Advertisements
Advertisements
Question
f(x) = x3 −6x2 − 19x + 84, g(x) = x − 7
Advertisements
Solution
It is given that f(x) = x3 −6x2 − 19x + 84, and g(x) = x − 7
By the factor theorem, g(x) is the factor of polynomial f(x), if f (7) = 0.
Therefore, in order to prove that (x − 7) is a factor of f(x).
It is sufficient to show that f(7) = 0
Now,
`f(7) = (7)^3 - 6(7)^2 - 19(7) + 84`
` = 343 - 294 - 133 + 84`
` = 427 - 427`
`=0`
Hence, (x − 7) is a factor of polynomial f(x).
APPEARS IN
RELATED QUESTIONS
Write the coefficient of x2 in the following:
`9-12x +X^3`
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
x4 − 2x3 − 7x2 + 8x + 12
Factorise the following:
z² + 4z – 12
Factorise the following:
5x2 – 29xy – 42y2
Factorise the following:
9 – 18x + 8x2
Factorise the following:
(a + b)2 + 9(a + b) + 18
(a + b – c)2 is equal to __________
