In Exercises 23–48, factor completely, or state that the polynomi...

Question

In Exercises 23–48, factor completely, or state that the polynomial is prime.2x³ - 8x

Accepted Answer

Hello, everyone. We are asked to completely factorize the following polynomial expression. If possible, other Rs declare if the expression is a prime polynomial, the expression we're given is three K cubed minus K. Our answer choices are a three K multiplied by the parentheses. K squared minus 15, B three K squared multiplied by the parentheses. K minus 15, C, 15 multiplied by the parentheses K over 3 -3 D. This polynomial is prime. Looking back at my original expression, I have three K cubed minus 45 K. Recall that when you go to factor any expression, the first thing you should check for is the greatest common factor or a value that can be taken evenly out of both terms. In this case, looking at my coefficients, I have three and 45. I know three goes evenly into three and it does go evenly into 45. So three is gonna be part of my greatest common factor. Next, I look at the variables. So I have K cubed and K, since there's A K in both terms, I could factor A K out as part of my greatest common factor also. Now I'm opening a set of parentheses and I'm going to divide each term in my original expression by my GCF of 3K. So three K cubed divided by three K, the threes will cancel out K cubed divided by K leaves me with K squared negative 45 K divided by three K will give me negative 45 divided by three is negative 15 K divided by K will cancel out. So I'm closing my parentheses. And at this step, I have three K multiplied by the parentheses. K squared minus 15. I wanna see if this can be factored any farther before I do any other step. There is nothing else I could factor out as a G C F and looking at the parentheses, K squared minus 15. I noticed this is not the difference of two squares as 15 is not a perfect square. So this cannot be factored any farther. So three K multiplied by the parentheses. K squared minus 15 is my solution and it is answer choice. A have a nice day.

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In Exercises 23–48, factor completely, or state that the polynomial is prime.2x³ - 8x

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