Answer: 97
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Step-by-step explanation
Let,
- f(x) = x^3 + 1331
- g(x) = x+11 = one factor
- h(x) = the other factor
The three items form this equation.
f(x) = g(x)*h(x)
Factors g(x) and h(x) multiply to get f(x).
You can use polynomial long division, or synthetic division, to determine h(x) and then plug in x = 3.
However, I'll use another approach.
Since all we care about is h(x) when x = 3, we can plug this value into x of the other functions.
f(x) = x^3 + 1331
f(3) = 3^3 + 1331
f(3) = 1358
g(x) = x+11
g(3) = 3+11
g(3) = 14
Then,
f(x) = g(x)*h(x)
f(3) = g(3)*h(3)
1358 = 14*h(3)
h(3) = 1358/14
h(3) = 97 is the value of the other factor when x = 3.
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Another approach:
1331 = 11^3
x^3+1331 = x^3+11^3 = sum of cubes
Use the sum of cubes factoring formula
x^3+11^3 = (x+11)(x^2-11x+11^2)
x^3+1331 = (x+11)(x^2-11x+121)
We see that x+11 is one factor, which matches the instructions.
The other factor is x^2-11x+121
h(x) = x^2-11x+121
h(3) = 3^2-11(3)+121
h(3) = 97 is the value of the other factor when x = 3.