Factor the expression completely. x^(4)-3x^(2)+2 Answer:

Recognize form: Recognize the form of the expression. The given expression x^4 - 3x^2 + 2 resembles a quadratic in form, where x^2 is the variable instead of x. We can substitute y = x^2 to make it look like a standard quadratic equation.Substitute y: Substitute y for x^2. Let y = x^2. Then the expression becomes y^2 - 3y + 2.Factor expression: Factor the quadratic expression. We need to factor y^2 - 3y + 2. To do this, we look for two numbers that multiply to 2 and add up to -3. These numbers are -1 and -2. So, y^2 - 3y + 2 factors as (y - 1)(y - 2).Substitute back: Substitute x^2 back in for y. Now we replace y with x^2 in the factored form to get the final factored expression of the original polynomial. The factored form is (x^2 - 1)(x^2 - 2).Check further factoring: Check if further factoring is possible. We notice that x^2 - 1 is a difference of squares and can be factored further. The expression x^2 - 2 cannot be factored over the integers. So, we factor x^2 - 1 as (x + 1)(x - 1).Write final form: Write the completely factored expression. The completely factored form of the original expression is (x + 1)(x - 1)(x^2 - 2).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor the expression completely.

x^(4)-3x^(2)+2
Answer:

Factor the expression completely. $\newline$ $x^{4}-3 x^{2}+2$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Composition of linear and quadratic functions: find an equation

Full solution

Q. Factor the expression completely.

\newline

x^{4}-3 x^{2}+2

\newline

Answer:

Recognize form: Recognize the form of the expression. $\newline$ The given expression $x^4 - 3x^2 + 2$ resembles a quadratic in form, where $x^2$ is the variable instead of $x$ . We can substitute $y = x^2$ to make it look like a standard quadratic equation.
Substitute $y$ : Substitute $y$ for $x^2$ . $\newline$ Let $y = x^2$ . Then the expression becomes $y^2 - 3y + 2$ .
Factor expression: Factor the quadratic expression. $\newline$ We need to factor $y^2 - 3y + 2$ . To do this, we look for two numbers that multiply to $2$ and add up to $-3$ . These numbers are $-1$ and $-2$ . $\newline$ So, $y^2 - 3y + 2$ factors as $(y - 1)(y - 2)$ .
Substitute back: Substitute $x^2$ back in for $y$ . Now we replace $y$ with $x^2$ in the factored form to get the final factored expression of the original polynomial. The factored form is $(x^2 - 1)(x^2 - 2)$ .
Check further factoring: Check if further factoring is possible. $\newline$ We notice that $x^2 - 1$ is a difference of squares and can be factored further. The expression $x^2 - 2$ cannot be factored over the integers. $\newline$ So, we factor $x^2 - 1$ as $(x + 1)(x - 1)$ .
Write final form: Write the completely factored expression. $\newline$ The completely factored form of the original expression is $(x + 1)(x - 1)(x^2 - 2)$ .