Factor completely. 1+12 x+36x^(2)=

Recognize expression type: Recognize the type of expression we are dealing with. The given expression is a quadratic in the form of ax^2 + bx + c. We need to determine if it can be factored into a product of two binomials of the form (dx + e)^2, since the coefficients suggest it might be a perfect square trinomial.Check for perfect square trinomial: Check if the expression is a perfect square trinomial. A perfect square trinomial is in the form (ax)^2 + 2axb + b^2, which factors to (ax + b)^2. We need to check if 1 + 12x + 36x^2 fits this pattern. 1 is the square of 1, and 36x^2 is the square of 6x. The middle term, 12x, is twice the product of 1 and 6x. Therefore, the expression is a perfect square trinomial.Factor perfect square trinomial: Factor the perfect square trinomial. Since 1 + 12x + 36x^2 is a perfect square trinomial, it can be factored into (1 + 6x)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

\newline

1+12x+36x^{2}=

Recognize expression type: Recognize the type of expression we are dealing with. $\newline$ The given expression is a quadratic in the form of $ax^2 + bx + c$ . We need to determine if it can be factored into a product of two binomials of the form $(dx + e)^2$ , since the coefficients suggest it might be a perfect square trinomial.
Check for perfect square trinomial: Check if the expression is a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(ax)^2 + 2axb + b^2$ , which factors to $(ax + b)^2$ . We need to check if $1 + 12x + 36x^2$ fits this pattern. $\newline$ $1$ is the square of $1$ , and $36x^2$ is the square of $6x$ . The middle term, $12x$ , is twice the product of $1$ and $6x$ . Therefore, the expression is a perfect square trinomial.
Factor perfect square trinomial: Factor the perfect square trinomial. $\newline$ Since $1 + 12x + 36x^2$ is a perfect square trinomial, it can be factored into $(1 + 6x)^2$ .