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2 years ago

Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.

Mathematics

1 answer:

goblinko [34]2 years ago

5 0

Answer:

Hi,

a=b+3

Step-by-step explanation:

$\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}$

$\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}$

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

a=b+3

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3 years ago

The formula below gives the sum of the degrees, S, of the interior angles of a polygon. If n represents the number of sides, whi

Helga [31]

Answer:

The equation representing the value of n is, $n=\frac{S}{180^{\text{o}}}+2$ .

Step-by-step explanation:

The formula to compute the sum of the degrees, S, of the interior angles of a polygon is:

$S=(n-2)\times 180^{\text{o}}$

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$S=(n-2)\times 180^{\text{o}}$

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3 years ago

8x = 7x + 3 Would I combine the 8x and the 7x at all in this equation?

Kryger [21]

Yes...thats what u want to do. you want to get the x terms on one side and everything else on the other side.

8x = 7x + 3....so we will subtract 7x from both sides
8x - 7x = 7x - 7x + 3....simplify
1x, or just x = 3 (because ur 7x's cancelled each other out)

so ur answer is : x = 3

and u can check ur answer by subbing it back into the original equation.
8x = 7x + 3
8(3) = 7(3) + 3
24 = 21 + 3
24 = 24 (correct)

3 0

4 years ago

Read 2 more answers

Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.​

Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.