8×4+8×3+8×2+8x=0

Factor 8x out of 8×4+8×3+8×2+8x.

Factor 8x out of 8×4.

8x(x3)+8×3+8×2+8x=0

Factor 8x out of 8×3.

8x(x3)+8x(x2)+8×2+8x=0

Factor 8x out of 8×2.

8x(x3)+8x(x2)+8x(x)+8x=0

Factor 8x out of 8x.

8x(x3)+8x(x2)+8x(x)+8x(1)=0

Factor 8x out of 8x(x3)+8x(x2).

8x(x3+x2)+8x(x)+8x(1)=0

Factor 8x out of 8x(x3+x2)+8x(x).

8x(x3+x2+x)+8x(1)=0

Factor 8x out of 8x(x3+x2+x)+8x(1).

8x(x3+x2+x+1)=0

8x(x3+x2+x+1)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

8x((x3+x2)+x+1)=0

Factor out the greatest common factor (GCF) from each group.

8x(x2(x+1)+1(x+1))=0

8x(x2(x+1)+1(x+1))=0

Factor.

Factor the polynomial by factoring out the greatest common factor, x+1.

8x((x+1)(x2+1))=0

Remove unnecessary parentheses.

8x(x+1)(x2+1)=0

8x(x+1)(x2+1)=0

8x(x+1)(x2+1)=0

Divide each term in 8x(x+1)(x2+1)=0 by 8.

8x(x+1)(x2+1)8=08

Simplify 8x(x+1)(x2+1)8.

Simplify terms.

Cancel the common factor of 8.

Cancel the common factor.

8x(x+1)(x2+1)8=08

Divide (x(x+1))(x2+1) by 1.

(x(x+1))(x2+1)=08

(x(x+1))(x2+1)=08

Apply the distributive property.

(x⋅x+x⋅1)(x2+1)=08

Simplify the expression.

Multiply x by x.

(x2+x⋅1)(x2+1)=08

Multiply x by 1.

(x2+x)(x2+1)=08

(x2+x)(x2+1)=08

(x2+x)(x2+1)=08

Expand (x2+x)(x2+1) using the FOIL Method.

Apply the distributive property.

x2(x2+1)+x(x2+1)=08

Apply the distributive property.

x2x2+x2⋅1+x(x2+1)=08

Apply the distributive property.

x2x2+x2⋅1+x⋅x2+x⋅1=08

x2x2+x2⋅1+x⋅x2+x⋅1=08

Simplify each term.

Multiply x2 by x2 by adding the exponents.

Use the power rule aman=am+n to combine exponents.

x2+2+x2⋅1+x⋅x2+x⋅1=08

Add 2 and 2.

x4+x2⋅1+x⋅x2+x⋅1=08

x4+x2⋅1+x⋅x2+x⋅1=08

Multiply x2 by 1.

x4+x2+x⋅x2+x⋅1=08

Multiply x by x2 by adding the exponents.

Multiply x by x2.

Raise x to the power of 1.

x4+x2+x1x2+x⋅1=08

Use the power rule aman=am+n to combine exponents.

x4+x2+x1+2+x⋅1=08

x4+x2+x1+2+x⋅1=08

Add 1 and 2.

x4+x2+x3+x⋅1=08

x4+x2+x3+x⋅1=08

Multiply x by 1.

x4+x2+x3+x=08

x4+x2+x3+x=08

x4+x2+x3+x=08

Divide 0 by 8.

x4+x2+x3+x=0

x4+x2+x3+x=0

Factor x out of x4+x2+x3+x.

Factor x out of x4.

x⋅x3+x2+x3+x=0

Factor x out of x2.

x⋅x3+x⋅x+x3+x=0

Factor x out of x3.

x⋅x3+x⋅x+x⋅x2+x=0

Raise x to the power of 1.

x⋅x3+x⋅x+x⋅x2+x=0

Factor x out of x1.

x⋅x3+x⋅x+x⋅x2+x⋅1=0

Factor x out of x⋅x3+x⋅x.

x(x3+x)+x⋅x2+x⋅1=0

Factor x out of x(x3+x)+x⋅x2.

x(x3+x+x2)+x⋅1=0

Factor x out of x(x3+x+x2)+x⋅1.

x(x3+x+x2+1)=0

x(x3+x+x2+1)=0

Reorder terms.

x(x3+x2+x+1)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

x((x3+x2)+x+1)=0

Factor out the greatest common factor (GCF) from each group.

x(x2(x+1)+1(x+1))=0

x(x2(x+1)+1(x+1))=0

Factor.

Factor the polynomial by factoring out the greatest common factor, x+1.

x((x+1)(x2+1))=0

Remove unnecessary parentheses.

x(x+1)(x2+1)=0

x(x+1)(x2+1)=0

x(x+1)(x2+1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x=0

x+1=0

x2+1=0

Set the first factor equal to 0.

x=0

Set the next factor equal to 0.

x+1=0

Subtract 1 from both sides of the equation.

x=-1

x=-1

Set the next factor equal to 0.

x2+1=0

Subtract 1 from both sides of the equation.

x2=-1

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x=±-1

The complete solution is the result of both the positive and negative portions of the solution.

Rewrite -1 as i.

x=±i

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

x=i

Next, use the negative value of the ± to find the second solution.

x=-i

The complete solution is the result of both the positive and negative portions of the solution.

x=i,-i

x=i,-i

x=i,-i

x=i,-i

The final solution is all the values that make x(x+1)(x2+1)=0 true.

x=0,-1,i,-i

Solve for x 8x^4+8x^3+8x^2+8x=0