# Factoring

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9 multiplied by zero = 0 Any number multipled by zero = zero. This is a basic rule of our mathematical system.

(t)(0) = 0. Therefore xy = 0 means that either x = 0 or y = 0 If x and y = 0 then there is no reason to have two variables.

(t + 4)(t -3) = 0 Either (t + 4) = 0 or (t -3) = 0 To determine what t = we set (t + 4) = 0 and (t -3) = 0

To solve the problem we need to know what is the value of t that makes (t + 4) = 0 or (t - 3) = 0. So we set each equal to zero and solve for t:

- (t + 4) = 0 → t + 4 = 0 → t = -4

or

- (t -3) = 0 → t - 3 = 0 → t = 3

Therefore the answer is t = - 4 or t = 3

If you substitute t = - 4 into (t + 4)(t -3) = 0 you get (-4 + 4)(t -3) = 0→ 0(t -3) = 0

If you substitute t = 3 into (t + 4)(t - 3) = 0 you get (t + 4)(3 -3) = 0 → (t + 4)0 = 0

Try these problem:

- (r + 5)(r - 2) = 0 answer

- (x + 1/3)(x - 1/5) = 0
answer

- (4t
^{2} + 4t - 15) = 0 factoring the left hand side and proceed as you did with the above problems.
answer

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