Question

Which of the following is a factor of 5y4+4y3+10y+8?

A.y-5
B.y^2-3
C.5y-4
D.y^3+2

Answer 1

D. y^3+2

Explanation:

Descartes' rule of signs tells you there are no positive real roots. That eliminates choices A, B, and C, leaving only choice D.

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Pairs of coefficients are in the ratio 5:4 suggesting that factoring by grouping can be effective.

(5y^4 +4y^3) +(10y +8)

= y^3(5y +4) +2(5y +4)

= (y^3 +2)(5y +4)