factoring trinomials? 3x ² – 5x + 2?

Question

the trinomial is 3x ²– 5x + 2
i keep getting the answer (2x+3)(x+1) but when i multiply it out to check i always get 2x ² +5x+3
help?

Answer 1

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

Answer 2

This looks like ax^2 + bx + c, with a= 3, b = -5, and c = 2.
Because when the a is positive, the c is also positive, you are looking for two factors of ac = 3(2) = 6 whose sum is 5. (If a and c had different signs, you would want the diffiernce to be 5.)
These would be 2 and 3. Rewrite the x term, -5x, as -2x + -3x, and factor by grouping.
So
3x^2 - 5x + 2 =
3x^2 - 2x - 3x + 2 =
x(3x - 2) - 1(3x - 2) =
(3x - 2)(x - 1)
or
3x^2 - 5x + 2 =
3x^2 - 3x - 2x + 2 =
3x(x - 1) - 2(x - 1) =
(x - 1)(3x - 2)
Since the order of the factors doesn't matter, this is the same answer.

Answer 3

Hello

There are several ways of factoring this. We can use the quadratic equation or we can guess in check.

We do know that two binomials multiply to equal our trinomial.

So we know the first terms mulitply to 3 -- so we have
(3x )(x ).

We also know that the two end terms multiply to positive 2.

So we have either
(3x-2)(x-1)
or
(3x-1)(x-2).

Multiply these out and we see our answer is (3x-2)(x-1) = 3x ² – 5x + 2.

Have a great day

Answer 4

(3x - 2) (x - 1)
Check
3x(x - 1) - 2 (x - 1)
= 3x² - 3x - 2x + 2
= 3x² - 5x + 2 (as required)

Answer 5

the factors are (x-1)(3x-2) not (2x+3)(x+1)

Answer 6

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

to check you answer:
(3x-2)(x -1)
=3x2 - 3x - 2x + 2
=3x2 -5x + 2

Hope I helped!

Answer 7

(ax+b)(cx+d)=acx^2+(ad+bc)x+bd.
So a and c must have a product of 3.
And b and d must have a product of 2.
And they also must satisfy ac+bd=-5, which means there are going to be negative numbers involved.

Answer 8

(3x-2 )(x-1)