the question says solve by factoring, and the equation is b^2-b-20=0, with b being a variable and the ^2 meaning squared. i already factored the equation (i think) fully or half way, with my answer being -20+b(b-1)=0. what do I do from here, also did i factor correctly?
-
When factoring quadratic equations, (which is what you have here), you usually want to put it in this form,
(b + x)(b + y).
For your problem, you need to find an x and y such that
x + y = -1 (coefficient in front of b)
x * y = -20. (number with no variable)
x = -5 and y = 4 will work. So you will have the factored form,
b^2 - b - 20 = (b - 5)(b + 4).
Now since the original equation equals zero you have,
(b - 5)(b + 4) = 0.
When you multiply two numbers together and the answer is zero then at least one of the two numbers must be zero. Therefore we can say
b - 5 = 0 or b + 4 = 0.
Then solve for b id both cases and you get
b = 5 or -4.
(b + x)(b + y).
For your problem, you need to find an x and y such that
x + y = -1 (coefficient in front of b)
x * y = -20. (number with no variable)
x = -5 and y = 4 will work. So you will have the factored form,
b^2 - b - 20 = (b - 5)(b + 4).
Now since the original equation equals zero you have,
(b - 5)(b + 4) = 0.
When you multiply two numbers together and the answer is zero then at least one of the two numbers must be zero. Therefore we can say
b - 5 = 0 or b + 4 = 0.
Then solve for b id both cases and you get
b = 5 or -4.
-
You have to factor it into product of binomials.
Factors of -20 that add to -1 are -5 and 4 so,
b^2 - b - 20 = 0 iff
(b - 5)(b + 4) = 0 [zero product property] iff
b - 5 = 0 or b + 4 = 0 iff
b = 5 or b = -4
Factors of -20 that add to -1 are -5 and 4 so,
b^2 - b - 20 = 0 iff
(b - 5)(b + 4) = 0 [zero product property] iff
b - 5 = 0 or b + 4 = 0 iff
b = 5 or b = -4