Question

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Answer 1

Answer:

We have the following polynomial:

f(x) = 2x³ + 9x² + 7x - 6

The problem states that one root is -3. Thus, it is true that (x + 3) is a factor of the polynomial. Given that this is fulfilled, it is also true that:

f(x) = (x + 3)Q(x) .°. Q(x) = f(x)/x + 3

where Q(x) has a degree of 2

We can find Q(x) by applying Ruffini's rule, thus:

2 9 7 - 6

-3

______________________

2 3 - 2 0

Therefore:

Q(x) = 2x² + 3x − 2 -

The roots of this polynomial can be get as follows:

x12 = -b ± √b² - 4ac → X12 = −3 ± √3²-4

___________ __________

2a 2(2)

x1 = 1/2 ; x2 = -2

These are the roots along with -3. Finally, the factored polynomial can be written as follows:

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

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