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O Hawkes L earning C https://learn hawkeslearning.com/ Portal/Lesson/lesson certify O Save & End Certify Lesson: 4.4 The Fundamental Theorem of A A.. 1/20 Question 3 of 10, Step 1 of 1 Correct Construct a polynomial function with the following properties: fifth degree, 3 is a zero of multiplicity 3, -4 is the only other zero, leading coefficient is 3. Answer f (x) SHELBY Keypad Hide Submit Answer

Solution

3 is a zero of multiplicity 3

So we have (x-3)³

The other zero is -4 And the degree of the polynomial is 5. So the zero that is -4 must have a multiplicity of 2

So we get (x+4)²

And the leading coefficient is 3

Therefore required polynomial is

f(x)=3(x-3)³(x+2)²

f(x)= 3x⁵ -3x⁴ -87x³+135x²+648x-1296