3 years ago

I posted this earlier but i never got a response. please help!

Mathematics

1 answer:

valina [46]3 years ago

3 0

I think that this is the right answers

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x-intercept =20

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What is the completely factored form of this polynomial? 2x5 + 12x3 − 54x

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$2x(x^2-3)(x^2+9)$

Step-by-step explanation:

Given polynomial:

$2x^5+12x^3-54x$

Factor out the common term $2x$ :

$\implies 2x(x^4+6x^2-27)$

To factor the trinomial $x^4+6x^2-27$ :

$\textsf{Let }u=x^2 \implies u^2+6u-27$

Factor the quadratic by finding two numbers that multiply to -27 and sum to 6: 9 and -3

Rewrite the middle term as the sum of these two numbers:

$\implies u^2+9u-3u-27$

Factorize the first two terms and the last two terms separately:

$\implies u(u+9)-3(u+9)$

Factor out the common term (u + 9):

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Substitute back $u=x^2$ :

$\implies (x^2-3)(x^2+9)$

Therefore, the factored form of the given polynomial is:

$\implies 2x(x^2-3)(x^2+9)$

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