Question

Hello, May I please get some assistance with this homework question? I posted an image below Q9

Answer 1

The given function is:

`f(x)=3x^4+2x^3-22x^2-14x+7`

Recall the rule of rational zero theorem

`(p)/(q)=\frac{a\text{ factor of the constant term}}{a\text{ factor of the leading cooficient}}`

From the given function

The contant term is 7

Factors of the constant term are

`\pm1,\pm7`

The leading coefficient is 3

Factors of the leading coefficient are

`\pm1,\pm3`

Using the the rational zero theorem

The posible zeros are

`(\pm1)/(\pm3),(\pm1)/(\pm1),(\pm7)/(\pm3),(\pm7)/(\pm1)`

This gives

`\pm(1)/(3),\pm1,\pm(7)/(3),\pm7`

Substitute the possible zeros into the equation to get the actual zeros

The roots are

`(1)/(3),-1`

Factorizing the given function gives

`f(x)=(x+1)(3x-1)(x^2-7)`