What are the solutions to the equation x^3+x^2=16x+16 ?

The solutions to the equation x^3+x^2=16x+16 are x=-1,x=-4,x=4

Find the zeros of x^3+x^2=16x+16

The zeros of x^3+x^2=16x+16 are x=-1,x=-4,x=4

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x^{3} + x^{2} = 16 x + 16

x = - 1, x = - 4, x = 4

Solution steps

x^{3} + x^{2} = 16 x + 16

Move

16

to the left side

x^{3} + x^{2} - 16 = 16 x

Move

16 x

to the left side

x^{3} + x^{2} - 16 - 16 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} + x^{2} - 16 x - 16 = 0

Factor

x^{3} + x^{2} - 16 x - 16 : (x + 1) (x + 4) (x - 4)

(x + 1) (x + 4) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x + 4 = 0 or x - 4 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x + 4 = 0 : x = - 4

Solve

x - 4 = 0 : x = 4

The solutions are

x = - 1, x = - 4, x = 4

x^{3} + 3 x^{2} + 4 = 0

x^{3} + 12 x^{2} + 48 x + 64 = 0

y^{4} - 17 y^{2} = - 16

3 (x^{3} - 1) = - 27

(x - 1) (x - 2) (x - 3) = 0

What are the solutions to the equation x^3+x^2=16x+16 ?
The solutions to the equation x^3+x^2=16x+16 are x=-1,x=-4,x=4
Find the zeros of x^3+x^2=16x+16
The zeros of x^3+x^2=16x+16 are x=-1,x=-4,x=4