Factor as the product of two binomials. x^(2)+6x+9=

Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (a + b)^2 = a^2 + 2ab + b^2. We need to check if x^2 + 6x + 9 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of x^2 is x, and the square root of 9 is 3. So, we have a = x and b = 3.Verify Middle Term: Check if the middle term fits the pattern 2ab. For our expression, the middle term is 6x. We need to see if this equals 2 * x * 3. 2 * x * 3 = 6x, which matches the middle term of our expression.Write as Square of Binomial: Write the expression as the square of a binomial. Since the expression fits the pattern of a perfect square trinomial, we can write it as (x + 3)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor as the product of two binomials.

\newline

x^{2}+6x+9=

Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $x^2 + 6x + 9$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $x^2$ is $x$ , and the square root of $9$ is $3$ . So, we have $a = x$ and $b = 3$ .
Verify Middle Term: Check if the middle term fits the pattern $2ab$ . $\newline$ For our expression, the middle term is $6x$ . We need to see if this equals $2 \times x \times 3$ . $\newline$ $2 \times x \times 3 = 6x$ , which matches the middle term of our expression.
Write as Square of Binomial: Write the expression as the square of a binomial. $\newline$ Since the expression fits the pattern of a perfect square trinomial, we can write it as $(x + 3)^2$ .