Question

If (x+3) is a factor of x^3+bx^2+11x−3.
what is the value of b?

Answer 1

We can use polynomial long division to divide x^3+bx^2+11x by x+3:

x^2 - 2x - 33

x + 3 | x^3 + bx^2 + 11x + 0

x^3 + 3x^2

--------

-bx^2 + 11x

-bx^2 - 3x^2

-----------

14x

Since (x+3) is a factor, the remainder must be 0. Therefore, we have:

- bx^2 + 11x + 0 = 0

- bx^2 = -11x

- b = -11/x

We can't determine the exact value of b without knowing the value of x.

Answer 2

To find the value of b when (x+3) is a factor of x^3+bx^2+11x-3, we can use the factor theorem. According to the factor theorem, if (x+3) is a factor of a polynomial, then substituting -3 for x should result in 0.

Let's substitute -3 for x in the given polynomial and set it equal to 0:

(-3)^3 + b(-3)^2 + 11(-3) - 3 = 0

Simplifying the equation:

-27 + 9b - 33 - 3 = 0

Combining like terms:

9b - 63 = 0

Adding 63 to both sides:

9b = 63

Dividing both sides by 9:

b = 7

Therefore, the value of b is 7.

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