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Which of these correctly rearranges the terms in this polynomial so like terms are next to each other?

3-6x + 4x² + 3x-6x² -4
a. 4x²- 6x²-6x+3x + 3 - 4
b. - 6x²-6x + 4x² + 3x + 3-4
c. - 6x²-6x + 4x²-4+3x + 3
d. 4x²- 6x² + 6x + 3x-3-4

User Chrissy P
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1 Answer

7 votes

The correct answer is - 6x²-6x + 4x² + 3x + 3-4. Hence the correct option is b.

The key to rearranging a polynomial for term grouping is identifying all the different types of terms present. In this case, we have:

x² terms: There are two of them, with coefficients -6 and +4.

x terms: There are three of them, with coefficients -6, +3, and +3.

Constant terms: There are two of them, +3 and -4.

To rearrange the terms for maximum clarity, we should group each type together:

Combine the x² terms by summing their coefficients: -6x² + 4x² = -2x².

Combine the x terms by summing their coefficients: -6x + 3x + 3x = -x.

Combine the constant terms by summing them: +3 - 4 = -1.

Therefore, the correct rearrangement with all like terms grouped together is:

-6x² + 4x² - 6x + 3x + 3 - 4

Simplifying further, we can combine the remaining x² terms and adjust the final constant:

-2x² - 3x - 1

Hence, option b. - 6x²-6x + 4x² + 3x + 3-4 is the first step towards the fully rearranged form, making it the closest representation of the correctly grouped terms. Hence the correct option is b.

User Fergmux
by
8.3k points
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