Quadratic facorisation?

Question

Factorise:

2x^2 - 5x + 3

Please go step by step and explain well and simply.

Answer 1

Factors of 2x² - 5x + 3:
(x -3)(2x + 1)

Coefficients of x must be 1 and 2, since when multiplied together they must produce a 2x² term

Constant values must be ±(1 and 3), since when multiplied together they must produce a +3 term (either -1 times -3, or positive 1 times 3 would be correct).

Since the coefficient of x is -5, the terms must be paired so that the sum of the outer product and the inner product is -5. Since this term is negative, the constant values (1 and 3) would then be negative to produce the negative coefficient of this middle term.

[If the factors are written as (Ax + B)(Cx + D), the outer product is ADx, and the inner product is BCx. In this case, ADx + BCx = -5x]

Answer 2

2x² - 5x + 3

Because I’m an optimist, and partially because the factor in the middle term is an integer, I’m hoping that the factors will also contain integers. Note: this is not always the case.

We know that the factors have to look like
(2x ± something)(x ± something)
That’s the only way we can get 2x²
And we also know that the factors have to look like
(something ± 1)(something ± 3)

Let’s try something I know will not work.
(2x +1)(x -3)
Multiplying it out we bet 2x² -+ x – 6x – 3 = 2x² - 5x – 3… it’s close, but incorrect. There’s a -3 where there should be a +3
The sign in the middle of the terms have to be the same, or we’re going to get a negative 3.

Let’s call the products of the 2x and x, and of the +1 and -3 the "end products."
And let’s call the 2x and -3, and of the 1 and x as the “cross products.”

The sum of the “cross products” has to be -5x. Well the only two negative numbers that add up to -5 are -2 and -3. There is already a 2x. So somehow we need to make it negative and to come up with a -3x. How do you make 2x negative? Multiply by a -1. That forces one of the terms to be (x – 1). To get an end product with the x of that term to be -3x, the other term has to be (2x – 3).

(2x - 3)(x – 1) gives 2x² - 3x – 2x + 3 = 2x² - 5x + 3

Answer 3

you need to look at 3 and find the factors of 3 that can give you the answer of 5. since 3 and 1 is 4 then you have to multiply 2 by 3.

so now, your equation will be: (x^2 - 5x + 6)

now, you can factor them. 3 and 2 are factors of 6 that you can add together to get 5. so your factors will be (x -3) (x -2).

you multiplied 2 by 3 earlier but you have to put them back again, so now your factors will look like this: (2x - 3) (2x - 2).

now, reduce them by dividing by 2. since, you can't divide 3 by 2, so you just divide the other factor.

now, your two factors will be: (2x - 3) (x - 1)

Answer 4

The factorization will be of the form (ax + b)(cx + d). ac must equal the coefficient of x^2, in this case 2, and bd must equal the constant term, in this case 3, while ad + bc is the coefficient of x, in this case -5. This isn't too hard, because 2 has only two factors, 2 and 1, and 3 also has only two factors, 3 and 1. Since the coefficient of x is negative, we know that it will actually be -3 and -1 in this case. So it must be (2x - 1)(x -3) or (2x - 3)(x - 1). Multiplying them out shows that it is (2x - 3)(x - 1).

Answer 5

just put it like this :

5 = 2+3

2x^2-5x+3 = 2x^2-2x-3x+3 = 2x(x-1) -3 (x-1) = (x-1)*(2x-3)

Answer 6

first put the equation in the form ax^2 + bx + c =0
then apply this formula

x = (-b +/- Sqrt(b^2-4ac) )/ 2a


that's x1 = (-b +Sqrt(b^2-4ac) )/ 2a

and x2 = (-b - Sqrt(b^2-4ac) )/ 2a

where sqrt(x) is the square root of x

Answer 7

_since:factorrisable quadratic function answer will be 2 brackets (....)(.....)
_since:2x^2= 2X x X
_therefore:(2X......)(X......)
_since:+3
_therefore: 2nd term is either [-3x-1] or [3x1]
_since:-5x
_therefore: 2nd term is [-3x-1]
_since: -5X
_therfore: [1st term in 1st bracket x 2nd term in second bracket]+[2nd tern in 1st bracket x 1st term in 2nd bracket]=-5X
_therefore: (2X-3)(X-1)