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The polynomial p is a functil functs of x. The graph of p has four zeros at-4, -, 0, and 9 Select ALL the expressions that could apply. O 3: (1 - 4) (x + 3)(+ 9) 0 -2 (2 + 4) (6 + 3) (2 -9) 32 (2 + 4) (3.2 + 2) (2 -- 9) 33 (1 + 4) (2.1 - 3) (1 - 9) 0 - 31 (2 + 4) (3x + 2) (z – 9)”

The polynomial p is a functil functs of x The graph of p has four zeros at4 0 and 9 Select ALL the expressions that could apply O 3 1 4 x 3 9 0 2 2 4 6 3 2 9 32 class=

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The correct option is;

[tex](-x)(x+4)(x+\frac{2}{3})(x-9)[/tex]

Here, we want to select the expressions that could be the factored form of the polynomial

From the question, we have roots at -4,-2/3,0,9

That means;

[tex]\begin{gathered} x\text{ = -4} \\ x\text{ = 0} \\ x\text{ = }\frac{-2}{3} \\ x\text{ = 9} \\ \\ So,\text{ we have;} \\ x+4,\text{ x + 0,x-9 and x+}\frac{2}{3} \\ \\ We\text{ can have x + }\frac{2}{3}\text{ as }3x+2 \\ \\ So,\text{ we have the products as;} \\ (x+4)(x)(x-9)(3x+2) \end{gathered}[/tex]

We have the correct options as;

Only the second option is correct

The reason we can have a leading negative x is because;

If;

[tex]-x\text{ = 0; then x = 0}[/tex]