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SAT Math 1.5 Algebra and Functions. If f (x) = x2 - 16 and g(x) = x4 - 256, what is f of x divided by g of x?
ACT Math 2.1 Intermediate Algebra 359 Views
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Description:
ACT Math Intermediate Algebra Drill 2, Problem 1. Solve the equation.
- Intermediate Algebra / Radical and rational expressions
- Intermediate Algebra / Fractional equations
- Product Type / ACT Math
- Foreign Language / Arabic Subtitled
- Foreign Language / Spanish Subtitled
- Foreign Language / Korean Subtitled
- Foreign Language / Chinese Subtitled
- Algebra / Write expressions in equivalent forms to solve problems
- Algebra / Interpret the structure of expressions
- Algebra / Interpret the structure of expressions
- Algebra / Write expressions in equivalent forms to solve problems
- Algebra / Interpret the structure of expressions
- Algebra / Interpret the structure of expressions
- Elementary Algebra / Solve quadratic equations by factoring
Transcript
- 00:02
Try this shmoopy question on for size...
- 00:05
Solve: The quantity a squared minus a minus 12 all over the quantity a squared plus 3a
- 00:10
plus 2 divided by the quantity a plus 3 over the quantity a plus 2.
- 00:15
And here are the potential answers...
- 00:20
Well, there are really 2 major steps going on here.
Full Transcript
- 00:23
One: multiplying by the inverse -- so we have to flip the 2nd fraction around and make
- 00:27
it times rather than divided by...
- 00:30
And then two: We clearly have a factorable expression here.
- 00:33
For the first one we have an a in each of these parts of the parentheses...
- 00:37
...then we have to figure out what 2 numbers multiply together to get negative 12 and also
- 00:41
add together to get negative 1.
- 00:44
What are the factors of 12? 1 and 12? Yeah... but that won't work.
- 00:49
2 and 6 don't work either, because when added, no matter which is positive and which
- 00:54
is negative, they won't total "1."
- 00:56
3 and 4 however... DO work.
- 00:59
So we want the ADDED part to be a negative 1... negative 4 plus 3 is negative 1, and
- 01:06
negative 4 times 3 is negative 12, so... we're good.
- 01:09
The first part of our answer is quantity a plus 3 times quantity a minus 4.
- 01:14
Now to the denominator.
- 01:16
We need 2 numbers that when multiplied are 2... and when added are 3.
- 01:20
Well... 2 only has 2 and 1 as factors... and luckily, if we add 2 and 1 we get 3. So the
- 01:26
bottom is a quick calculation.
- 01:26
It's quantity a plus 2 times quantity a plus 1.
- 01:29
Now we just rewrite everything so it's fully factored and... cross-out-able.
- 01:34
The quantity a plus 3 over the quantity a plus 3 becomes 1; we can trash it.
- 01:39
Same deal with the quantity a plus 2.
- 01:41
And we are left with just quantity a minus 4 over a plus 1...
- 01:45
...and the answer is C.
- 01:48
Phew.
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