Question

provide your answer below:
$3x^3 - 10x^2 - 29x - 14$
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question 2 · 1 point
solve $2(3f + 10) - 5f - 10 = 2(10f - 3) - 10f - 10(f + 1)$.
provide your answer below:

Explanation:

Step1: Expand all parentheses

Left side: $2(3f+10)-5f-10 = 6f + 20 - 5f - 10$
Right side: $2(10f-3)-10f-10(f+1) = 20f - 6 - 10f - 10f - 10$

Step2: Simplify both sides

Left side: $6f - 5f + 20 - 10 = f + 10$
Right side: $20f - 10f - 10f - 6 - 10 = -16$

Step3: Isolate the variable $f$

Subtract 10 from both sides:
$f + 10 - 10 = -16 - 10$
$f = -26$

Step1: Use Rational Root Theorem

Test possible rational roots $\pm1,\pm2,\pm7,\pm14,\pm\frac{1}{3},\pm\frac{2}{3},\pm\frac{7}{3},\pm\frac{14}{3}$. Find $x=7$ is a root, so $(x-7)$ is a factor.

Step2: Perform polynomial division

Divide $3x^3 - 10x^2 - 29x - 14$ by $(x-7)$:
$$\frac{3x^3 - 10x^2 - 29x - 14}{x-7} = 3x^2 + 11x + 2$$

Step3: Factor the quadratic

$3x^2 + 11x + 2 = (3x+1)(x+2)$

Answer:

$f = -26$

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For the cubic polynomial $3x^3 - 10x^2 - 29x - 14$, since no specific task (e.g., factoring, solving for roots) is provided, we assume factoring is intended: