Rewrite the expression as a product of four linear factors: (x^(2)+3x)^(2)-22(x^(2)+3x)+72 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)+3x)^(2)-22(x^(2)+3x)+72 Answer:

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Identify Given Quadratic Expression: Identify the given quadratic expression and recognize that it resembles a quadratic in form, where the variable part is (x^2 + 3x) instead of a simple x. The expression is: (x^2 + 3x)^2 - 22(x^2 + 3x) + 72Set Variable and Simplify: Notice that the expression is a quadratic in terms of (x^2 + 3x), which can be factored like a standard quadratic equation. Let's set y = x^2 + 3x, then the expression becomes: y^2 - 22y + 72Factor Quadratic Expression: Factor the quadratic expression y^2 - 22y + 72. We are looking for two numbers that multiply to 72 and add up to -22. These numbers are -18 and -4, so we can write: y^2 - 22y + 72 = (y - 18)(y - 4)Substitute Back and Simplify: Now, substitute back x^2 + 3x for y to get the expression in terms of x: (y - 18)(y - 4) becomes ((x^2 + 3x) - 18)((x^2 + 3x) - 4)Expand First Binomial: Expand each binomial to find the linear factors. For the first binomial, we have: (x^2 + 3x - 18) = (x^2 + 6x - 3x - 18) = x(x + 6) - 3(x + 6) = (x - 3)(x + 6)Expand Second Binomial: Expand the second binomial to find the linear factors. For the second binomial, we have: (x^2 + 3x - 4) = (x^2 + 4x - x - 4) = x(x + 4) - 1(x + 4) = (x - 1)(x + 4)Combine Factors: Combine the factors from both binomials to express the original expression as a product of four linear factors: (x - 3)(x + 6)(x - 1)(x + 4)

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+3 x\right)^{2}-22\left(x^{2}+3 x\right)+72$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2+3x)2−22(x2+3x)+72 \left(x^{2}+3 x\right)^{2}-22\left(x^{2}+3 x\right)+72 (x2+3x)2−22(x2+3x)+72\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+3 x\right)^{2}-22\left(x^{2}+3 x\right)+72$ $\newline$ Answer: