Factor. z^2 + 10z + 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. We need to check if z^2 + 10z + 25 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of z^2 is z, and the square root of 25 is 5. So, we have a = z and b = 5.Verify Middle Term: Check if the middle term is twice the product of a and b. The middle term is 10z, and twice the product of a and b is 2 * z * 5 = 10z. Since they are equal, the expression is a perfect square trinomial.Write Factored Form: Write the factored form using the square root of the first and last terms. The factored form is (z + 5)^2 because (z + 5)(z + 5) = z^2 + 5z + 5z + 25 = z^2 + 10z + 25.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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z^2 + 10z + 25

Check Quadratic Form: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $z^2 + 10z + 25$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $z^2$ is $z$ , and the square root of $25$ is $5$ . So, we have $a = z$ and $b = 5$ .
Verify Middle Term: Check if the middle term is twice the product of $a$ and $b$ . The middle term is $10z$ , and twice the product of $a$ and $b$ is $2 \times z \times 5 = 10z$ . Since they are equal, the expression is a perfect square trinomial.
Write Factored Form: Write the factored form using the square root of the first and last terms. $\newline$ The factored form is $(z + 5)^2$ because $(z + 5)(z + 5) = z^2 + 5z + 5z + 25 = z^2 + 10z + 25$ .