Kathryn is thinking of four numbers from 1 through 9 with a sum of 18. Each number is used only once

Mathematics

1 answer:

maksim [4K]3 years ago

3 0

The numbers would be 1, 2, 7, and 8.

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Step-by-step explanation:

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4 years ago

Based on the polynomial remainder theorem, what is the value of the function when x=−6 ?

Vaselesa [24]

ANSWER

$f( - 6) = 10$

EXPLANATION

The given function is
$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$

According to the remainder theorem,

$f( - 6) = R$
where R is the remainder when
$f(x)$

is divided by
$x + 6$

We therefore substitute the value of x and evaluate to obtain,

$f( - 6) = { (- 6)}^{4} + 8 {( - 6)}^{3} + 10 { (- 6)}^{2} - 7( - 6)+ 40$

$f( - 6) = 1296 + 8 ( - 216) + 10 (36) - 7( - 6)+ 40$

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This will evaluate to,

$f( - 6) = 10$

Hence the value of the function when
$x = - 6$

is
$10$

According to the remainder theorem,
$10$
is the remainder when

$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$
is divided by
$x + 6$

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3 years ago

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guajiro [1.7K]

Answer:

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Step-by-step explanation:

We know this because it follows the rule of perfect squares in which the ends are both squares and the middle term is -2 times each term.

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4 years ago