CONCEPT PREVIEW Work each problem.

Match each polynomial in Colu...

Question

CONCEPT PREVIEW Work each problem.

Match each polynomial in Column I with its factored form in Column II.

I                                     II
a. 8x³ - 27                 A. (3 - 2x) (9 + 6x + 4x²)
b. 8x³ + 27                B. (2x - 3) (4x² + 6x + 9)
c. 27 - 8x³                 C. (2x + 3) (4x² - 6x + 9)

Accepted Answer

Hello, everyone. We are asked to factorize the following polynomial expression. 343 minus 64 K cubed. Our answer choices are a, the parentheses four K minus seven multiplied by the parentheses. 16 K squared plus 28 K plus B. The parentheses four K minus seven multiplied by the parentheses. 16 K squared minus 28 K minus C negative parentheses. Four K minus seven multiplied by the parentheses. 16 K squared minus 28 K minus 49 D negative parentheses. Four K minus seven multiplied by the parentheses, 16 K squared plus 28 K plus 49. So looking at the expression we are given so 64. Oops, I'm sorry. That's the second part. 343 minus 64 K cubed. What I was doing without realizing it is I was rearranging this. So my variable was first and I can do that by factoring a negative one to the outside of the parentheses and then rewriting this in the parentheses as 64 K cubed minus 343. We would do this just so the variables first from there. I recognize that what's in my parentheses, looks like the difference of cubes. And I recall that the difference of cubes, if I had something like X cubed minus Y cubed, that would be the parentheses of X minus Y multiplied by the parentheses of X squared plus XY plus Y squared. So let's see if we can match this up to figure out what our X and our Y would be in this case. So matching this up, I'm gonna rewrite negative one. And then in parentheses 64 K cubed minus 343. So matching this initially, I would think this is Y cube or sorry, X cubed minus Y cubed. So X cubed for our problem is 64 K cubed, Y cubed is 343. So if I take the cube root of both of those, I can find out what X and Y will be. So the cube group of 64 K cubed will be four K and the cube root of 343 is seven. So now knowing that my X is four K and my Y is seven. Let's follow the format that we have set up here. So my first parentheses are X minus Y. So that's gonna be four K minus seven and I don't want to lose my minus one that was on the outside. So I'm gonna bring that right down right now before I forget. Then opening my second set of parentheses, I have X squared. So four K squared, four squared is 16 K squared is K squared. The middle term is X multiplied by Y. So four K multiplied by seven, which would be 28 K. And our last term is Y squared. So seven squared, which is 49. So now this is factored, I don't have to leave the one there if I don't want to, but I need to leave the negative sign. So I have negative open parentheses. Four K minus seven closed parentheses multiplied by the parentheses. 16 K squared plus 28 K plus 49 closed parentheses. And when I check my answer choices, this matches with answer choice. D have a nice day.

CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. 8x³ - 27 A. (3 - 2x) (9 + 6x + 4x²) b. 8x³ + 27 B. (2x - 3) (4x² + 6x + 9) c. 27 - 8x³ C. (2x + 3) (4x² - 6x + 9)

Key Concepts

Factoring Polynomials

Sum and Difference of Cubes

Polynomial Degree and Leading Coefficient

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