Explain in your own words how to reverse FOIL when factoring a polynomial of the form ax2 + bx + c when a = 1.

Question

Please help : (

Answer 1

x^2 +bx+c
1st check to see if b^2 = 4c. If it does then:
x^2+bx+c=(x+b/2)^2
If b^2 < 4c then there are no real factors.
If b^2 >4c, then factors are (x+ (b +sqrt(b^2-4c)/2)) and
(x+ (b -sqrt(b^2-4c)/2))

Answer 2

Find two numbers that multiply to give you c and add to give you b. If you call those numbers s and t, then the factorization will be (x-s)(x-t), and it should be equal to the expression you started with.

Example: If you are given x^2 + 5x + 6, then you are looking for numbers that multply to give you 6 and add up to 5. A little thought should reveal that these numbers are 2 and 3. Then the factorization will be (x+2)(x+3).

Answer 3

First it is meant to be on your individual words. 2nd: while the sqaured volume's coefficient is a million, purely locate the climate that muliply to offer the c term and upload at the same time to create the bx term. 0.33: We call this the "grasp Product technique" or the "AC technique" in college.

Answer 4

x^2+bx+c
= (x+x1)(x+x2)
= x^2+ (x1+x2)x+x1x2
Compare coefficients,
x1+x2 = b
x1x2 = c

Method 1: Factor x^2+bx+c is to factor c into x1 and x2 such that x1+x2 = b.

Method 2: Factor x^2+bx+c is to break b into x1+x2 such that x1x2 = c.
-----
Example
x^2 + 5x + 6

Method 1:6 = 2*3 and 2+3 = 5 =>(x+2)(x+4)

Method 2:5 = 2+3, 2*3 = 6 =>(x+2)(x+4)

Answer 5

Hi,

Given x² +8x - 20 Start both parentheses with x.
(x.......)(x..........) First sign goes in first parentheses.
(x..+....)(x..........) Product of signs goes in 2nd parentheses.
(x..+....)(x..-...) <== neg is because pos x neg = negative

Now list factors of your third number. Ignore the signs - you've already done them. So, out to the side list pairs of factors of 20.

20
------
1, 20
2, 10
4,5

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(x..+....)(x..-...) Your signs are different, so you want to subtract factors to get 8. Those factors are 2 and 10. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(x.+.10)(x.-.2) <-- Those are your factors.


Given x² -9x + 20 Start both parentheses with x.
(x.......)(x..........) First sign goes in first parentheses.
(x..-....)(x..........) Product of signs goes in 2nd parentheses.
(x..-....)(x..-...) <== neg is because neg x pos = negative

Now list factors of your third number. Ignore the signs - you've already done them. So, out to the side list pairs of factors of 20.

20
------
1, 20
2, 10
4,5

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(x..-....)(x..-...) Your signs are the same, so you want to add factors to get 9. Those factors are 4 and 5. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(x.-.5)(x.-.4) <-- Those are your factors.

I hope that helps!! :-)
(something similar works when "a" is NOT 1 too)