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

Identify Structure: Identify the structure of the expression. The given expression is x^4 + 4x^2 + 3, which resembles a quadratic in form, where x^2 is the variable.Substitute Variable: Substitute y for x^2. Let y = x^2. Then the expression becomes y^2 + 4y + 3.Factor Quadratic: Factor the quadratic expression. We need to find two numbers that multiply to 3 and add up to 4. These numbers are 1 and 3. So, y^2 + 4y + 3 can be factored as (y + 1)(y + 3).Substitute Back: Substitute back x^2 for y. Replace y with x^2 in the factors to get (x^2 + 1)(x^2 + 3).Check Further Factoring: Check if further factoring is possible. Both x^2 + 1 and x^2 + 3 are sums of squares and cannot be factored further over the real numbers.

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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 1

Evaluate integers raised to rational exponents

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Q. Factor the expression completely.

\newline

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

\newline

Answer:

Identify Structure: Identify the structure of the expression. $\newline$ The given expression is $x^4 + 4x^2 + 3$ , which resembles a quadratic in form, where $x^2$ is the variable.
Substitute Variable: Substitute $y$ for $x^2$ .\ Let $y = x^2$ . Then the expression becomes $y^2 + 4y + 3$ .
Factor Quadratic: Factor the quadratic expression. $\newline$ We need to find two numbers that multiply to $3$ and add up to $4$ . These numbers are $1$ and $3$ . $\newline$ So, $y^2 + 4y + 3$ can be factored as $(y + 1)(y + 3)$ .
Substitute Back: Substitute back $x^2$ for $y$ . Replace $y$ with $x^2$ in the factors to get $(x^2 + 1)(x^2 + 3)$ .
Check Further Factoring: Check if further factoring is possible. $\newline$ Both $x^2 + 1$ and $x^2 + 3$ are sums of squares and cannot be factored further over the real numbers.