared, we could say look, 4x to the fourth y is the same thing as 2x squared, times 4x to the fourth y, over 2x squared.

Note how they all have an xso it look like x will be involved. So what we can do now is we can think about each of these terms as the product of the 2x squared lroblem something else. To factor a polynomial, first identify the greatest common factor of the terms.

This method of factoring only works in some cases. 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. Factor 45 c 2 d 2.

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Rewrite each term with the GCF as one factor. The largest number that can be divided out of those factorinh is 3. So this first term over here, this simplifies to 2x squared times– now you get 4 divided by 2 is 2, x to the fourth divided by x squared is x squared.

## Factoring by grouping

Their greatest common factor is 10, since 10 is the greatest factor that both numbers have in common. This problem looks a little different, because now our GCF is a probblem.

We can also do this with polynomial expressions. If we use the exponent 8, we are in trouble. If you want to test this, go ahead and divide both and by 42—they are both evenly divisible by this number! Math Algebra I Factorization Factoring polynomials by taking common factors. Factor the common factor, xout porblem the first group and the common factor, 4, out of the second group.

When two or more monomials are combined either added or subtractedthe resulting expression is called a polynomial. Factoring is very helpful in simplifying and solving equations using polynomials. However, what do you do if the terms within the polynomial do not share any common factors?