Factor out the greatest common factor from each polynomial. Se...

Question

Factor out the greatest common factor from each polynomial. See Example 1. (4z-5)(3z-2)-(3z-9)(3z-2)

Accepted Answer

Hello everyone in this video, we're going to be looking at this practice problem where we want to factor the expression m minus six times seven M minus 11 plus two M minus seven times seven M minus 11. So in order to factor an expression, we want to try to find a common factor amongst all the terms. So if we look at the terms we have M minus six times seven M minus and two M minus seven times seven M minus 11. Well it seems like seven M minus 11 appears in both terms. So we can say that seven m minus 11 is the common factor. So now we want to write the expression taking out 7M -11 from each of the terms. So if I take out 7M -11 from the first term I have -6. And if I do the same to the second term I'm left with two M -7. So notice that I can take out seven M minus 11 because when I say that I'm taking out the common factor, I'm really just bringing it to the outside Of this expression so I'll have 7M -11 times this new expression. So if I were to multiply it back into each of the terms, I would get the exact same expression I was given. But now that we've taken out the common factor we can focus on sort of factoring this portion of the expression. So if we just focus on the second part of this expression, I can say I have M minus six plus two M minus seven and notice that I took away the parentheses because in front of these parentheses is just a one. So if I distribute that one, I get The exact same value that's inside the parentheses. So M -6 and two and -7. So I can take away those parentheses. And from here you can see that we have some like terms. So I have these M terms and then I have these constant terms. So I have M plus two M. Which is three M. And then I have negative six minus seven Which is -13. And you can see that I can't really take out any other term from three of -13. So my final factory ization, once I bring back my common factor would be seven M - Times three M -13. So this becomes my final answer for this practice problem and you can see that that aligns with answer choice D. You just have to rearrange this. So if I were to write the three M minus 13 1st and then seven M minus 11, that is the exact same as answer choice D. So hopefully this video helped and see you next time

Factor out the greatest common factor from each polynomial. See Example 1. (4z-5)(3z-2)-(3z-9)(3z-2)

Key Concepts

Greatest Common Factor (GCF)

Distributive Property

Factoring Polynomials

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