Factor each polynomial completely. See Example 6. 8x³y⁴ + 12x²...

Question

Factor each polynomial completely. See Example 6. 8x³y⁴ + 12x²y³ + 36xy⁴

Accepted Answer

Hey, everyone here we are asked to rewrite the following expression by factoring it completely. Here we are given 15 A cubed multiplied by B raised to the fourth power plus A squared multiplied by B squared plus 40 A multiplied by B cubed. Here we have four answer choice options, answer choice A where we have factored out five A B squared answer B you factor two A B squared answer C, we factored out five A squared B squared and answer D where we factored out two A squared B squared. So to begin factoring our given expression, we want to begin by assessing our given coefficients. So we have the values 15, 2040 for our coefficients. And now we want to start by finding the greatest common factor between each of these coefficients. So we want to start with the smallest value here, which is 15. And we want to begin by factoring out the largest possible value from 15, which we know is five because five times three gives us 15. And so now since the largest value of the smallest coefficient is five, we want to see that we can factor out five from the rest of our coefficients. So moving on to 20 we know that five times four gives us 20. And lastly with 40 we have that five times eight gives us 40. So we can in fact factor out five from each of our coefficients. So we see that five is our greatest common factor. And now we just want to move on to the variables of each term. So starting with variable A, from the first term, we have a cut from the second term, we have a squared. And from the third term, we just have a raised to the first power. So here between all of these A's, we see that the highest power or the smallest power is just of one. So this tells us that since the smallest power is one that we can factor out A from each of our terms. Now repeating this process for our B variable, we have B raised to the fourth power. We also have B squared. And lastly, we have B cubed. Now with our variable BS, we see that the smallest power is two. So from each of the B terms, we can factor out B squared. So now we see that we can factor out five A and B squared from each of our terms. So we just want to factor out these values. So we have five a multiplied by B squared. And now we multiply this term by the expression which will contain the values of our remaining terms. So our remaining terms become three A squared multiplied by B squared plus four A plus A B. So with our factored expression, we are left with answer choice A where again, the factored form is five, A multiplied by B squared multiplied by the expression three A squared multiplied by B squared plus four A plus A B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Factor each polynomial completely. See Example 6. 8x³y⁴ + 12x²y³ + 36xy⁴

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Exponents and Variables in Factoring

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