Factor completely: 3x^(3)-45x^(2)+150 x Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the polynomial 3x^3 - 45x^2 + 150x. The GCF of 3x^3, 45x^2, and 150x is 3x, since 3x is the largest term that divides all three terms.Factor out GCF: Factor out the GCF from each term in the polynomial. 3x^3 - 45x^2 + 150x = 3x(x^2 - 15x + 50) Check that each term in the polynomial is divisible by 3x. 3x^3 ÷ 3x = x^2, 45x^2 ÷ 3x = 15x, 150x ÷ 3x = 50.Check divisibility: Look for factors of the quadratic x^2 - 15x + 50 that multiply to give the constant term (50) and add to give the middle coefficient (-15). The factors of 50 that add up to -15 are -5 and -10.Find quadratic factors: Factor the quadratic x^2 - 15x + 50 using the factors found in the previous step. x^2 - 15x + 50 = (x - 5)(x - 10)Factor quadratic: Combine the GCF factored out earlier with the factored quadratic to get the completely factored form of the polynomial. 3x(x^2 - 15x + 50) = 3x(x - 5)(x - 10)

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Q. Factor completely:

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3 x^{3}-45 x^{2}+150 x

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the polynomial $3x^3 - 45x^2 + 150x$ . The GCF of $3x^3$ , $45x^2$ , and $150x$ is $3x$ , since $3x$ is the largest term that divides all three terms.
Factor out GCF: Factor out the GCF from each term in the polynomial. $\newline$ $3x^3 - 45x^2 + 150x = 3x(x^2 - 15x + 50)$ $\newline$ Check that each term in the polynomial is divisible by $3x$ . $\newline$ $3x^3 \div 3x = x^2$ , $45x^2 \div 3x = 15x$ , $150x \div 3x = 50$ .
Check divisibility: Look for factors of the quadratic $x^2 - 15x + 50$ that multiply to give the constant term ( $50$ ) and add to give the middle coefficient ( $-15$ ). $\newline$ The factors of $50$ that add up to $-15$ are $-5$ and $-10$ .
Find quadratic factors: Factor the quadratic $x^2 - 15x + 50$ using the factors found in the previous step. $\newline$ $x^2 - 15x + 50 = (x - 5)(x - 10)$
Factor quadratic: Combine the GCF factored out earlier with the factored quadratic to get the completely factored form of the polynomial. $\newline$ $3x(x^2 - 15x + 50) = 3x(x - 5)(x - 10)$