Factor completely. 6x^(2)-30 x+24=

Identify the form: Identify the form of the quadratic trinomial. 6x^2 - 30x + 24 represents the form ax^2 + bx + c.Look for GCF: Look for a greatest common factor (GCF) that can be factored out from all terms. The GCF of 6x^2, -30x, and 24 is 6.Factor out GCF: Factor out the GCF from the quadratic trinomial. 6x^2 - 30x + 24 = 6(x^2 - 5x + 4)Factor the trinomial: Now, factor the trinomial inside the parentheses. We need to find two numbers that multiply to 4 (the constant term) and add up to -5 (the coefficient of the middle term). The numbers that satisfy these conditions are -4 and -1.Write factored form: Write the factored form of the trinomial inside the parentheses using the numbers found in the previous step. x^2 - 5x + 4 = (x - 4)(x - 1)Combine GCF with factored form: Combine the GCF factored out earlier with the factored form of the trinomial. 6(x^2 - 5x + 4) = 6(x - 4)(x - 1)

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Algebra 2

Factor quadratics

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Q. Factor completely.

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6x^{2}-30x+24=

Identify the form: Identify the form of the quadratic trinomial. $6x^2 - 30x + 24$ represents the form $ax^2 + bx + c$ .
Look for GCF: Look for a greatest common factor (GCF) that can be factored out from all terms. $\newline$ The GCF of $6x^2$ , $-30x$ , and $24$ is $6$ .
Factor out GCF: Factor out the GCF from the quadratic trinomial. $\newline$ $6x^2 - 30x + 24 = 6(x^2 - 5x + 4)$
Factor the trinomial: Now, factor the trinomial inside the parentheses. $\newline$ We need to find two numbers that multiply to $4$ (the constant term) and add up to $-5$ (the coefficient of the middle term). $\newline$ The numbers that satisfy these conditions are $-4$ and $-1$ .
Write factored form: Write the factored form of the trinomial inside the parentheses using the numbers found in the previous step. $\newline$ $x^2 - 5x + 4 = (x - 4)(x - 1)$
Combine GCF with factored form: Combine the GCF factored out earlier with the factored form of the trinomial. $6(x^2 - 5x + 4) = 6(x - 4)(x - 1)$