Question

given the function f(x)=x^3+7x^2+10x-6, give the seven steps you would take to determine the zeros of this function. you do not need to find the answer, just list the steps

Answer 1

Given the function:

`f(x)=x^3+7x^2+10x-6`

Let's list the steps to find the zeros of the function.

To find the zeros of the function, apply the following steps:

• Step 1:

Set the function, f(x) = 0:

`x^3+7x^2+10x-6=0`

• Step 2:

Factor the expression on the left using the rational roots test

`.`

• Step 3:

Divide the polynomial (x³+7x²+10x-6) by (x+3).

After the division, we have:

`(x+3)(x^2+4x-2)`

• Step 4:

Write the given polynomial as a set of factors

`(x+3)(x^2+4x-2)=0`

Step 5:

Set each individual factor to zero

`\begin{gathered} (x+3)=0 \\ \\ x^2+4x-2=0 \end{gathered}`

Step 6:

Solve for x in the first factor: (x + 3) = 0

Step 7:

Solve for x in the second factor: (x² + 4x - 2) = 0

• ANSWER:

• Step 1: Set the function f(x) = 0

,

• Step 2: Factor the expression on the left using the rational roots test

,

• Step 3: Divide the polynomial by the factor derived in step 2.

,

• Step 4: Write the factor gotten in step 2 and the quotient in step 3 as a set of factors.

,

• Step 5: Set each individual factor to zero.

,

• Step 6: Solve for x in the first factor

,

• Step 7: Solve for x in the second factor.