Question

in exercises 23-28, solve the

1. $5n^3 - 30n^2 + 40n = 0$
2. $x^3 + x^2 = 4x + 4$
3. $12s - 3s^3 = 0$

Explanation:

Step1: Factor out GCF of 5n

$5n(n^2 - 6n + 8) = 0$

Step2: Factor quadratic trinomial

$5n(n-2)(n-4) = 0$

Step3: Set each factor to 0

$5n=0, \ n-2=0, \ n-4=0$

Step4: Solve for n

$n=0, \ n=2, \ n=4$

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Step1: Rearrange all terms to left side

$x^3 + x^2 - 4x - 4 = 0$

Step2: Factor by grouping

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

Step3: Factor out common binomial

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

Step4: Factor difference of squares

$(x-2)(x+2)(x+1) = 0$

Step5: Set each factor to 0

$x-2=0, \ x+2=0, \ x+1=0$

Step6: Solve for x

$x=2, \ x=-2, \ x=-1$

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Step1: Factor out GCF of -3s

$-3s(s^2 - 4) = 0$

Step2: Factor difference of squares

$-3s(s-2)(s+2) = 0$

Step3: Set each factor to 0

$-3s=0, \ s-2=0, \ s+2=0$

Step4: Solve for s

$s=0, \ s=2, \ s=-2$

Answer:

1. $n=0$, $n=2$, $n=4$
2. $x=2$, $x=-2$, $x=-1$
3. $s=0$, $s=2$, $s=-2$