3 algebra problems please read!?

Question

x^2-3x-40

x^2-9x+14

5x^2+16x+3

plz show step-by-step and explain so i can understand!

thanks so much!

Answer 1

1.(x-8) (x+5)

2.(x-7) (x-2)

3.(x+3) (5x+1)

                            (Example based on #1)

Step 1: Factorize the first and last to get a middle number.

so, x^2= x & x ; 40( 1,40) (2,20) (4,10) (5,8) { since 8-5 = 3 we choose that.

Put both variables & numbers in parantheses. (cross-multiplying form)...Well, you do the FOIL thing..first, outer inner, and last...to check if you get the same as b4. BTW, you can do that to determine what kind of operation to use...either + or -....(That's the best I could do....

Answer 2

x^2-3x-40, this translates into (x-8)(x+5).  The rule is first, outer, inner, last.  So, first: x times x = x^2, outer: x times 5 = 5x, inner: x times -8 = -8x, and last -8 times 5 = -40.  So you have an x^2, a 5x and a -8x, which is -3x, and you have a -40.  So your final answer is (x-8)(x+5).  The trick is to figure out how you get the -3x, well you do this by figuring out what multipliers make 40, in this case a negative 40.  So 5 and 8 work.  You see right off that 8 is three more that 5 (lightbulb should go off in your head).  But the 3 is negative, so the eight must be negative and the five must be positive to make the -3x.

Answer the the second equation: (x-2)(x-7).  In this equation you have to figure out what multipliers make up 14, well 7 times 2 does, but the 9x is negative, and the 14 is positive.  That is because if you multipy two negatives you get a positive.  Remember, when multiplying if the signs are different, the result is always negative.  If the signs are the same, the result is always positive.  

Answer to the third equation:  (5x+1)(x+3).  Remember the rule.  First: 5x times x = 5x^2, Outer:  5x times 3 = 15x, Inner: 1 times x = 1x, Last:  1 times 3 = 3.  So you have a 5x^2, you have 15x plust 1x = 16X, and you have a 1 times 3 = 3, so the result is 5x^2 + 16x + 3.

Good luck.