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hjlf
3 years ago
7

How does the value of the 9 in 857.9 differ from the value of 9 in 798.21

Mathematics
1 answer:
goldenfox [79]3 years ago
4 0

Step-by-step explanation: The 9 in 857.9 differs from the value of 9 in 798.21 because in 857.9, the 9 is in the tenths place, while in 798.21, it is in the tens place.

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Step-by-step explanation:

By the Factor Theorem, if we divide <em>q(x)</em> into <em>p(x) </em>and the resulting remainder is 0, then <em>p(x)</em> is divisible by <em>q(x)</em> (i.e. there are no remainders).

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We are given:

p(x)=x^3+3x^2+3x+1\text{ and } q(x)=x+1

We should find the remainder when dividing <em>p(x)</em> and <em>q(x)</em>. We can use the Polynomial Remainder Theorem. When dividing a polynomial <em>p(x)</em> by a binomial in the form of (<em>x</em> - <em>a</em>), then the remainder will be <em>p(a).</em>

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Problem 2)

We are given:

p(x)=x^3-2x^2+6x-27\text{ and } q(x)=x-3

Again, use the PRT. In this case, <em>a</em> = 3. So:

p(3)=(3)^3-2(3)^2+6(3)-27=0

It satisfies the Factor Theorem.

Problem 3)

We are given:

p(x)=x^n-10^n\text{ and } q(x)=x-10

Use the PRT. In this case, <em>a</em> = 10. So:

p(10)=(10)^n-10^n=0

It satisfies the Factor Theorem.

Since all three cases satisfy the Factor Theorem, <em>p(x)</em> is divisible by <em>q(x)</em> in all three instances.

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