# 2y3 − 5y2 − 19y + 42 - Mathematics

2y3 − 5y2 − 19y + 42

#### Solution

Let f(y) =2y3 − 5y2 − 19y + 42 be the given polynomial.

Now, putting  y=2,we get

f(2) = 2(2)^3 - 5(2)^2 - 19(2) + 42

 = 16 - 20 - 38 + 42 = -58 + 58

 = 0

Therefore, (y - 2)is a factor of polynomial f(y).

Now,

f(y) = 2y^2 (y-2) - y(y - 2) -21(y - 2)

 = (y -2){2y^2 - y - 21}

 = (y-2){2y^2 - 7y + 6y - 21}

 = (y-2)(y + 3)(2y - 7)

Hence  (y - 2),(y+3) and (2y - 7) are the factors of polynomial f(y).

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.5 | Q 10 | Page 33