Advertisements
Advertisements
Question
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
Advertisements
Solution
Let f(x) = 3x2 + 2x2 – 19x + 6
Using hit and trial method,
f(1) = 3 + 2 – 19 + 6 ≠ 0
f(−1) =–3 + 2 + 19 + 6 ≠ 0
f(2) = 24 + 8 – 38 + 6 = 0
Hence, (x – 2) is a factor of f(x)
To factorise 3x2 + 8x − 3
= 3x2 + 9x − x − 3
= 3x(x + 3) −1(x + 3)
= (3x − 1)(x + 3)
Hence 3x3 + 2x3 −19x + 6 = (x − 2)(3x − 1)(x + 3)
APPEARS IN
RELATED QUESTIONS
Check whether 7 + 3x is a factor of 3x3 + 7x.
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
Polynomials bx2 + x + 5 and bx3 − 2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m − n = 0 then find the value of b.
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
