Question

1. $-n^2 + 10n - 24$
2. $6m^4 - 9m^3 - 6m^2$

directions: solve each equation by factoring.

1. $-r^2 - 6 = -7r$
2. $-3x^2 + x - 6 = -4x^2$
3. $-19r = 5r^2 - 4$
4. $2m^3 + m^2 - 98m = -3m^2 - 2m$

Explanation:

Problem 15: $-n^2 + 10n - 24$

Step1: Factor out -1

$-(n^2 - 10n + 24)$

Step2: Factor quadratic trinomial

$-(n-4)(n-6)$

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Problem 16: $6m^4 - 9m^3 - 6m^2$

Step1: Factor out GCF $3m^2$

$3m^2(2m^2 - 3m - 2)$

Step2: Factor quadratic trinomial

$3m^2(2m+1)(m-2)$

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Problem 17: $-r^2 - 6 = -7r$

Step1: Rearrange to standard form

$r^2 -7r +6=0$

Step2: Factor quadratic trinomial

$(r-1)(r-6)=0$

Step3: Solve for $r$

$r-1=0 \text{ or } r-6=0$

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Problem 18: $-3x^2 + x - 6 = -4x^2$

Step1: Rearrange to standard form

$x^2 +x -6=0$

Step2: Factor quadratic trinomial

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

Step3: Solve for $x$

$x+3=0 \text{ or } x-2=0$

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Problem 19: $-19r = 5r^2 - 4$

Step1: Rearrange to standard form

$5r^2 +19r -4=0$

Step2: Factor quadratic trinomial

$(5r-1)(r+4)=0$

Step3: Solve for $r$

$5r-1=0 \text{ or } r+4=0$

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Problem 20: $2m^3 + m^2 - 98m = -3m^2 - 2m$

Step1: Rearrange to standard form

$2m^3 +4m^2 -96m=0$

Step2: Factor out GCF $2m$

$2m(m^2 +2m -48)=0$

Step3: Factor quadratic trinomial

$2m(m+8)(m-6)=0$

Step4: Solve for $m$

$2m=0 \text{ or } m+8=0 \text{ or } m-6=0$

Answer:

1. $-(n-4)(n-6)$
2. $3m^2(2m+1)(m-2)$
3. $r=1$ or $r=6$
4. $x=-3$ or $x=2$
5. $r=\frac{1}{5}$ or $r=-4$
6. $m=0$ or $m=-8$ or $m=6$