Question

algebra ii kap
solving polynomials equations
name _______________________________ per

1. $15x^4 + 26x^3 + 7x^2 = 0$
2. $9x^3 - 39x^2 + 12x = 0$

Explanation:

Step1: Factor out common term

$15x^4 + 26x^3 + 7x^2 = x^2(15x^2 + 26x + 7) = 0$

Step2: Solve $x^2=0$

$x^2=0 \implies x=0$ (double root)

Step3: Factor quadratic trinomial

$15x^2 + 26x + 7 = (3x+1)(5x+7) = 0$

Step4: Solve linear factors

$3x+1=0 \implies x=-\frac{1}{3}$
$5x+7=0 \implies x=-\frac{7}{5}$
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Step1: Factor out common term

$9x^3 - 39x^2 + 12x = 3x(3x^2 -13x +4) = 0$

Step2: Solve $3x=0$

$3x=0 \implies x=0$

Step3: Factor quadratic trinomial

$3x^2 -13x +4 = (3x-1)(x-4) = 0$

Step4: Solve linear factors

$3x-1=0 \implies x=\frac{1}{3}$
$x-4=0 \implies x=4$

Answer:

1. $x=0$ (multiplicity 2), $x=-\frac{1}{3}$, $x=-\frac{7}{5}$
2. $x=0$, $x=\frac{1}{3}$, $x=4$