Factor. c^2 - 6c + 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 c^2 - 6c + 9 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of c^2 is c, and the square root of 9 is 3. So, we have a = c and b = 3.Verify Middle Term: Check if the middle term fits the pattern 2ab. For our expression, 2ab should be 2 * c * 3 = 6c, which matches the middle term of our quadratic.Write Factored Form: Write the factored form using the square of a binomial. Since the quadratic fits the pattern of a perfect square trinomial, we can write it as (c - 3)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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c^2 - 6c + 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 $c^2 - 6c + 9$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $c^2$ is $c$ , and the square root of $9$ is $3$ . So, we have $a = c$ and $b = 3$ .
Verify Middle Term: Check if the middle term fits the pattern $2ab$ . For our expression, $2ab$ should be $2 \times c \times 3 = 6c$ , which matches the middle term of our quadratic.
Write Factored Form: Write the factored form using the square of a binomial. $\newline$ Since the quadratic fits the pattern of a perfect square trinomial, we can write it as $(c - 3)^2$ .