Factor the expression completely. x^(4)-7x^(2)-18 Answer:

Identify type of polynomial: Identify the type of polynomial and look for a strategy to factor it. The given expression is a quadratic in form, with x^2 as the variable instead of x. We can use substitution to make it look like a standard quadratic equation. Let u = x^2, then the expression becomes u^2 - 7u - 18.Factor quadratic expression: Factor the quadratic expression u^2 - 7u - 18. We look for two numbers that multiply to -18 and add up to -7. These numbers are -9 and +2.Write factored form: Write the factored form of the quadratic using the numbers found in the previous step: (u - 9)(u + 2).Substitute back in for u: Substitute x^2 back in for u to get the factored form in terms of x: (x^2 - 9)(x^2 + 2).Factor difference of squares: Notice that x^2 - 9 is a difference of squares and can be factored further into (x - 3)(x + 3).Combine fully factored terms: Combine the fully factored terms to get the final factored expression: (x - 3)(x + 3)(x^2 + 2).

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Q. Factor the expression completely.

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x^{4}-7 x^{2}-18

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Answer:

Identify type of polynomial: Identify the type of polynomial and look for a strategy to factor it. The given expression is a quadratic in form, with $x^2$ as the variable instead of $x$ . We can use substitution to make it look like a standard quadratic equation. Let $u = x^2$ , then the expression becomes $u^2 - 7u - 18$ .
Factor quadratic expression: Factor the quadratic expression $u^2 - 7u - 18$ . We look for two numbers that multiply to $-18$ and add up to $-7$ . These numbers are $-9$ and $+2$ .
Write factored form: Write the factored form of the quadratic using the numbers found in the previous step: $(u - 9)(u + 2)$ .
Substitute back in for u: Substitute $x^2$ back in for $u$ to get the factored form in terms of $x$ : $(x^2 - 9)(x^2 + 2)$ .
Factor difference of squares: Notice that $x^2 - 9$ is a difference of squares and can be factored further into $(x - 3)(x + 3)$ .
Combine fully factored terms: Combine the fully factored terms to get the final factored expression: $(x - 3)(x + 3)(x^2 + 2)$ .