Determine the possible rational zeros of this polynomial function using the rational zeros theorem: p(x) = 4x^4 + 13x^3 – 49x^2 – 73x –15

Step-by-step explanation:

Hello,

Let's determine the possible rational zeros of this polynomial function using the rational zeros theorem:

First of all, what is the rational zeroes theorem?

If P(x) is a polynomial with integer coefficients

and if (p and q being integer)

is a zero of P(x), meaning

then p is a factor of the constant term of P(x) and

q is a factor of the leading coefficient of P(x).

How to apply it here?

The constant term of P(x) is -15

The leading coefficient of P(x) is 4

so p is a factor of -15

q is a factor of 4

15 = 1 * 5 * 3

4 = 2 * 2 * 1

q can be 1, 2, 4

-p can be 1, 3, 5, 15

so it gives the following potential solutions

-1, -3, -5, -15

Let's compute P(x) for x in this list of potential solutions

xP(x)

-10

-3-264

-50

-15148680

-0.57.875

-1.5-39.375

-2.5-185.625

-7.54948.125

-0.250

-0.757.96875

-1.25-15.9375

-3.75-324.84375

It gives -1, -5 and -0.25

Conclusion

The possible rational zeroes of P(x) are

-1

-5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3