Question

factor theorem
y+3;2y³+y²-13y+6

Answer 1

Answer:  Yes, y+3 is a factor of the given polynomial.

Step-by-step explanation:  We are given to apply factor theorem to check whether (y + 3) is a factor of the following polynomial or not :

$p(y)=2y^3+y^2-13y+6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Factor theorem :  The linear expression (x - a) is a factor of a polynomial f(x) if f(a) = 0.

We have

$y+3=0\\\\\Rightarrow y=-3.$

Substituting y = -3 in (i), we get

$f(y)\\\\=2\times(-3)^3+(-3)^2-13\times(-3)+6\\\\=-54+9+39+6\\\\=-5454\\\\=0.$

Therefore, (y + 3) is a factor of the given polynomial.