Factor the expression completely. x^(4)-x^(2)-12 Answer:

Recognize Form: Recognize the form of the expression. The given expression x^4 - x^2 - 12 resembles a quadratic equation in form, where x^2 is like the variable 'x' in a quadratic. We can substitute y = x^2 to make it look more familiar.Substitute y: Substitute y for x^2. Substitute y = x^2 into the expression to get: y^2 - y - 12 Now, we have a quadratic equation in terms of y.Factor Quadratic: Factor the quadratic equation. We need to factor y^2 - y - 12. We are looking for two numbers that multiply to -12 and add up to -1 (the coefficient of y). These numbers are -4 and 3. So, we can write the factored form as: (y - 4)(y + 3)Substitute x^2: Substitute x^2 back in for y. Now we need to replace y with x^2 in the factored form: (x^2 - 4)(x^2 + 3)Recognize Difference of Squares: Recognize the difference of squares. The term (x^2 - 4) is a difference of squares and can be further factored into: (x - 2)(x + 2)Write Final Expression: Write the final factored expression. The fully factored expression is: (x - 2)(x + 2)(x^2 + 3)

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Factor the expression completely.

x^(4)-x^(2)-12
Answer:

Factor the expression completely. $\newline$ $x^{4}-x^{2}-12$ $\newline$ Answer:

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Algebra 1

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Q. Factor the expression completely.

\newline

x^{4}-x^{2}-12

\newline

Answer:

Recognize Form: Recognize the form of the expression. $\newline$ The given expression $x^4 - x^2 - 12$ resembles a quadratic equation in form, where $x^2$ is like the variable ' $x$ ' in a quadratic. We can substitute $y = x^2$ to make it look more familiar.
Substitute $y$ : Substitute $y$ for $x^2$ . $\newline$ Substitute $y = x^2$ into the expression to get: $\newline$ $y^2 - y - 12$ $\newline$ Now, we have a quadratic equation in terms of $y$ .
Factor Quadratic: Factor the quadratic equation. $\newline$ We need to factor $y^2 - y - 12$ . We are looking for two numbers that multiply to $-12$ and add up to $-1$ (the coefficient of $y$ ). These numbers are $-4$ and $3$ . $\newline$ So, we can write the factored form as: $\newline$ $(y - 4)(y + 3)$
Substitute $x^2$ : Substitute $x^2$ back in for $y$ . $\newline$ Now we need to replace $y$ with $x^2$ in the factored form: $\newline$ $(x^2 - 4)(x^2 + 3)$
Recognize Difference of Squares: Recognize the difference of squares. The term $(x^2 - 4)$ is a difference of squares and can be further factored into: $(x - 2)(x + 2)$
Write Final Expression: Write the final factored expression. $\newline$ The fully factored expression is: $\newline$ $(x - 2)(x + 2)(x^2 + 3)$