Factor Quadratic

Question

-25x^2-45x-18

and 

60x^+95x+25

 

I am not sure how to figure this question out.

Answer 1

-25x²-45x-18

25*18=5*5*2*3*3 and (5*3)+(5*2*3)=15+30=45, the coefficient of the middle term (without the sign)

(-5x-6)(5x+3) or (-1)(5x+6)(5x+3) to show that (5x+3) could have been multiplied by (-1) to get (-5x-3)

 

60x²+95x+25

factor out a 5

12x²+19x+5

12*5=2*2*3*5 and (3*5)+(2*2)=19

(4x+5)(3x+1)

Answer 2

If I asked you to break the number 6 into its lowest factors, you might say 2 *3 which is the same as 6.

 

You do the same for quadratic expressions - break them into expressions that when multiplied together, they re-create the expression.

 

Note these ARE expressions, since they are NOT equations. (An equation would have an  = sign in it).

 

So you are 'breaking these down' meaning for a quadractic, NO x has a power greater than 1. 

 

Meaning, with a quadratic expression like x^2 + 3x + 2 , I would expect to see (x + 2) * (x + 1) .

 

Some rules of thumb: to have a negative number, like in the first example, (-25x^ -45x - 18) one of the x will have to be a negative, and the other a positive.

The same is true for the constant.

 

Since it is -25, there are only 3 factors of 25: 1,5 , 25. Doubt 25 will work, so I'll start with (-5x - ?) * (5x + ?).  That works for the -25x^2, so now I can figure out the last half. -18 means 2 * 9, or 3 * 6, or 1*18. if it were 2 and 9, (one would have to be negative) I can't multiply those times -5x and +5x to get a sum of 45x. BUT let's try 3 and 6. 3*5 x = 15, 6*5x = 30 Ah - those COULD add up to 45 if I get the signs right!

 

So we see: (-5x -3) * (5x +6) and check it out to proof it:

 -3 * + 6 = -18. That checks. -3 * 5x = -15x, +6 *-5x = -30x. And -15x -30x = -45.

 

So, factored, the first answer is (-25x^2  - 45x - 18) factored is:  (-5x - 3) (5x+6)

 

Does that give you a hint on solving the second one?