Polynomial Equivalentcy

Hi this was a multiple choice question and i was wondering if when doing this problem, you have to distribute each numbers in the parenthesis. Do you have to distribute the 2 to the x+1, x-2, and 3x+1??? the question is:

Which polynomial expression is equivalent to y=2(x+1)(x-2)(3x+1) ?

A.) 6x^3 + 5x-2

B.) 6x^3-4x^2-14x-4

C.) 3x^3-2x^2-7x-2

D.) 6x^3-4

Thank you so much!!

Cranberry557 said:

Hi this was a multiple choice question and i was wondering if when doing this problem, you have to distribute each numbers in the parenthesis. Do you have to distribute the 2 to the x+1, x-2, and 3x+1??? the question is:

Which polynomial expression is equivalent to y=2(x+1)(x-2)(3x+1) ?

A.) 6x^3 + 5x-2

B.) 6x^3-4x^2-14x-4

C.) 3x^3-2x^2-7x-2

D.) 6x^3-4

Thank you so much!!

Click to expand...

You need to multiply out 2*(x + 1)*(x - 2)*(3x + 1)

You can start by multiplying ANY TWO of those factors together. Then take that result, and multiply it by one of the remaining factors. Finally, take THAT result and multiply by the fourth factor.

For example, you might start by multiplying 2*(x + 1) to get (2x + 2)....now you have
(2x + 2)*(x - 2)*(3x + 1)

Take two of those three factors and multiply them together. And multiply that result by the remaining factor.

Hello, Cranberry557!

Which polynomial expression is equivalent to: .\(\displaystyle y\;=\;2(x+1)(x-2)(3x+1)\) ?

. . \(\displaystyle (A)\;6x^3 + 5x-2 \qquad (B)\;6x^3-4x^2-14x-4\qquad(C)\;3x^3-2x^2-7x-2\qquad( D)\;6x^3-4\)

Click to expand...

Since this is a multiple-choice question (among dozens of them, I assume),
. . I'd do my best to guess the answer before doing all that multiplying.


\(\displaystyle \text{Look at the first terms of the factors: }\2)(x)(x)(3x)\)
. . \(\displaystyle \text{The first term of the product will be: }\:6x^3\)
\(\displaystyle \text{We can eliminate answer }(C).\)


\(\displaystyle \text{Look at the last terms of the factors: }\2)(+1)(-2)(+1)\)
. . \(\displaystyle \text{The last term of the product will be: }\:-4\)
\(\displaystyle \text{We can eliminate answer }(A).\)


\(\displaystyle \text{Look at answer }\D)\;6x^3 - 4\)
. . \(\displaystyle \text{We can factor out a 2: }\:2(3x^3 - 2)\)

\(\displaystyle \text{Do you think that }\,3x^3-2\,\text{ will factor to: }\x+1)(x-2)(3x+1)\;?\)
. . \(\displaystyle \text{The only way we could factor }\,3x^3 -2\,\text{ is if it were a difference of cubes }\hdots\text{ and it is not.}\)

\(\displaystyle \text{So we can eliminate answer }(D).\)


\(\displaystyle \text{If I were a gambling man, I'd bet the answer is }(B).\)