Someone thats amazing at math helppp

F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

Given function:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find a, compare the coefficients of x³:

$\implies a=3$

To find b, substitute the found value of a into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find c, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

Zero Product Property

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

11 months ago

How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution?

elena-s [515]

Suppose you add x liters of pure water to the 10 L of 25% acid solution. The new solution's volume is x + 10 L. Each L of pure water contributes no acid, while the starting solution contains 2.5 L of acid. So in the new solution, you end up with a concentration of (2.5 L)/(x + 10 L), and you want this concentration to be 10%. So we have

$\dfrac{2.5}{x+10}=0.1\implies25=x+10\implies x=15$

and so you would need to add 15 L of pure water to get the desired concentration of acid.

8 0

3 years ago

Which statement is true?

Nina [5.8K]

Answer: I think the answer is 1 in my opinion but not sure

4 0

2 years ago

Find the value of x.

Zolol [24]

Answer:

34

Step-by-step explanation:

8 0

2 years ago

Simplify the following :

dlinn [17]

Answer:

1. 95/96

2. 27/7

3. -8/245

Explanation:

1. First add together the two fractions 3/4 + 5/6. Find the least common denominator. In this case we can use 12. The 3/4 changes to 9/12 and the 5/6 changes to 10/12. adding these together we get 19/12. Next we divide 8/5 by 19/12. We use the keep, change, flip method to change the divide to multiply. keep the first fraction, change divide into multiply, and then take the reciprocal of the second fraction. You will now do 5/8 x 19/12. We now get 95/96 (I made a mistake in the answers the first time because I was rushing)

2. Divide the 3/2 and the 8/9 first. I will use the KCF (keep, change, flip) method to divide. 3/2 x 9/8 = 27/16 Now we divide the 7/16. After using KCF we can simplify and cross cancel (simplfy after changing the fraction and signs) 27/16 x 16/7 --> 27/1 x 1/7 The answer will come out to be 27/7

3. since there are no parentheses divide first. Use KCF and after you get the answer multiply (it is the same using negative numbers just watch out for signs)

7 0

2 years ago