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

Identify Polynomial Type: Identify the type of polynomial and look for a factoring strategy. The given expression is a quadratic in form, but with a variable to the fourth power: x^4 - 4x^2 + 3 This can be treated as a quadratic with x^2 taking the place of x.Factor as Quadratic: Factor the expression as if it were a quadratic. We are looking for two binomials that multiply to give x^4 - 4x^2 + 3. The factors of 3 that subtract to give 4 are -1 and -3. (x^2 - 1)(x^2 - 3)Check for Further Factoring: Check if the binomials can be factored further. The binomial x^2 - 1 is a difference of squares and can be factored further. x^2 - 1 = (x + 1)(x - 1) The binomial x^2 - 3 cannot be factored further over the integers.Write Completely Factored Form: Write the completely factored form of the expression. The completely factored form of the expression is: (x + 1)(x - 1)(x^2 - 3)

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Factor the expression completely.

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

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

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. Factor the expression completely.

\newline

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

\newline

Answer:

Identify Polynomial Type: Identify the type of polynomial and look for a factoring strategy. $\newline$ The given expression is a quadratic in form, but with a variable to the fourth power: $\newline$ $x^4 - 4x^2 + 3$ $\newline$ This can be treated as a quadratic with $x^2$ taking the place of $x$ .
Factor as Quadratic: Factor the expression as if it were a quadratic. $\newline$ We are looking for two binomials that multiply to give $x^4 - 4x^2 + 3$ . The factors of $3$ that subtract to give $4$ are $-1$ and $-3$ . $\newline$ $(x^2 - 1)(x^2 - 3)$
Check for Further Factoring: Check if the binomials can be factored further. $\newline$ The binomial $x^2 - 1$ is a difference of squares and can be factored further. $\newline$ $x^2 - 1 = (x + 1)(x - 1)$ $\newline$ The binomial $x^2 - 3$ cannot be factored further over the integers.
Write Completely Factored Form: Write the completely factored form of the expression. $\newline$ The completely factored form of the expression is: $\newline$ $(x + 1)(x - 1)(x^2 - 3)$