Factor completely. 3x^(2)+30 x+75=

Find common factor: Look for a common factor in the terms 3x^2, 30x, and 75. All terms are divisible by 3. Factor out the greatest common factor (GCF). 3(x^2 + 10x + 25)Factor out GCF: Now, factor the quadratic expression inside the parentheses. We need two numbers that multiply to (3*25) and add up to 10. The numbers 5 and 5 fit this requirement. So, the quadratic x^2 + 10x + 25 can be factored as (x + 5)(x + 5) or (x + 5)^2.Factor quadratic expression: Write the final factored form by combining the GCF with the factored quadratic. The final factored form is 3(x + 5)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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3x^{2}+30x+75=

Find common factor: Look for a common factor in the terms $3x^2$ , $30x$ , and $75$ . $\newline$ All terms are divisible by $3$ . $\newline$ Factor out the greatest common factor (GCF). $\newline$ $3(x^2 + 10x + 25)$
Factor out GCF: Now, factor the quadratic expression inside the parentheses. $\newline$ We need two numbers that multiply to $3 \times 25$ and add up to $10$ . $\newline$ The numbers $5$ and $5$ fit this requirement. $\newline$ So, the quadratic $x^2 + 10x + 25$ can be factored as $x + 5)(x + 5)$ or x + \(5)^ $2$ \.
Factor quadratic expression: Write the final factored form by combining the GCF with the factored quadratic. $\newline$ The final factored form is $3(x + 5)^2$ .