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IgorLugansk [536]
3 years ago
7

Use the Remainder Theorem to find the remainder: (16x^4 – 8x^3 – 4x + 1) ÷ (2x + 1)

Mathematics
1 answer:
vodka [1.7K]3 years ago
3 0

Answer:

5

Step-by-step explanation:

This illustrates the Remainder Theorem. If a polynomial f(x) is divided by x−a , the remainder is the constant f(a) , and f(x)=q(x)⋅(x−a)+f(a) , where q(x) is a polynomial with degree one less than the degree of f(x) . Synthetic division is a simpler process for dividing a polynomial by a binomial.

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He borrowed "a" at 7% and "b" at 8.25%

now, whatever "a" and "b" are, we know, his student loan was 9000, thus
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now, he owes 7% or 7/100 for "a", what's 7% of a? well, 7/100 * a or 0.07a

he owes 8.25% of "b", how much is 8.25% of b? well, 8.25/100 * b or 0.0825b

now, we know, at the end of the year, he owed for both loans, 706.25 in interest
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thus   \bf \begin{cases}
a+b=9000\implies \boxed{b}=9000-a\\
0.07a+0.0825b=706.25\\
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0.07a+0.0825\left(\boxed{9000-a}  \right)=706.25
\end{cases}

solve for "a", to see how much he borrowed at 7%

what about "b"? well, b = 9000-a
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