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(x + 4) is a factor of x4 + 4x3 − ax2 – bx + 24. Also, a + b = 29. Find the value of b?
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(x + 4) is a factor of x4 + 4x3 − ax2 – bx + 24. Also, a + b = 29. Fin...
Given:

(x^4 - 4x^3 - ax^2 - bx - 24) is divisible by (x - 4)

a + b = 29


To Find:

The value of b


Solution:

To find the value of b, we need to use the concept of polynomial long division. Let's perform the division step by step.

Step 1: Divide the first term of the dividend (x^4) by the first term of the divisor (x). It gives us x^3. Write this quotient above the line.

                                                                                                                                                                        (x^3

Step 2: Multiply the divisor (x - 4) with the quotient obtained in the previous step (x^3). It gives us x^4 - 4x^3. Write this product below the dividend, aligning it with the like terms.

                                                                                
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(x + 4) is a factor of x4 + 4x3 − ax2 – bx + 24. Also, a + b = 29. Find the value of b?
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