Question

given the equation $y=x^2+5x+6$, what are its x-intercepts?
select one:
a. -2, 3
b. 2, 3
c. 2, -3
d. -2, -3

simplify: $\frac{x^3y^3}{x^3y^2}$
select one:
a. y
b. $\frac{xy}{x}$
c. xy
d. x

Explanation:

First Problem:

Step1: Set $y=0$ for x-intercepts

$0 = x^2 + 5x + 6$

Step2: Factor the quadratic equation

$(x+2)(x+3) = 0$

Step3: Solve for $x$

$x+2=0 \implies x=-2$; $x+3=0 \implies x=-3$

Step1: Apply exponent quotient rule

$\frac{x^3}{x^3} \cdot \frac{y^3}{y^2}$

Step2: Simplify each term

$x^{3-3} \cdot y^{3-2} = x^0 \cdot y^1$

Step3: Evaluate $x^0=1$

$1 \cdot y = y$

Answer:

d. -2, -3

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Second Problem: