Question

3
write a polynomial function with the given roots:
-3 and -2
(x+3)(x+2)
x²-3x-2

x² + 5x + 6 \tx² + 5x - 6 \tx² - x - 6
x² + x + 6 \tx² + 4x + 8 \tx² + x - 6

write a polynomial function with the given roots:
-1, -2, and -3
(x+1)(x+2)(x+3)
x²-3x-2

x³ + 5x² + 8x + 4 \tx³ + 7x² + 16x + 12 \tx³ + 6x² + 11x +
x³ + 8x² + 19x + 12 \tx³ + 7x² + 14x + 8

draw mr. trevor.

Explanation:

Step1: Form factors from roots (-3,-2)

$(x+3)(x+2)$

Step2: Expand the product

$x^2 + 2x + 3x + 6 = x^2 + 5x + 6$

Step3: Form factors from roots (-1,-2,-3)

$(x+1)(x+2)(x+3)$

Step4: Expand step by step

First multiply $(x+1)(x+2) = x^2 + 3x + 2$, then multiply by $(x+3)$: $(x^2 + 3x + 2)(x+3) = x^3 + 3x^2 + 3x^2 + 9x + 2x + 6 = x^3 + 6x^2 + 11x + 6$

Answer:

1. $x^2 + 5x + 6$
2. $x^3 + 6x^2 + 11x + 6$ (assuming the incomplete option is this standard result)