Solving Polynomial Equations in Factored FormBy L.D.

Problem 1

Solve (x – 5)(x + 4) = 0

Problem 1

Solve (x – 5)(x + 4) = 0

Immediate Tips

-Solve means find x value

-Don’t EVER use F.O.I.L. for these kinds of problems.

-There is more than one answer to “x”, in this problem there are two in fact.

Problem 1Solve (x – 5)(x + 4) = 0

So to solve for x in this case we need to not use the FOIL method. First we need to split the problem in half to get two separate problems that equal zero. Our first problem is x – 5 = 0 and our second is x + 4 = 0. Now we need to solve for x on both of them. The x on the former (x – 5 = 0 ) is equal to 5. The x on the latter (x + 4 = 0) is equal to negative 4.

(x – 5)(x + 4) = 0

x = 5 x = –4

Those are our two answers and we are done with problem 1.

Example Problems

1. (x + 6)(x -3) = 0 2. (2x – 3)(5x + 10) = 0

Example Problems

1. (x + 6)(x -3) = 0 2. (2x – 3)(5x + 10) = 0

x = -6 x = 3 x = 1.5 x = -2

Problem 2

1. 3x (x + 2) = 0

Problem 2

1. 3x (x + 2) = 0

Besides not being able to use FOIL, we aren’t able to use the distributive property either so we are going to treat 3x like a separate problem.

3x = 0 x + 2= 0

x = 0 x = -2

Those are our answers.

Problem 3

Factor out a GCF using 16x + 40y

Problem 3

Factor out a GCF using 16x + 40y

Basically what we are doing is reverse distributive. We are trying to make this problem look something like problem two in a way. To achieve this we first need the GCF of the two numbers. It happens to be 8. Divide 16x + 40y by 8. The answer is 2x + 5y. Put that in brackets. (2x + 5y), now plop the 8 next to it, 8(2x + 5y). This is our answer. Now, to check your work distribute the 8 to get the problem we started with, 16x + 40y.

Example Problems: Factor out a GCF

1. 6x2 – 30y2 2. -3t6 + 8t4

Example Problems: Factor out a GCF

1. 6x2 – 30y2 2. -3t6 + 8t4

6 (x2 – 5y2) t4(-3t2 + 8)

Problem 4

Solve the equation and factor out the GCF in 5x2 -15x =0

Problem 4

Solve the equation and factor out the GCF in 5x2 -15x =0

So first we reformat the problem to get 5x (x – 3) = 0, then we solve for the xs to get x = 0 (5x) and x = 3 (x – 3).

Problem 5

Solve the equation and factor out the GCF in 6x2 = 15x

Problem 5

Solve the equation and factor out the GCF in 6x2 = 15x

First we need to try to get a zero on one side, so move the 15x via subtracting it from both sides, our new equation should look like 6x2 - 15x = 0. Now reformat it, 3x (2x – 5) = 0, now solve for the 0s, x = 0 (3x) and x = -2.5 ((2x – 5)).

Problem 6

Find the zeroes in f(x) = 3x2 – 2x

Problem 6

Find the zeroes in f(x) = 3x2 – 2x

Now, we know f(x) is just a fancy way to say y, so our problem can also be seen as y = 3x2 – 2x. To solve this we set our y as a 0 and treat it like we have the problems before it.

3x2 – 2x = 0

x (3x – 2) = 0

x = 0 x= 2/3 or 0.66 __

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