Question

polynomial operations reteach (teacher manually grades)
bonus
bonus #1 what 2 numbers multiply to give you 36 and add to give you 20? (5pts)
$square$ and $square$

Explanation:

Step1: Define variables for the numbers

Let the two numbers be $x$ and $y$. We get the system:

$$\begin{cases} x \times y = 36 \\ x + y = 20 \end{cases}$$

Step2: Rearrange the sum equation

Express $y$ in terms of $x$:
$y = 20 - x$

Step3: Substitute into product equation

Substitute $y$ into $x \times y = 36$:
$x(20 - x) = 36$

Step4: Rearrange to quadratic form

Expand and rearrange into standard quadratic:
$20x - x^2 = 36$
$x^2 - 20x + 36 = 0$

Step5: Factor the quadratic

Factor the quadratic expression:
$(x - 2)(x - 18) = 0$

Step6: Solve for x

Set each factor equal to 0:
$x - 2 = 0 \implies x=2$; $x - 18 = 0 \implies x=18$

Step7: Find corresponding y values

If $x=2$, $y=20-2=18$; if $x=18$, $y=20-18=2$

Answer:

2 and 18