Advertisements
Advertisements
Question
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
Advertisements
Solution
Let P(x) = 3x3 + 2x2 – 19x + 6
By hit and trial method,
P(1) = 3(1)3 + 2(1)2 – 19(1) + 6
= 3 + 2 – 19 + 6
= –8 ≠ 0
P(–1) = 3(–1)3 + 2(–1)2 – 19(–1) + 6
= –3 + 2 + 19 + 6
= 24 ≠ 0
P(2) = 3(2)3 + 2(2)2 – 19(2) + 6
= 24 + 8 – 38 + 6
= 0
Thus, (x – 2) is a factor of P(x).
Now,
3x2 + 8x – 3
`x - 2")"overline(3x^3 + 2x^2 - 19x + 6)`
3x3 – 6x2
– +
8x2 – 19x + 6
8x2 – 16x
– +
– 3x + 6
– 3x + 6
+ –
0
∴ 3x3 + 2x2 – 19x + 6 = (x – 2)(3x2 + 8x – 3)
= (x – 2)(3x2 + 9x – x – 3)
= (x – 2)(3x(x + 3) – 1(x + 3))
= (x – 2)(x + 3)(3x – 1)
APPEARS IN
RELATED QUESTIONS
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:
x3 + x2 – 4x – 4
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.
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
When x3 – 3x2 + 5x – 7 is divided by x – 2,then the remainder is
What is the remainder when x2018 + 2018 is divided by x – 1
If x51 + 51 is divided by x + 1, the remainder is ______.
