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# Solving polynomial equations in factored form

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### Solving polynomial equations in factored form

1. 1. Solving PolynomialEquations in FactoredFormBy L.D.
2. 2. Problem 1Solve (x – 5)(x + 4) = 0
3. 3. Problem 1Solve (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.
4. 4. Problem 1Solve (x – 5)(x + 4) = 0So to solve for x in this case we need to not use the FOILmethod. First we need to split the problem in half to gettwo separate problems that equal zero. Our first problemis x – 5 = 0 and our second is x + 4 = 0. Now we need tosolve 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 tonegative 4.(x – 5)(x + 4) = 0x = 5 x = –4Those are our two answers and we are done withproblem 1.
5. 5. Example Problems1. (x + 6)(x -3) = 0 2. (2x – 3)(5x + 10) = 0
6. 6. Example Problems1. (x + 6)(x -3) = 0 2. (2x – 3)(5x + 10) = 0 x = -6 x = 3 x = 1.5 x = -2
7. 7. Problem 21. 3x (x + 2) = 0
8. 8. Problem 21. 3x (x + 2) = 0Besides not being able to use FOIL, we aren’t ableto use the distributive property either so we aregoing to treat 3x like a separate problem.3x = 0 x + 2= 0x=0 x = -2Those are our answers.
9. 9. Problem 3Factor out a GCF using 16x + 40y
10. 10. Problem 3Factor out a GCF using 16x + 40yBasically what we are doing is reverse distributive.We are trying to make this problem look somethinglike problem two in a way. To achieve this we firstneed the GCF of the two numbers. It happens to be8. Divide 16x + 40y by 8. The answer is 2x + 5y. Putthat in brackets. (2x + 5y), now plop the 8 next toit, 8(2x + 5y). This is our answer. Now, to check yourwork distribute the 8 to get the problem we startedwith, 16x + 40y.
11. 11. Example Problems: Factor out a GCF1. 6x2 – 30y2 2. -3t6 + 8t4
12. 12. Example Problems: Factor out a GCF1. 6x2 – 30y2 2. -3t6 + 8t4 6 (x2 – 5y2) t4(-3t2 + 8)
13. 13. Problem 4Solve the equation and factor out the GCF in 5x2 -15x =0
14. 14. Problem 4Solve the equation and factor out the GCF in 5x2 -15x =0So 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).
15. 15. Problem 5Solve the equation and factor out the GCF in 6x2 =15x
16. 16. Problem 5Solve the equation and factor out the GCF in 6x2 = 15xFirst we need to try to get a zero on one side, so movethe 15x via subtracting it from both sides, our newequation should look like 6x2 - 15x = 0. Now reformatit, 3x (2x – 5) = 0, now solve for the 0s, x = 0 (3x) andx = -2.5 ((2x – 5)).
17. 17. Problem 6Find the zeroes in f(x) = 3x2 – 2x
18. 18. Problem 6Find the zeroes in f(x) = 3x2 – 2xNow, we know f(x) is just a fancy way to say y, soour problem can also be seen as y = 3x2 – 2x. Tosolve this we set our y as a 0 and treat it like wehave the problems before it.3x2 – 2x = 0x (3x – 2) = 0 __x = 0 x= 2/3 or 0.66
19. 19. Thank You ForViewing This!