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10x^4+7x^3-12x^2 .Factor the Polynomial completely .Set each of the factors equal to 0 .Solve each of those equations for x

10x^4+7x^3-12x^2 .Factor the Polynomial completely .Set each of the factors equal to 0 .Solve each of those equations for x
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10x^4+7x^3-12x^2

.Factor the Polynomial completely
.Set each of the factors equal to 0
.Solve each of those equations for x

User Michael Andrews
by
7.3k points

1 Answer

4 votes
10x^4+ 7x^3-12x^2
= x^2(10x^2+ 7x- 12)
= x^2(10x^2 -8x+ 15x -12)
= x^2[ 2x(5x-4)+ 3(5x-4)]
= x^2(5x-4)(2x+3)

x^2(5x-4)(2x+3)= 0
⇒ x= 0
or 5x-4= 0
or 2x+3= 0
⇒ x= 0
or x= 4/5
or x= -3/2

The final answer is x= 0 or x= 4/5 or x= -3/2~

User Ari Pratomo
by
8.4k points
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