If -2×3 + 6×2 + 17x – 21 is divided by (x + 1), then the remainder is

Q: If -2×3 + 6×2 + 17x – 21 is divided by (x + 1), then the remainder is

If -2x3 + 6x2 + 17x - 21 is divided by (x + 1), then the remainder is -30 ✓ 32 30 -32 Explanation Use the Remainder Theorem: when a polynomial is divided by parenthesis x minus a, the remainder equals the polynomial evaluated at x equals a. Here we divide by parenthesis x plus 1, which is parenthesis x minus negative 1, so evaluate at x equals negative 1. Substitute x equals negative 1 into negative 2x³ plus 6x² plus 17x minus 21. Calculate each term: negative 2 times parenthesis negative 1 ³ equals negative 2 times negative 1 equals 2. Then 6 times parenthesis negative 1 ² equals 6 times 1 equals 6. Continue: 17 times negative 1 equals negative 17, and the constant is negative 21. Add all terms: 2 plus 6 minus 17 minus 21 equals 8 minus 38 equals negative 30. The remainder is negative 30.

Question

Answer 1

If -2×3 + 6×2 + 17x – 21 is divided by (x + 1), then the remainder is

-30 ✓
32
30
-32

Explanation

Use the Remainder Theorem: when a polynomial is divided by parenthesis x minus a, the remainder equals the polynomial evaluated at x equals a. Here we divide by parenthesis x plus 1, which is parenthesis x minus negative 1, so evaluate at x equals negative 1.

Substitute x equals negative 1 into negative 2x³ plus 6x² plus 17x minus 21. Calculate each term: negative 2 times parenthesis negative 1 ³ equals negative 2 times negative 1 equals 2. Then 6 times parenthesis negative 1 ² equals 6 times 1 equals 6.

Continue: 17 times negative 1 equals negative 17, and the constant is negative 21. Add all terms: 2 plus 6 minus 17 minus 21 equals 8 minus 38 equals negative 30. The remainder is negative 30.