How do i factor x^4+2x^2+9 using the following method?. Created by gabrielchrissean. Math

Answer:Step-by-step explanation:The given trinomial is a perfect example of a trinomial that can be solved using the second method shown on the book. The first step that you should do is to add and subtract . So, the trinomial should look like this, You'll notice that instead of an , was added and subtracted instead. By doing so, we are transforming into a perfect square, The second step involves factoring the perfect square, The third step is to get the difference of squares, Then, finally we have . So, the most important step here is to think of a coefficient of that will make the first two terms of a trinomial into a perfect square. Then, you can follow the rest of the steps shown on your book.

How do i factor x^4+2x^2+9 using the following method?...

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gabrielchrissean @gabrielchrissean

September 2022 1 5 Report

How do i factor x^4+2x^2+9 using the following method?

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mlpetere

Answer:

Step-by-step explanation:

The given trinomial $x^{4} + 2x^{2} + 9$ is a perfect example of a trinomial that can be solved using the second method shown on the book.

The first step that you should do is to add and subtract $x^{2}$ . So, the trinomial should look like this,

$[x^{4} + (2x^{2} + 4x^{2}) + 9]-4x^{2}$

You'll notice that instead of an $x^{2}$ , $4x^{2}$ was added and subtracted instead. By doing so, we are transforming $x^{4} + 2x^{2}$ into a perfect square,

$(x^{4} + 6x^{2}) + 9)-4x^{2}$

The second step involves factoring the perfect square,

$(x^{2} + 3)^{2} -4x^{2}$

The third step is to get the difference of squares,

$[(x^{2} + 3) -2x] [(x^{2} + 3) +2x]$

Then, finally we have

$(x^{2} + 3 -2x) (x^{2} + 3 +2x)$ .

So, the most important step here is to think of a coefficient of $x^{2}$ that will make the first two terms of a trinomial into a perfect square. Then, you can follow the rest of the steps shown on your book.