Question

11) -4, -1, -3

Answer 1

Answer:

The required polynomial is:

$f\left(x\right)=x^3+8x^2+19x+12$

Step-by-step explanation:

Given the zeros

-4, -1, -3

Zeros can be written as:

x = -4, x = -1, x = -3

Finding the factors

x = -4

x +4 = 0

x = -1

x + 1 = 0

x = -3

x + 3 = 0

Thus, the factor are:

(x+4) (x+1) (x+3)

The original function can be computed by multiplying the factors

$\left(x+4\right)\left(x+1\right)\left(x+3\right)=0$

as

$\left(x+4\right)\left(x+1\right)=x^2+5x+4$

so the expression becomes

$\left(x^2+5x+4\right)\left(x+3\right)=0$

Distribute parentheses

$x^2x+x^2\cdot \:3+5xx+5x\cdot \:3+4x+4\cdot \:3=0$

$x^2x+3x^2+5xx+5\cdot \:\:3x+4x+4\cdot \:\:3=0$

$x^3+3x^2+5x^2+15x+4x+12=0$

Add similar elements: $3x^2+5x^2=8x^2$

$x^3+8x^2+15x+4x+12 = 0$

Add similar elements: $15x+4x=19x$

$x^3+8x^2+19x+12=0$

Thus, the required polynomial is:

$f\left(x\right)=x^3+8x^2+19x+12$

Note: your answer choices are a little ambiguous, but I have explained the entire procedure. Hopefully, it will clear your concept.