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NARA [144]
3 years ago
11

P(x)=x^3+2x^2-4x-8 how do you factor this polynomial function

Mathematics
1 answer:
Wewaii [24]3 years ago
3 0
<h2>Steps:</h2>

So for this, I will be factoring by grouping. Firstly, factor x³ + 2x² and -4x - 8 separately. Make sure that they have the same quantity inside of the parentheses:

p(x)=x^2(x+2)-4(x+2)

Now we can rewrite it as:

p(x)=(x^2-4)(x+2)

However, we aren't finished factoring yet. The first factor, x² - 4, can be factored further using the difference of squares. The difference of squares goes by the formula here: x^2-y^2=(x+y)(x-y) . In this case:

x^2-4=(x+2)(x-2)\\p(x)=(x+2)(x-2)(x+2)

<h2>Answer:</h2>

<u>In short, the answer is p(x)=(x+2)(x-2)(x+2)\ \textsf{OR}\ p(x)=(x-2)(x+2)^2</u>

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