We are factoring polynomials in math and I have a question..?
2008-06-19 6:07 pm
My equation is this: x-squared - 19x - 8466 I am not looking for an answer, but I was wondering how to figure out what 2 numbers will equal 8466, without a whole bunch of trial and error. I am not looking for 2(4233). I need bigger numbers to play with, and I am not sure how to get it.
回答 (6)
2008-06-19 6:18 pm
✔ 最佳答案
x^2 - 19x - 8466= x^2 + 83x - 102x - 8466
= x(x + 83) - 102(x + 83)
= (x + 83)(x - 102)
2008-06-20 1:11 am
you should use quadratic formula
2008-06-20 1:20 am
To factor a binomial like this, use the quadratic formula.
Let x^2 - 19x - 8466 = 0. Using the quadratic formula:
x = (19 +- sqrt((19 * 19) - (4 * 1 * -8466))) / (2 * 1)
x = (19 +- 185) / 2
x = 102 or -83
That means that plugging in x = 102 or x = -83 makes the whole polynomial zero. That means the way to factor it is:
(x - 102)(x + 83)
That way, x = 102 makes it zero, and x = -83 makes it zero. To check your work, 102 * 83 = 8466.
Let x^2 - 19x - 8466 = 0. Using the quadratic formula:
x = (19 +- sqrt((19 * 19) - (4 * 1 * -8466))) / (2 * 1)
x = (19 +- 185) / 2
x = 102 or -83
That means that plugging in x = 102 or x = -83 makes the whole polynomial zero. That means the way to factor it is:
(x - 102)(x + 83)
That way, x = 102 makes it zero, and x = -83 makes it zero. To check your work, 102 * 83 = 8466.
2008-06-20 1:20 am
Here's how to do it by using a quadratic formula.
This equation is of form ax^2+bx+c
a = 1 b = -19 c = -8466
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[19 +/-sqrt(-19^2-4(1)(-8466)]/(2)(1)
discriminant is b^2-4ac =34225
x=[19 +â(34225)] / (2)(1)
x=[19 -â(34225)] / (2)(1)
x=[19+185] / 2
x=[19-185] / 2
The roots are 102 and -83
If you're factoring , (x-102)(x+83) = x^2-19x-8466
-102+83 = -19
-102 x 83 = -8466
This equation is of form ax^2+bx+c
a = 1 b = -19 c = -8466
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[19 +/-sqrt(-19^2-4(1)(-8466)]/(2)(1)
discriminant is b^2-4ac =34225
x=[19 +â(34225)] / (2)(1)
x=[19 -â(34225)] / (2)(1)
x=[19+185] / 2
x=[19-185] / 2
The roots are 102 and -83
If you're factoring , (x-102)(x+83) = x^2-19x-8466
-102+83 = -19
-102 x 83 = -8466
2008-06-20 1:20 am
x^2 - 19x - 8466
You want factors of -8466 that add to -19
The factors will have opposite signs
I usually develop the prime factors and examine the results
8466
. . / \
. .2 4233
. . . . . / \
. . . . .3 1411
. . . . . . . . / \
. . . . . . . .17 83
2*3*17 = 102
102 - 83 = 19
(x - 102)(x + 83)
You want factors of -8466 that add to -19
The factors will have opposite signs
I usually develop the prime factors and examine the results
8466
. . / \
. .2 4233
. . . . . / \
. . . . .3 1411
. . . . . . . . / \
. . . . . . . .17 83
2*3*17 = 102
102 - 83 = 19
(x - 102)(x + 83)
2008-06-20 1:18 am
use this equation
x=[-b+or-sqrt(b^2-4ac)] / 2a
a=1 b=-19 c=-8466
x=[-b+or-sqrt(b^2-4ac)] / 2a
a=1 b=-19 c=-8466
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