when solving x squared - 5x + 6= 0 by factoring, what should the signs be in the parentheses.Justify ur answer

Question

help please. confused

thx

Answer 1

Factor: x^2 - 5x + 6 = 0

First: multiply the 1st & 3rd coefficient to get "6." Find two numbers that give you "6" when multiplied & "-5" (2nd/middle coefficient) when added/subtracted. The numbers are: (-3 & -2).

Sec: rewrite the expression with the new middle coefficients...

x^2 - 3x - 2x + 6 = 0

Third: factor - when you have 4 terms, group "like" terms...

(x^2 - 3x) - (2x + 6) = 0
x(x - 3) - 2(x - 3) = 0
(x - 3)(x - 2) = 0

Fourth: solve the x-variables > set both parenthesis to "0"...

a. x - 3 =0
x - 3 + 3 = 0 + 3
x = 3

b. x - 2 = 0
x - 2 + 2 = 0 + 2
x = 2

Solution: 2 and 3

P.S. When you have an equation set to "0" > you have to find the values for the x-variables after you factor the expression.

Answer 2

First, as I'm sure you know, the answer to that particular problem is x = 2, x = 3. That can be found either using the quadratic formula or by asking yourself:

what two numbers have a product of 6 (meaning x * y = 6), but a difference or sum of -5?

We quickly see that 3 * 2 = 6 and that 3+2=5. Now, the sign used in the orginal polynomial are your guide. When you F.O.I.L to check your answer, you must come up with the same equation you started with.

Example:

Let's say we picked 3 and 2 but orginally guessed the wrong signs:

(x+3)(x-2)

then we F.O.I.L.

multiplying the two first terms (x+ )(x- ) gives us x^2

multiplying the two outer terms (x+ )( -2) gives us -2x

multiplying the two inner terms ( +3)(x- ) gives us 3x

finally, multiplying the two last terms ( +3)( -2) gives us -6

putting them together: x^2 - 2x + 3x - 6 which is the same as x^2 + x - 6. That is NOT our orignal equation.

but checking (x-2)(x-3) DOES give the orignal equation, since there are only four possibilities (both minus, both plus, first one plus second one minus, and first one minus and second one plus) it doesn't take that long to check each one.

I hope this helps!!

Answer 3

(x-3)(X-2)

the signs should be negative
When the equation is Ax^2+Bx+C=0 these are the rules for signs of the factors
If C>0, signs are the same: If B>0 both signs are positive. If B<0 both signs are negative
If C<0, signs are different. If B>0 then the greater # is positve, else the greater # is negative

Answer 4

x^2-5x+6=0

STEP ONE(x )(x )
STEP TWO(x- )(x- )
STEP THREE (x-3(x-2)


this is how i was taught to do it:

Step one: put the squared term in both parentheses.




Step two: as you can see its x^2-5x+6. THE PLUS(2nd sign) tells you that the terms in the parantheses will both be the same. THE MINUS(first sign) will tell you that they will both be minuses.




STEP THREE:Pick two numbers that when you multiply, they will equal 6 (x^2-5x+[6]) and when you add those two numbers, they equal negative five. (x^2[-5]+6).

Answer 5

(x-3) (x-2). The only way to get a plus sign for the last number in the equation is by multiplying two negatives together. Then, to check yourself just use FOIL, and you see that it comes out right.

Answer 6

(x + a)(x + b) = x^2 + (a + b)x + ab

x^2 - 5x + 6
[a+b = -5 and ab = 6,,,,,,think........(-3)+(-2)= -5 and -3x-2 = 6]
= x^2 - 3x - 2x + 6
= x(x - 3) - 2(x - 3)
= (x - 3)(x -2)

Answer 7

(x - 3)(x - 2)

The signs have to both be negative in order to have -5x.
Also, the signs have to both be negative in order to have +6.

Answer 8

(x-3)(x-2)

Answer 9

(x-3)(x-2)

Answer 10

(x-3)(x-2) because when you mulitiply these you get x^2-5x+6