Solving this equation.?

Question

Can someone please explain as simply as possible how to factorise the following: 2x^2-35x+98.

lol and i really mean simply!!

Answer 1

I'll try to keep this as simple as possible.

Step one:
Multiply the 2 by the 98 = 196

Step two:
You need to find two numbers that multiply to 196 and add to -35
(Since you need to multiply to a positive and add to a negative, the only way to do this is to have two negative numbers)
(-7)(-28) = 196
-7 + -28 = -35

Step three:
Replace the middle term (-35x) with the two numbers you found above.
2x^2-28x-7x+98

Step four:
Factor by grouping.
2x^2-28x = 2x(x-14)
-7x+98 = -7(x-14)

Step five:
Factor out the common terms in the parenthesis
2x(x-14)-7(x-14) from factoring above
(x-14)(2x-7)

Yay for the completely factored form. Hope this helps. :)

Answer 2

Well the first 2x^2 shows that the one set of numbers has to have 2x. So then it's just seeing which numbers fit.
7 x 14 = 98 (Did this by guessing)
14 x 2 = 28
28 + 7= 35
Since it's -35 X then you are subtracting, so
(2x-7)(x-14) = 2x^2 -28x-7x+98 or 2x^2 -35x + 98

Answer 3

2x^2 - 35x + 98

(2x - 7) (x - 14)

2x - 7 = 0 x - 14 = 0

x = 7/2 and x = 14

1. First you have to factor out the polynomial
2. then just solve for x

Or you can just use the quadratic equation
Using A= 2 B= -35 C= 98

Answer 4

There's not a common factor, so that won't help. There's no easy way except a guess and check method. You try to find combinations of numbers that multiply to 2, and other numbers that multiply to 98. Then check your answer with FOIL to see if the -35 comes up.

Let's try.

(2x - 49)(x - 2) When you do FOIL, you'll get the 2 and the 98, but the middle number is -53.

(2x - 7)(x - 14) This time FOIL gives you the right middle number.

I wish there were an easier way. Unfortunately, on problems like this, just make a list of factors of 98 to try until you get the right combination. One hint to save time: If the original problem doesn't have a common factor, don't put numbers that have common factors together in your binomials.

Answer 5

2x^2 -35x +98
In such case you multiply the coefficient of x^2 by the last term,which gives you 196.
Now if this a positive number you try to find two numbers whose product is 196 and sum is 35. If the product were -196 we would find two numbers whose product was 196 and difference was 35. In this case we get two numbers as 28 and 7. ( which was very easy. I tried dividing by 4,5,6 7 etc)
Thus you write
the term as
2x^2 -28x - 7x + 98
From the first two terms you get 2x as common and from the third and fourth term you get 7 common.
Thus we have
2x( x-14) - 7(x-14)
or (x-14)*(2x-7)
The factors are (x-14) and (2x-7)

Answer 6

2x^2-35x+98
=2x^2-28x-7x+98
=2x[x-14]-7[x-14]
=[2x-7][x-14]
note:
2*98
=2*49*2
=2*7*7*2
=28*7
you have to factorise and
select the factors to suit the
coefficient of the middle term

Answer 7

hi,
1.Try finding the factors of 2*98 i.e.,28 and 7
2.now convert middle term i.e.,35x as -28x and -7x
3.now write 2x^2-28x-7x+98
4.Now group first two term and last two terms
5.2x(x-14)-7(x-14)
6.take (x-14) common
7.(x-14)(2x-7)
8..OVER

Answer 8

the answer is nineteen! centred how-to below: to make this much less complicated, team the x's which includes, of direction, their +/- signs and indications: 3x - 2x + 17 + 2 now that's an equation, and in case you spot no equivalent sign (=), then you definitely ought to anticipate that if there grew to become into, the whole equation ought to be equivalent to 0: 3x - 2x + 17 + 2 = 0 now simplify-- use elementary subtraction whilst coping with the variables (ignoring the x's, yet remembering to place them interior the result) this implies which you are able to respond to "3-2": 1x + 19 = 0 i've got been given the nineteen by way of including 17 and a pair of. you presently have a "1x", yet you are able to do away with the "a million", via fact writing down merely "x" extremely skill "1x" x + 19 = 0 now to sparkling up it, the variable ought to be on one area, and the known fee on the different area. undergo in ideas that in case you're taking a quantity or a variable around the equivalent sign, you may desire to continually substitute it extremely is +/- sign! : x = -19 or 19 = -x now you have the answer! x is comparable to "adverse 19" or "-19" or you are able to study it as "adverse x is comparable to 19", that's a similar concern. wish this grew to become into adequate component.

Answer 9

Use the quadratic equation. It will give you two answers. The factors will be (x+or-one)(x+or-the other)