In this tutorial we are going to look at two ways to factor polynomial expressions, factoring out the greatest common factor and factoring by grouping. If you want to test this, go ahead and divide both and by 42—they are both evenly divisible by this number! The fully factored polynomial will be the product of two binomials. Factor out the common factor, 2 x — 3 , from both terms. And then you have minus 2 divided by 2 is 1. To factor a number is to rewrite it as a product. When we divide it out of the second term, we are left with
Notice that when you factor two terms, the result is a monomial times a polynomial. Now, if you were to undistribute 2x squared out of the expression, you’d essentially get 2x squared times this term, minus this term, minus this term. Well 4 divided by 2 is 2. Identify the GCF of the polynomial. Introduction Factoring is to write an expression as a product of factors.
So the GCF of our variable part is xy. That simplifies to 1, maybe I fachoring write it below. Notice that in the example below, the first term is x 2and x is the only variable present. And y divided by 1, you can imagine, is just y. The polynomial is now factored.
And to figure that something else we can fcf 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.
Rewrite each term as the product of the GCF and the remaining terms.
Factoring by grouping (article) | Khan Academy
Just as any integer can be written as the product of factors, ffactoring too can any monomial or polynomial be expressed as a product of factors.
Factor 45 c 2 d 2. And then you have minus 8 divided by 2 is 4. Well, the biggest coefficient that divides all of these is a 2, so let me put that 2, let me factor 2 out. You might say OK, let me look at each of these. Well 4 divided by 2 is 2.
problemm Take the numbers 50 and 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.
Find the GCF of the second pair of terms. Likewise to factor a polynomialyou rewrite it as a product. In this case, it does check out.
Greatest Common Factor (GCF) Calculator
Let me factor an x ffactoring out. Note that if we multiply our answer out that we do get the original polynomial. It involves organizing the polynomial in groups. Factor the GCF, 4 aout of the first group. Product of a number and a sum: The largest monomial that we can factor out of each term is.
Example Problem Find the greatest common factor of 81 c 3 d and 45 c 2 d 2.
Others will be asking you for help with factoring. Notice that when you factor two terms, the result is a monomial times a polynomial. The entire term xy 3 is not a factor of either monomial.
Note that this is not in factored form because of the minus sign we have before the 7 in the problem. We can also do this with polynomial dolving.
Greatest Common Factor
But the factored form of a four-term polynomial is the product of two binomials. And the reason why I kind of of went through great pains to show you exactly what we’re doing is so you know exactly what we’re doing. So it’s 2x squared times 2x squared y, and then you have minus 2x squared probem, 8 divided by 2 is 4.
Pulling out common factors, you find: Find the greatest common factor of 56 xy and 16 y 3.