Knowee
Questions
Features
Study Tools

If  f(x)  =  x3 + x2 − ax + b  is divisible by  x2 − x , then the value of  a + b  = Select an answerA–2B0C2D6

Question

If  f(x)  =  x³ + x² − ax + b is divisible by  x² − x, then the value of  a + b  =

Select an answer
A. –2
B. 0
C. 2
D. 6

🧐 Not the exact question you are looking for?Go ask a question

Solution

The given polynomial f(x) = x^3 + x^2 - ax + b is divisible by x^2 - x.

This means that when we divide f(x) by x^2 - x, there should be no remainder.

We can write x^2 - x as x(x - 1).

So, the roots of the divisor are x = 0 and x = 1.

According to the Factor theorem, if a polynomial f(x) is divisible by x - a, then f(a) = 0.

So, we can say that f(0) = 0 and f(1) = 0.

Let's calculate these values:

f(0) = 0^3 + 0^2 - a*0 + b = b. Since f(0) = 0, we have b = 0.

f(1) = 1^3 + 1^2 - a*1 + b = 1 + 1 - a + 0 = 2 - a. Since f(1) = 0, we have 2 - a = 0, which gives a = 2.

So, a + b = 2 + 0 = 2.

Therefore, the correct answer is C. 2.

This problem has been solved

Similar Questions

If  f(x)  =  x3 + x2 − ax + b  is divisible by  x2 − x , then the value of  a + b  = Select an answerA–2B0C2D6

Given that Ax3 + Bx2 + x + 6 is exactly divisible by (x + 1)(x – 2), find the value of Aand the value of B

Given that the remainder when f(x) = x3 − 2x2 − ax + b is divided by x − 1is 96 and that x − 4 is a factor, determine the values of a and b.

When f(x) = 15x3 – 14x2 – 4x + 10 is divided by (3x + 2), then the remainder is:

f  A(0, −3), B(5, 6), C(2k + 1, −43k) are given points in which  C divides  AB in  2  :  3. Find the value of  2k.

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.