Factor completely: 21 x+18x^(2)-3x^(3) Answer:

Identify GCF: First, identify the greatest common factor (GCF) of the terms in the polynomial 21x + 18x^2 - 3x^3. The GCF of 21x, 18x^2, and -3x^3 is 3x.Factor out GCF: Factor out the GCF from each term in the polynomial. 3x(7 + 6x - x^2)Rearrange terms: Rearrange the terms inside the parentheses in descending order of the powers of x. 3x(-x^2 + 6x + 7)Factor quadratic expression: Now, factor the quadratic expression inside the parentheses. To factor -x^2 + 6x + 7, we look for two numbers that multiply to -7 (the product of the coefficient of x^2 and the constant term) and add up to 6 (the coefficient of x). The numbers that satisfy these conditions are 7 and -1.Write factored form: Write the factored form of the quadratic expression using the two numbers found in the previous step. 3x(-(x - 7)(x + 1))Factor out negative sign: Since there is a negative sign in front of the quadratic, we can factor out -1 to simplify the expression. 3x(-1)(x - 7)(x + 1)Combine constants: Combine the constants to get the final factored form. -3x(x - 7)(x + 1)

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Factor completely:

21 x+18x^(2)-3x^(3)
Answer:

Factor completely: $\newline$ $21 x+18 x^{2}-3 x^{3}$ $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. Factor completely:

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21 x+18 x^{2}-3 x^{3}

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Answer:

Identify GCF: First, identify the greatest common factor (GCF) of the terms in the polynomial $21x + 18x^2 - 3x^3$ . The GCF of $21x$ , $18x^2$ , and $-3x^3$ is $3x$ .
Factor out GCF: Factor out the GCF from each term in the polynomial. $3x(7 + 6x - x^2)$
Rearrange terms: Rearrange the terms inside the parentheses in descending order of the powers of $x$ . $3x(-x^2 + 6x + 7)$
Factor quadratic expression: Now, factor the quadratic expression inside the parentheses. $\newline$ To factor $-x^2 + 6x + 7$ , we look for two numbers that multiply to $-7$ (the product of the coefficient of $x^2$ and the constant term) and add up to $6$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $7$ and $-1$ .
Write factored form: Write the factored form of the quadratic expression using the two numbers found in the previous step. $\newline$ $3x(-(x - 7)(x + 1))$
Factor out negative sign: Since there is a negative sign in front of the quadratic, we can factor out $-1$ to simplify the expression. $\newline$ $3x(-1)(x - 7)(x + 1)$
Combine constants: Combine the constants to get the final factored form. $\newline$ $-3x(x - 7)(x + 1)$