Advertisements
Advertisements
Question
Factorise the following:
(p – q)2 – 6(p – q) – 16
Advertisements
Solution
Let (p – q) = x
(p – q)2 – 6(p – q) – 16 = x2 – 6x – 16
Product = – 16, sum = – 6
Split the middle term as – 8x and 2x
x2 – 6x – 16 = x2 – 8x + 2x – 16
= x(x – 8) + 2(x – 8)
= (x – 8)(x + 2)
...(But x = p – q)
= (p – q – 8)(p – q + 2)
APPEARS IN
RELATED QUESTIONS
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following cases, if 2R1 − R2 = 0.
f(x) = x3 −6x2 − 19x + 84, g(x) = x − 7
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
3x3 − x2 − 3x + 1
2y3 − 5y2 − 19y + 42
If x140 + 2x151 + k is divisible by x + 1, then the value of k is
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Factorise the following:
m2 + 2mn – 24n2
