Factor completely X⁴-10x²+9. Please show all work.

Mathematics

1 answer:

Tanya [424]4 years ago

3 0

Answer:

Let y=x² . Then:

x4−10x2+9=y2−10y+9

y²-10y+9=(y-9)(y-1)

Substitute x² for y:

x4−10x2+9=(x2−9)(x2−1)

x²-9=(x+3)(x-3)

x²-1=(x+1)(x-1)

x4−10x2+9=(x+3)(x−3)(x+1)(x−1)

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Let f(x)= 2x-3/9 and g(x)=9x+3/2<br><br> Find (f o g)(x)<br> Find (f o g)(x)

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These seem tough, but they are not that bad.
(f o g)(x)

That means to take function g when x = x (It just means that you don't need to do anything with the function) and substitute it into function f wherever there is a x value. (So basically g becomes what x equals)
Here is a visual representation of it.

(f o g)(x) = 2(9x + (3/2)) - (3/9)

We need to distribute the 2 to everything inside the parenthesis.

(f o g)(x) = 18x + (6/2) - (3/9)

Let's simplify the fraction on the right and left, then find a common denominator so we can add / subtract the two fractions.

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Combine like terms.

(f o g)(x) = 18x + (8/3)

Our final answer is:
(f o g)(x) = 18x + 8/3

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