Find factors of quadratic equation: 3x^(4)+10x^(2)+8

Identify Form and Simplify: Identify the form of the polynomial and simplify if possible. We have 3x^4 + 10x^2 + 8. Notice it's a quadratic in form of x^2. Let u = x^2. Then the polynomial becomes 3u^2 + 10u + 8.Factor Quadratic: Factor the quadratic 3u^2 + 10u + 8. We need two numbers that multiply to 3*8=24 and add up to 10. The numbers 6 and 4 work because 6*4=24 and 6+4=10. So, 3u^2 + 10u + 8 factors as (3u + 4)(u + 2).Substitute Back: Substitute back x^2 for u. Replace u with x^2 in the factored form: (3x^2 + 4)(x^2 + 2).

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Find factors of quadratic equation:
3x^(4)+10x^(2)+8

Find factors of quadratic equation: $\newline$ $3x^{4}+10x^{2}+8$

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Find factors of quadratic equation:

\newline

3x^{4}+10x^{2}+8

Identify Form and Simplify: Identify the form of the polynomial and simplify if possible. $\newline$ We have $3x^4 + 10x^2 + 8$ . Notice it's a quadratic in form of $x^2$ . $\newline$ Let $u = x^2$ . Then the polynomial becomes $3u^2 + 10u + 8$ .
Factor Quadratic: Factor the quadratic $3u^2 + 10u + 8$ . We need two numbers that multiply to $3\times8=24$ and add up to $10$ . The numbers $6$ and $4$ work because $6\times4=24$ and $6+4=10$ . So, $3u^2 + 10u + 8$ factors as $(3u + 4)(u + 2)$ .
Substitute Back: Substitute back $x^2$ for $u$ . Replace $u$ with $x^2$ in the factored form: $(3x^2 + 4)(x^2 + 2)$ .