A. Find the possible rational zeros of each polynomial function. Then, find the rational zeros.
1. P(x)=x²-7x-6
3. P(x) = 2x³-5x²-22x-15
5. P(x) = 8x³ + 34x²-81x + 18
for ax^2+bx+c, the possible rational roots are ±p/q where
p is a factor of c
q is a factor of a
So, for #3, that makes the list
±1/1, ±3/1, ±5/1, ±15/1, ±1/2, ±3/2, ±5/2, ±15/2
In fact, trying the easy ones first, we get
2x^3 - 5x^2 - 22x - 15
= (x+1)(2x^2-7x-15)
and now you can factor the quadratic as usual.
For questions 3 and 5.
In google pastee:
polynomial factorisation emath help
When you see list of results click on:
Factoring Polynomials Calculator-eMathHelp
When page be open in rectangle Enter a polynomial paste your function and click:
CALCULATE
You will see factirisation step-by-step
To find the possible rational zeros of a polynomial function, we can make use of the Rational Root Theorem. According to this theorem, if a rational number p/q is a zero of a polynomial function, then p must be a factor of the constant term and q must be a factor of the leading coefficient.
1. P(x) = x² - 7x - 6:
The leading coefficient is 1, and the constant term is -6. So the possible rational zeros are the factors of -6. These factors are ±1, ±2, ±3, and ±6.
To find the actual rational zeros, you can test each possible zero by substituting it into the polynomial equation and checking if it gives a zero value. The synthetic division method can be used to test the roots systematically.
3. P(x) = 2x³ - 5x² - 22x - 15:
The leading coefficient is 2, and the constant term is -15. So the possible rational zeros are the factors of -15. These factors are ±1, ±3, ±5, and ±15.
5. P(x) = 8x³ + 34x² - 81x + 18:
The leading coefficient is 8, and the constant term is 18. So the possible rational zeros are the factors of 18. These factors are ±1, ±2, ±3, ±6, ±9, and ±18.
You can repeat the process for each polynomial to find the rational zeros. Remember to use the Rational Root Theorem to determine the possible zeros, and then test those possibilities using synthetic division or other methods to verify the actual zeros.