Advertisements
Advertisements
Question
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Solution
By remainder theorem we know that when a polynomial f(x) is divided by x – a, then the remainder is f(a).
Let f(x) = 2x3 + 3x2 – 5x – 6
f(–1) = 2(–1)3 + 3(–1)2 – 5(–1) – 6
= –2 + 3 + 5 – 6
= 0
Thus, (x + 1) is a factor of the polynomial f(x).
APPEARS IN
RELATED QUESTIONS
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
When the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
When x3 – 3x2 + 5x – 7 is divided by x – 2,then the remainder is
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
