Factor. q^2 - 10q + 25 ______

Check Quadratic Form: 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, where a and b are real numbers. We need to check if the given quadratic fits this form.Identify First Term: Identify the square of the first term. The first term is q^2, which is the square of q. So, a = q.Identify Last Term: Identify the square of the last term. The last term is 25, which is the square of 5. So, b = 5.Check Middle Term: Check if the middle term fits the pattern of 2ab. The middle term is -10q, and for a perfect square trinomial, we expect it to be -2ab. With a = q and b = 5, we calculate -2ab = -2 * q * 5 = -10q. The middle term of the quadratic matches -2ab, so it confirms that we have a perfect square trinomial.Write Factored Form: Write the factored form using the values of a and b. Since the quadratic is a perfect square trinomial, it factors to (a - b)^2. Substitute a = q and b = 5 to get (q - 5)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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q^2 - 10q + 25

Check Quadratic Form: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a - b)^2 = a^2 - 2ab + b^2$ , where $a$ and $b$ are real numbers. $\newline$ We need to check if the given quadratic fits this form.
Identify First Term: Identify the square of the first term. $\newline$ The first term is $q^2$ , which is the square of $q$ . So, $a = q$ .
Identify Last Term: Identify the square of the last term. $\newline$ The last term is $25$ , which is the square of $5$ . So, $b = 5$ .
Check Middle Term: Check if the middle term fits the pattern of $2ab$ . The middle term is $-10q$ , and for a perfect square trinomial, we expect it to be $-2ab$ . With $a = q$ and $b = 5$ , we calculate $-2ab = -2 \times q \times 5 = -10q$ . The middle term of the quadratic matches $-2ab$ , so it confirms that we have a perfect square trinomial.
Write Factored Form: Write the factored form using the values of $a$ and $b$ . Since the quadratic is a perfect square trinomial, it factors to $(a - b)^2$ . Substitute $a = q$ and $b = 5$ to get $(q - 5)^2$ .