Question

What should be subtracted from 8y4 – 17y2 + 2 so that (4y3 – 8y) becomes its factor?
​

Answer 1

Answer:

$f(y) = 8 {y}^{4} - 17 {y}^{2} + 2$

$let \: g(x) = 4 {y}^{3} - 8y = 0$

$= > 4y( {y}^{2} - 2) = 0$

$= > y = \sqrt{2}$

$let \: f( \sqrt{2} ) =0$

$= > f( \sqrt{2}) = 8( { \sqrt{2} })^{4} - 17 ({ \sqrt{2} })^{2} + 2 = 0$

$= > 8 \times 4 - 17 \times 2 + 2 = 0$

$= > 32 - 34 + 2 = 0$

$= > 34 - 34 = 0$

Hence, g(x) is multiple of f(x) and 0 must be subtracted from it.

Hope this answer helps you ^_^ !