Question
Using factor theorem, factorize the following polynomials:
2y3 - 5y2 - 19y + 42
2y3 - 5y2 - 19y + 42
✓
Answer
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) = 2y2(y - 2) - y(y - 2) - 21(y - 2)
= (y - 2)(2y2 - y - 21)
= (y - 2)(2y2 - 7y + 6y - 21)
= (y - 2)(y + 3)(2y - 7)
Hence (y - 2), (y + 3) and (2y - 7) are the factors of polynomial f(y).
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) = 2y2(y - 2) - y(y - 2) - 21(y - 2)
= (y - 2)(2y2 - y - 21)
= (y - 2)(2y2 - 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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