HOW can you find the equivalent expression in factored form of x(squared)+7x+12?

Question

HOW can you find the equivalent expression in factored form of x(squared)+7x+12?

Answer 1

a million. x^2 + 5x + 4 (x + 4)(x + a million) 2. x^2 + 6x + 8 (x + 4)(x + 2) 3. x^2 -7x + 10 (x - 5)(x -2) 4. x^2 + 7x x(x + 7) x = 0 x = -7 5. x^2 +5x - 6 (x + 6)(x - a million) 6. 2x^2 -5x - 12 (2x + 3)( x - 4) 7. x^2 -7x -8 (x + 8)(x -a million) 8, x^2 - 5x x(x - 5) x = 0 x = 5

Answer 2

You can explain like this.

Let x(squared)+7x+12 be equal to (x + a) (x + b)

x(squared)+7x+12 =(x + a) (x + b)

..............................= x (x + b) + a (x + b)

..............................= x square + bx + ax + ab

x(squared)+7x+12.= x square + (a+b) x + ab.



Comparing the two equations we find



a + b =7 and ab = 12.



Therefore the problem is now to find a and b.

Find two numbers whose sum is 7 and product is 12.



By trial and error we find the numbers as 3 and 4 and substitute in the form.

Answer 3

Use F.O.I.L.: first times first (x times x) + outside (x times 4) + inside (x times 3) + last (3 times 4)

= x(squared) + 4x + 3x + 12

= x(squared) + 7x + 12

= (x+3)(x+4)

Answer 4

By trial and error, or using synthetic division.

Answer 5

your answer is wrong

The right one is

x(x+7)+12

Answer 6

check for a list of properties. it should list the one that relates to this, and is the correct mathematical explanation.

Answer 7

well for basic factoring, you find 2 numbers that add to the middle term (7 in this case) and multiply to the last term (12 in this case). it might take a while, but if it can be factored, it shouldnt be that hard.

in this case, the numbers are 3 and 4 (3+4=7, 3*4=12).

so then the factored form is just (x+3)(x+4). i really dont know how to explain it.



if you want more complicated forms (as in like having a number before the x^2 term or having an expression where its hard to find 2 numbers that add to the middle term and multiply to the last or somethin), then just let me know and ill try to help

Answer 8

x(squared)+7x+12



get the factors of +12 (last term) in which when you add them it will result to +7x (which is the middle term)



factors of are 12 = +12*+1 , -12*-1 , +4*+3 , -4*-3 , +6*+2 and -6*-2



choose +4 and +3 since when added it equals to +7

4+3=+7 therefore the factors are 4 and 3



(x+3)(x+4)

Answer 9

x^2 means x(square) for conveniance

x^2+7x+12=x^2+3x+4x+12=x(x+3)+4(x+3)=(x+3)(x+4)

you should try to factor the constant term (12 in this case)and those tow factors should add up to the coefficient of the x term, only then can you use this technique, hope i am clear.

Answer 10

EDIT: ** Baah. When I typed this answer I was first. Then at the end, I'm like the 3rd. Oh well..**



There are two ways. Which one is easier depends greatly on your thinking skills.



You can take the expression x2+7x+12 and assume it should break up in two factors:

(x+ ? )(x+ ?)

Then, search for two numbers that add up to the 7, but when multiplied equal 12.

It helps if you break down 12 into it's components, 12= 2*2*3. So, obviously, the answers could be:



2 * (2*3) = 2 * 6 (but 2+6 is not =7)

3 * (2*2) = 3 * 4, voila! 3+4 also = 7, so:



(x+3)(x+4).



The second way could be just solving the cuadratic formula for second degree equations:



b=(-b +/- SQRT(b2 - 4ac))/2a



Where ax2 + bx + c, so you'll have: a=1, b=7, c=12.



Replace, then solve twice: Once for the + value of the SQRT, another for the - value of the SQRT. You should get something like:



First run:

x= -3



Second run:

x= -4



x=-3 is the same thing as (x+3)=0

and

x=-4 is also (x+4)=0



Notice the two factors are precisely (x+3) and (x+4)?



Hope this helped..