complete the equation.
-6x^2+15x-6=-(2x-1)(x+__)
a. 2
b. -2
c. -3
d. 6
I'm really lost and i dont understand how to solve this problem. any help would be appreciated.
-6x^2+15x-6
= -(x^2 - 15x + 6)
= -(2x-1)(x + __ )
The reason you don't understand is that their second line is incorrect.
Perhaps you typed it wrong
This is what I would do:
-6x^2+15x-6
= -3(2x^2 - 5x + 2)
= -3(2x - 1)(x - 2)
To complete the equation -6x^2+15x-6=-(2x-1)(x+__), you need to find the missing factor in the right-hand side.
First, let's expand -(2x-1)(x+__). To do this, we can use the distributive property:
-(2x-1)(x+__) = -(2x)(x) -(2x)(__) + (-1)(x) + (-1)(__)
This simplifies to:
-2x^2 - 2x(__) -x - __
Now, let's compare this with the left-hand side -6x^2+15x-6:
-2x^2 - 2x(__) -x - __ = -6x^2 + 15x - 6
By comparing the corresponding terms on both sides, we can equate them:
-2x^2 = -6x^2 (Comparing the x^2 terms)
15x = -2x(__) (Comparing the x terms)
-6 = -(__) (Comparing the constant terms)
Let's solve each of these equations one by one:
Equating the x^2 terms:
-2x^2 = -6x^2
Divide both sides by -2 to isolate x^2:
x^2 = -6 / -2
x^2 = 3
Taking the square root of both sides (remember to consider both the positive and negative square roots):
x = ±√3
Now let's equate the x terms:
15x = -2x(__)
Distribute -2x:
15x = -2x^2(__) -2x
Since we already found x^2 = 3, we can substitute it in:
15x = -2(3)(__) -2x
15x = -6(__) -2x
Comparing the x terms:
15x = -2x
17x = 0
Divide both sides by 17:
x = 0
Now let's equate the constant terms:
-6 = -(__)
Solve for __ by multiplying both sides by -1:
6 = __
So, the missing factor in -(2x-1)(x+__) is __ = 6.
Therefore, the correct answer is d. 6.
Hope this helps!
To complete the equation, we need to find the missing factor in the expression -(2x-1)(x+__).
To determine the missing factor, we can use the technique called "FOIL," which stands for First, Outer, Inner, and Last.
First, we multiply the first terms of each binomial:
-(2x) * (x) = -2x^2
Next, we multiply the outer terms:
-(2x) * (+__) = -2x * (+__) = -2x(__)
Then, we multiply the inner terms:
(+1) * (x) = 1x = x
Lastly, we multiply the last terms of each binomial:
(+1) * (+__) = +1 * (+__) = +__
Combining all these results, we get:
-2x^2 + x -2x(__) + (+__)
Now, we simplify this expression by combining like terms:
-2x^2 + x - 2x(__) + (+__) = -6x^2 + 15x - 6
Comparing the above equation with the given equation:
-6x^2 + 15x - 6 = -(2x-1)(x+__)
We can notice that the terms -2x(__) + (+__) in the simplified expression correspond to the terms 15x in the given equation. So, the missing factor must be the factor that gives us 15x when multiplied by -2x.
The only option that satisfies this condition is option c. -3.
Therefore, the correct answer is: c. -3