QuestionJuly 15, 2025

Use synthetic division to divide f(x) by x-c then write f(x) in the form f(x)=(x-c)q(x)+r f(x)=x^3+13x^2-13x-14;x+1 f(x)= square

Use synthetic division to divide f(x) by x-c then write f(x) in the form f(x)=(x-c)q(x)+r f(x)=x^3+13x^2-13x-14;x+1 f(x)= square
Use synthetic division to divide f(x) by x-c then write f(x) in the form f(x)=(x-c)q(x)+r f(x)=x^3+13x^2-13x-14;x+1 f(x)= square

Solution
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Answer

f(x) = (x+1)(x^2 + 12x - 25) + 11 Explanation 1. Set up synthetic division Use c = -1 for x + 1. Write coefficients of f(x): 1, 13, -13, -14. 2. Perform synthetic division Bring down the leading coefficient (1). Multiply by -1, add to next coefficient. Repeat: - Bring down 1. - 1 \times (-1) = -1, 13 + (-1) = 12. - 12 \times (-1) = -12, -13 + (-12) = -25. - -25 \times (-1) = 25, -14 + 25 = 11. 3. Interpret results Quotient is x^2 + 12x - 25, remainder is 11.

Explanation

1. Set up synthetic division<br /> Use $c = -1$ for $x + 1$. Write coefficients of $f(x)$: $1, 13, -13, -14$.<br /><br />2. Perform synthetic division<br /> Bring down the leading coefficient (1). Multiply by $-1$, add to next coefficient. Repeat:<br />- Bring down 1.<br />- $1 \times (-1) = -1$, $13 + (-1) = 12$.<br />- $12 \times (-1) = -12$, $-13 + (-12) = -25$.<br />- $-25 \times (-1) = 25$, $-14 + 25 = 11$.<br /><br />3. Interpret results<br /> Quotient is $x^2 + 12x - 25$, remainder is 11.
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