Factor completely. (x^(2)+x-6)(2x^(2)+4x)=

Factor Quadratic Expression: First, we need to factor the quadratic expression x^2 + x - 6. To factor x^2 + x - 6, we look for two numbers that multiply to -6 and add to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2. So, we can write x^2 + x - 6 as (x + 3)(x - 2).Factor Second Expression: Now, we look at the second expression 2x^2 + 4x. We can factor out the common factor of 2x from each term. So, 2x^2 + 4x can be written as 2x(x + 2).Multiply Factored Expressions: Finally, we multiply the factored forms of both expressions together. The completely factored form of the original expression is (x + 3)(x - 2) * 2x(x + 2).

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Algebra 2

Factor sums and differences of cubes

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Q. Factor completely.

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\left(x^{2}+x-6\right)\left(2 x^{2}+4 x\right)=

Factor Quadratic Expression: First, we need to factor the quadratic expression $x^2 + x - 6$ . To factor $x^2 + x - 6$ , we look for two numbers that multiply to $-6$ and add to $1$ (the coefficient of $x$ ). The numbers that satisfy these conditions are $3$ and $-2$ . So, we can write $x^2 + x - 6$ as $(x + 3)(x - 2)$ .
Factor Second Expression: Now, we look at the second expression $2x^2 + 4x$ . We can factor out the common factor of $2x$ from each term. So, $2x^2 + 4x$ can be written as $2x(x + 2)$ .
Multiply Factored Expressions: Finally, we multiply the factored forms of both expressions together. $\newline$ The completely factored form of the original expression is $(x + 3)(x - 2) \times 2x(x + 2)$ .