Solve 4x^4+18x^3+12x^2div6x^2

$$4 { x }^{ 4 } +18 { x }^{ 3 } +12 { x }^{ 2 } \div 6 { x }^{ 2 }$$

Evaluate

$$6\left(x+3\right)x^{3}$$

Solution Steps

Divide 12x^{2} by 6 to get 2x^{2}.

$$4x^{4}+18x^{3}+2x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$4x^{4}+18x^{3}+2x^{4}$$

Combine 4x^{4} and 2x^{4} to get 6x^{4}.

$$6x^{4}+18x^{3}$$

Factor

$$6\left(x+3\right)x^{3}$$

Solution Steps

Factor out 2.

$$2\left(2x^{4}+9x^{3}+x^{2}x^{2}\right)$$

Consider 2x^{4}+9x^{3}+x^{4}. Factor out x^{3}.

$$x^{3}\left(2x+9+x\right)$$

Consider 2x+9+x. Multiply and combine like terms.

$$3x+9$$

Consider 3x+9. Factor out 3.

$$3\left(x+3\right)$$

Rewrite the complete factored expression.

$$6x^{3}\left(x+3\right)$$

Simplify.

$$6\left(x+3\right)x^{3}$$