How do you factor 7x2 - 9x - 10?

Answer 1

Factor 7x2 - 9x - 10 = 0.

7 * -10 = -70

70 = 2 * 35 = 2 * 5 * 7

Factors of 70: 1,2,5,7,10,14,35,70

1 x 70 = 70

2 x 35 = 70

5 x 14 = 70

7 x 10 = 70

The sum should be negative, so the larger number in the sum must be negative.

product of -70 (sum of -9) :

1 + (-70) = -69

2 + (-35) = -33

5 + (-14) = -9

7 + (-10) = -3

The sums match up, so now we have the factors.

(x+5)(x+(-14)) = 0

(x+5)(x-14) = 0

However, the x2 must have a 7 in front of it, so divide the 14 by 7.

(7x+5)(x-2) = 0

And, if you have extra time, you can foil it back out to make sure you did it correctly.

7x2 - 14x + 5x -10 = 0

7x2 - 9x - 10 = 0

This confirms that the factorization is correct.

Finally, if you want to solve for x, just set each term equal to zero.

7x+5 = 0 or x-2 = 0

7x = -5 or x = 2

x = -5/7 or 2