Consider the equation xy = 0. in this equation, two variables are multiplied and the result is 0. can the equation be true if neither variable is equal to 0? can the equation be true if only one variable is equal to 0? if so, which one needs to be equal to 0? can the equation be true if both variables are equal to 0? what process could you use to solve equations of the form (x + a)(x + b) = 0? in this case there are only two factors (values being multiplied) that are being set equal to 0. how would you solve the equation if there were more than two factors? explain.

Ok, first of all

xy = 0

**To solve this expression, either x or y must be zero. They could also be zero at the same time.

(0)y = 0 TRUE
x(0) = 0TRUE
(0)(0) =0TRUE

**Can the equation be true if neither variable is equal to 0?No it cannot be

**Can the equation be true if only one variable is equal to 0?Yes, as shown in the example.

**Which one needs to be equal to 0? Either one, or both.

**Can the equation be true if both variables are equal to 0? Yes, as shown in the example (remember this is not a function)

**What process could you use to solve equations of the form (x + a)(x + b) = 0?

**With this kind of expressions (quadratic equation) either (x+a) =0 or (x+b) =0
 x = -aand x= -b , are the roots.

(Since we are talking about a function, there can be only one value of x at the same time)

**How would you solve the equation if there were more than two factors?

We apply the same technique>>>

Suppose we have (X+a)(X+b)(X+c)(X+d)(X+e)(X+f)(X+g)(X+h) = 0

Then the roots are

(X+a)=0 X=-a
(X+b)=0 X=-b
(X+c)=0 X=-c
(X+d)=0 X=-d
(X+e)=0 X=-e
(X+f)=0 X=-f
(X+g)=0 X=-g
(X+h)=0 X=-h

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