Question

unit 6 quiz 2 algebra ii - semester b / unit 6 - polynomials 6 h. choose the correct roots for each polynomial equation. ( x^3 - 7x + 6 = (x - 1)(x + 3)(x - 2) ) ( circ x = -1, -3, -2 ) ( circ x = 1, -3, 3 ) ( circ x = 1, 3, 3 ) ( circ x = -1, 3, -2 ) 7. choose where the graphs of the polynomial functions would cross the ( x )-axis. ( f(x) = x^2 - 4x - 12 ) ( circ x = 1, 12 ) ( circ x = -1, 12 ) ( circ x = 3, 4 ) ( circ x = -2, 6 ) 8. choose where the graphs of the polynomial functions would cross the ( x )-axis. ( f(x) = 5x^2 - 12x - 35 ) ( circ x = 3 ) ( circ x = -6, 2 ) ( circ x = 3, -9 ) ( circ x = 0, -2 )

Explanation:

Step1: Solve for roots of Q1

Set each factor to 0:
$x-1=0 \implies x=1$
$x+3=0 \implies x=-3$
$x-2=0 \implies x=2$

Step2: Solve for roots of Q2

Set $f(x)=0$:
$x^2-4x-12=0$
Factor: $(x-6)(x+2)=0$
$x-6=0 \implies x=6$; $x+2=0 \implies x=-2$

Step3: Solve for roots of Q3

Set $f(x)=0$:
$3x^2-12x-36=0$
Divide by 3: $x^2-4x-12=0$
Factor: $(x-6)(x+2)=0$
$x-6=0 \implies x=6$; $x+2=0 \implies x=-2$

Answer:

1. $\boldsymbol{x=1,-3,2}$
2. $\boldsymbol{x=-2,6}$
3. $\boldsymbol{x=-2,6}$