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Algebra Level 2

Given that x 3 + 8 x = 2 x^3 + 8x = 2 , compute x 5 + 10 x 3 − 2 x 2 + 16 x + 10 x^5 + 10x^3 - 2x^2 + 16x + 10 .


The answer is 14.

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Paola Ramírez by Paola Ramírez , 24, Mexico

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2 solutions

Paola Ramírez
Jun 21, 2015

x 5 + 10 x 3 − 2 x 2 + 16 x + 10 = x 2 ( x 3 + 8 x − 2 ) + + 2 x 3 + 16 x + 10 x^5+10x^3-2x^2+16x+10=x^2(x^3+8x-2)++2x^3+16x+10

x 5 + 10 x 3 − 2 x 2 + 16 x + 10 = x 2 ( 0 ) + 2 x 3 + 16 x + 10 x^5+10x^3-2x^2+16x+10=x^2(0)+2x^3+16x+10

x 5 + 10 x 3 − 2 x 2 + 16 x + 10 = 2 x 3 + 16 x + 10 x^5+10x^3-2x^2+16x+10=2x^3+16x+10

x 5 + 10 x 3 − 2 x 2 + 16 x + 10 = 2 ( x 3 + 8 x − 2 ) + 10 + 4 x^5+10x^3-2x^2+16x+10=2(x^3+8x-2)+10+4

x 5 + 10 x 3 − 2 x 2 + 16 x + 10 = 2 ( 0 ) + 10 + 4 x^5+10x^3-2x^2+16x+10=2(0)+10+4

∴ x 5 + 10 x 3 − 2 x 2 + 16 x + 10 = 14 \therefore \boxed{x^5+10x^3-2x^2+16x+10=14}

7 Helpful 0 Interesting 1 Brilliant 0 Confused

you can finish the solution after the second line coz

2x^3 +16x is nothing but 2*(x^3+8x) which is 4

Gokul Kumar - 5 years, 10 months ago
Hardik Parnami
Jun 22, 2015

It was as simple as anything ... If we have an expression which is equal to 0 an we want to find the value of another expression ..we should divide the second by the first...here ib this problem x^3+8x=2 X^3+8x-2=0 And divide it by x^5+10x^3-2x^2×16x+10 The answer is 14 as it is the remainder

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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