QuestionAugust 25, 2025

Expand the expression to a polynomial in standard form: (-x+4)(3x^2-2x-7) Answer Attempt 1 out of 2 square

Expand the expression to a polynomial in standard form: (-x+4)(3x^2-2x-7) Answer Attempt 1 out of 2 square
Expand the expression to a polynomial in standard form: (-x+4)(3x^2-2x-7) Answer Attempt 1 out of 2 square

Solution
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Answer

-3x^3 + 14x^2 - x - 28 Explanation 1. Distribute -x across (3x^2 - 2x - 7) Multiply -x by each term: -x \cdot 3x^2 = -3x^3, -x \cdot (-2x) = 2x^2, -x \cdot (-7) = 7x. 2. Distribute 4 across (3x^2 - 2x - 7) Multiply 4 by each term: 4 \cdot 3x^2 = 12x^2, 4 \cdot (-2x) = -8x, 4 \cdot (-7) = -28. 3. Combine like terms Combine: -3x^3 + (2x^2 + 12x^2) + (7x - 8x) - 28 = -3x^3 + 14x^2 - x - 28.

Explanation

1. Distribute $-x$ across $(3x^2 - 2x - 7)$<br /> Multiply $-x$ by each term: $-x \cdot 3x^2 = -3x^3$, $-x \cdot (-2x) = 2x^2$, $-x \cdot (-7) = 7x$.<br />2. Distribute $4$ across $(3x^2 - 2x - 7)$<br /> Multiply $4$ by each term: $4 \cdot 3x^2 = 12x^2$, $4 \cdot (-2x) = -8x$, $4 \cdot (-7) = -28$.<br />3. Combine like terms<br /> Combine: $-3x^3 + (2x^2 + 12x^2) + (7x - 8x) - 28 = -3x^3 + 14x^2 - x - 28$.
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