Advertisements
Advertisements
Question
y3 − 7y + 6
Advertisements
Solution
Let f(y) =y3 − 7y + 6 be the given polynomial.
Now, putting y= 1,we get
`f(y) = (1)^3 -7(1) + 6 = 1-7 +6`
` = 7-7 = 0`
Therefore, (y-1)is a factor of polynomial f(y).
Now,
`f(y) = y^2 (y-1) + y(y-1) -6(y-1)`
` = (y-1){y^2 + y y-6}`
` = y-1{y^2 + 3y - 2y - 6}`
`= (y -1)(y+2)(y+3)`
Hence (y-1),(y-2) and (y+3)are the factors of polynomial f (y).
APPEARS IN
RELATED QUESTIONS
Identify polynomials in the following:
`p(x)=2/3x^3-7/4x+9`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
If `x = 2` is a root of the polynomial `f(x) = 2x2 – 3x + 7a` find the value of a.
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
If x + a is a factor of x4 − a2x2 + 3x − 6a, then a =
If both x − 2 and \[x - \frac{1}{2}\] are factors of px2 + 5x + r, then
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
Factorise the following:
(p – q)2 – 6(p – q) – 16
Which of the following has x – 1 as a factor?
