Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 28, 2024

Find the roots of the polynomial equation $9x^3 + 13x^2 = 8x + 15$ by factoring or using other methods.

STEP 1

Assumptions
1. We are given a polynomial equation: $9 x^{3}+13 x^{2}=8 x+15$
2. We want to solve for the variable $x$ .
3. The polynomial is not in standard form (all terms on one side and equal to zero).

STEP 2

The first step in solving the polynomial equation is to bring all terms to one side to set the equation to zero. This is done by subtracting $8x$ and $15$ from both sides of the equation.

STEP 3

Subtract $8x$ from both sides of the equation:
$9 x^{3}+13 x^{2} - 8x = 8 x + 15 - 8x$

STEP 4

Subtract $15$ from both sides of the equation:
$9 x^{3}+13 x^{2} - 8x - 15 = 8 x + 15 - 8x - 15$

STEP 5

Simplify both sides of the equation:
$9 x^{3}+13 x^{2} - 8x - 15 = 0$
The first step in solving the polynomial equation is to rewrite it in standard form as shown above.

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