Advertisements
Advertisements
Question
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Advertisements
Solution
Let the number to be subtracted from the given polynomial be k.
Let f(y) = 3y3 + y2 – 22y + 15 – k
It is given that f(y) is divisible by (y + 3).
∴ Remainder = f(–3) = 0
3(–3)3 + (–3)2 – 22(–3) + 15 – k = 0
– 81 + 9 + 66 + 15 – k = 0
9 – k = 0
k = 9
RELATED QUESTIONS
Factorise the expression f(x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q, factorize the given polynomial completely.
Using remainder Theorem, factorise:
2x3 + 7x2 − 8x – 28 Completely
If the polynomials ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
f 2x3 + ax2 – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.
If (2x + 1) is a factor of both the expressions 2x2 – 5x + p and 2x2 + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.
