Question

Approximate the real number solution(s) to the polynomial function f(x) = x3 − 4x2 + x + 6.

x = −3, x = −1, x = 2
x = 3, x = 1, x = −2
x = 3, x = −1, x = 2
x = −3, x = 1, x = −2

Answer 1

C is the correct answer because that's the only answer where all the numbers (i.e. 3, -1, 2) all, when plugged into the function, equal 0. For example:

3³ - (4 × 3²) + 3 + 6 = 0
-1³ - (4 × (-1)²) + (-1) + 6 = 0
2³ - (4 × 2²) + 2 + 6 = 0

As we see, everything adds up to 0. So, C is the correct answer.

Answer 2

The real number solution(s) to the polynomial function f(x) = x3 − 4x2 + x + 6 are x = 3, x = −1, x = 2 since option (c) is correct.

What is synthetic division?

A more straightforward approach to dividing a polynomial of the first degree by another polynomial of the same degree involves only writing down the coefficients of the various powers of the variable and changing the sign of the constant term in the divisor to substitute additions for the more common subtractions.

How to find the factor of f(x)?

The given function is p(x) = x³ + 7x² + 11x + 5.

We have to find factors in this function.

First, find the value of a function on x=-5.

Function value is zero

then use synthetic division:

2 I  1    -4    1     6

   I        2   -4   -6

   ----------------------

      1    -2    -3      0

the remainder is 0.

So (x-2) is a factor

therefore, f(x) = (x-2)(x²-2x-3)

                       = (x-2)(x+1)(x-3)

hence the solutions of the equations are x = 3, x = −1, x = 2

Learn more about synthetic division here: brainly.com/question/24662212

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