Rewrite the expression as a product of four linear factors: (x^(2)+x)^(2)-18(x^(2)+x)+72 Answer:

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Rewrite the expression as a product of four linear factors:  (x^(2)+x)^(2)-18(x^(2)+x)+72 Answer:

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Recognize Structure: Recognize the structure of the given expression. The given expression is a quadratic in form of (x^2 + x)^2 - 18(x^2 + x) + 72, which resembles the structure of (a + b)^2 - 18(a + b) + 72, where a = x^2 and b = x.Factor Quadratic Expression: Factor the quadratic expression. We can treat (x^2 + x) as a single variable, let's call it 'y'. So the expression becomes y^2 - 18y + 72. Now we need to factor this quadratic expression.Find Factors of 72: Find the factors of 72 that add up to 18. The factors of 72 that add up to 18 are 6 and 12. So we can write the quadratic expression as (y - 6)(y - 12).Substitute Back: Substitute back (x^2 + x) for y. Now we substitute back (x^2 + x) for y to get ((x^2 + x) - 6)((x^2 + x) - 12).Expand Factors: Expand each factor to find the linear factors. We need to factor (x^2 + x - 6) and (x^2 + x - 12) further to find the linear factors. Let's start with (x^2 + x - 6).Factor x^2 + x - 6: Factor (x^2 + x - 6). The factors of -6 that add up to 1 (the coefficient of x) are 3 and -2. So we can write (x^2 + x - 6) as (x + 3)(x - 2).Factor x^2 + x - 12: Factor (x^2 + x - 12). The factors of -12 that add up to 1 (the coefficient of x) are 4 and -3. So we can write (x^2 + x - 12) as (x + 4)(x - 3).Combine Linear Factors: Combine all the linear factors. Now we have all the linear factors: (x + 3), (x - 2), (x + 4), and (x - 3). So the expression as a product of four linear factors is (x + 3)(x - 2)(x + 4)(x - 3).

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+x\right)^{2}-18\left(x^{2}+x\right)+72$ $\newline$ Answer:

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Rewrite the expression as a product of four linear factors:\newline(x2+x)2−18(x2+x)+72 \left(x^{2}+x\right)^{2}-18\left(x^{2}+x\right)+72 (x2+x)2−18(x2+x)+72\newlineAnswer:

Rewrite the expression as a product of four linear factors: $\newline$ $\left(x^{2}+x\right)^{2}-18\left(x^{2}+x\right)+72$ $\newline$ Answer: