Factor completely. 486+108 x+6x^(2)= +=^(+)

Recognize the structure: Recognize the structure of the expression. The given expression is a quadratic in the form of ax^2 + bx + c. We need to factor it completely.Look for a common factor: Look for a common factor in all terms. All terms in the expression 486 + 108x + 6x^2 have a common factor of 6.Factor out the GCF: Factor out the greatest common factor (GCF). 6(81 + 18x + x^2)Recognize the structure of the quadratic: Recognize the structure of the quadratic inside the parentheses. The quadratic 81 + 18x + x^2 is a perfect square trinomial because it can be written as (9 + x)^2.Factor the perfect square trinomial: Factor the perfect square trinomial. (9 + x)^2Combine the factored parts: Combine the factored parts to write the final factored form. 6(9 + x)^2

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

\newline

486+108 x+6 x^{2}=

Recognize the structure: Recognize the structure of the expression. $\newline$ The given expression is a quadratic in the form of $ax^2 + bx + c$ . We need to factor it completely.
Look for a common factor: Look for a common factor in all terms. $\newline$ All terms in the expression $486 + 108x + 6x^2$ have a common factor of $6$ .
Factor out the GCF: Factor out the greatest common factor (GCF). $6(81 + 18x + x^2)$
Recognize the structure of the quadratic: Recognize the structure of the quadratic inside the parentheses. $\newline$ The quadratic $81 + 18x + x^2$ is a perfect square trinomial because it can be written as $(9 + x)^2$ .
Factor the perfect square trinomial: Factor the perfect square trinomial. $(9 + x)^2$
Combine the factored parts: Combine the factored parts to write the final factored form. $6(9 + x)^2$