Find the zeros of the function
f(x)=x2+7x+12

-4,  -3

Step-by-step explanation:

So here we have a quadratic equation (meaning the highest exponent is 2).

To solve a question like this we either factor or use the quadratic formula.  

Here we can factor.

To factor we must find two numbers that can be multiplied to make the last term, and summed to make the middle term.  In this equation it means we are finding two numbers such that:

___ * ___ = 12

and

___ + ___ = 7

We start by thinking of the factors of 12.

Lets start by trying 6 and 2.

6 * 2 = 12

but

6 + 2 = 8

So 6 and 2 dont work because they do not sum to 7.

Now lets try 4 and 3

4 * 3 = 12

and

4 + 3 = 7

This pair of numbers works because they can be multiplied to make 12 and added to make 7.

So we can write

as

Knowing this we can can find the zeros of the function.  Remember that a zero of a function is whatever can be plugged into x to make 0.  Since we know zero times any number equals 0, this equation will be 0 when x + 4 equals 0 or x + 3 equals 0.  

So we can solve for those two equations

x + 4 = 0

x = -4

x + 3 = 0

x = -3

So the two zeros of this equation are -4 and -3

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1