Answer:
B. (3x + 1)(3x − 1)(x + 4)
Step-by-step explanation:
1. Use the rational roots theorem to find a root.
The general formula for a third-degree polynomial is
f(x) = ax³ + bx² + cx + 3
Your polynomial is
ƒ(x) = 9x³ + 36x² − x − 4
a = 9; d = -4
According to the Rational Roots Theorem, the possible rational roots are the factors of d divided by the factors of a.
Factors of d = ±1, ±2, ±4,
Factors of a = ±1, ±3, ±9
This gives us 20 possible roots ranging from x = -4 to x = 4.
Let's try x = -4.
f(-4) = 9(-4)³ + 36(-4)² − (-4) − 4 = 9(-64) + 36(16) + 4 - 4 = -576 + 576 =0
So, x = -4 is a root, and (x+ 4) is a factor of the polynomial
2. Use synthetic division to discover the other factors
Divide the polynomial by (x+4).
[tex]\begin{array}{rrrrr}-4| & 9 & 36 & -1 & -4\\|& & -36& 0 & 4\\& 9 & 0& -1 & 0\\\end{array}[/tex]
So, (9x² - 1) is another factor
3. Factor the quadratic.
9x² - 1 = (3x + 1)(3x - 1)
4. Write the complete factorization
ƒ(x) = (x + 4)(3x + 1)(3x - 1)
The figure below shows the graph of your function. with zeros at -4, -⅓, and ⅓.
Answer:
Option B
Step-by-step explanation:
Took the test and got it right.
