Question

factor
the other
of (3x²-x-8) is (x-2) what is
the other factor ?​

Answer 1

Answer:

The solution is: (3x+4)(x−2)

Step-by-step explanation:

The polynomial is of the type ax2+bx+c.

There are two ways to factor.

The first one:

we have to find two numbers whose sum is −2 (that is c) and whose product is −24 (that is a⋅c).

−24=−1⋅24

−24=−24⋅1

−24=−2⋅12

−24=−12⋅2

−24=−3⋅8

−24=−8⋅3

−24=−4⋅6

−24=−6⋅4

The couple of numbers whose sum is −2 is −6,4.

Now we have to "split" the monomial −2x in two parts: −2x=−6x+4x.

So our polynomial becomes:

3x2−6x+4x−8=3x(x−2)+4(x−2)=(x−2)(3x+4).

If it is known the way to solve an equation of 2° degree, here there is the second way to factor it:

We can imagine that this polynomial "becomes" an equation:

3x2−2x−8=0, we can calculate the quantity

Δ=b2−4ac=4+ 96 = 100

and than we have to use this formula:

x1,2=−b±√Δ2a=2±106⇒x1=−43;x2=2.

And now we have to use the formula:

ax2+bx+c=a(x−x1)(x−x2).

So:

3x2−2x−8=3(x+43)(x−2)=(3x+4)(x−2)