# ACT Math : Polynomials

## Example Questions

### Example Question #61 : Variables

Factor the following expression:

Explanation:

Remember that when you factor a trinomial in the form , you need to find factors of  that add up to .

First, write down all the possible factors of .

Then add them to see which one gives you the value of

Thus, the factored form of the expression is

### Example Question #4 : How To Factor A Trinomial

Factor the expression completely

Explanation:

First, find any common factors. In this case, there is a common factor:

Now, factor the trinomial.

To factor the trinomial, you will need to find factors of  that add up to .

List out the factors of , then add them.

Thus,

### Example Question #5 : How To Factor A Trinomial

Which expression is equivalent to the polynomial .

Explanation:

This question calls for us to factor the polynomial into two binomials. Since the first term is  and the last term is a number without a variable, we know that how answer will be of the form  where a and b are positive or negative numbers.

To find a and b we look at the second and third term. Since the second term is  we know . (The x comes from a and b multiplying by x and then adding with each other). The +10 term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & -10 and -1 & 10 are the possible pairs. Now we can look and see which one adds up to make 9. This gives us the pair -1 & 10 and we plug that into the equation as a and b to get our final answer.

### Example Question #1 : How To Factor A Trinomial

Which expression is equivalent to the following polynomial:

Explanation:

This question calls for us to factor the polynomial into two binomials. Since the first term is  and the last term is a number without a variable, we know that how answer will be of the form  where a and b are positive or negative numbers.

To find a and b we look at the second and third term. Since the second term is  we know . (The x comes from a and b multiplying by x and then adding with each other). The -14 term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & -14, 2 & -7, -2 & 7, and -1 & 14 are the possible pairs. Now we can look and see which one adds up to make 5. This gives us the pair -2 & 7 and we plug that into the equation as a and b to get our final answer.

### Example Question #7 : How To Factor A Trinomial

Which expression is equivalent to the following polynomial:

Explanation:

This question calls for us to factor the polynomial into two binomials. Since the first term is  and the last term is a number without a variable, we know that how answer will be of the form  where a and b are positive or negative numbers.

To find a and b we look at the second and third term. Since the second term is  we know . (The x comes from a and b multiplying by x and then adding with each other). The  term tells us that . Using these two pieces of information we can look at possible values. The third term tells us that 1 & 8, 2 & 4, -2 & -4, and -1 & -8 are the possible pairs. Now we can look and see which one adds up to make -9. This gives us the pair -1 & -8 and we plug that into the equation as a and b to get our final answer.

### Example Question #1 : Trinomials

Simplify the following:

Explanation:

To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.

Now we treat this as the addition of three monomials multiplied by a trinomial.

Now combine like terms and order by degree, largest to smallest.

### Example Question #2 : How To Multiply Trinomials

Solve:

Explanation:

The  is distributed and multiplied to each term , and .

### Example Question #3 : How To Multiply Trinomials

Which of the following is equal to ?

Explanation:

is multiplied to both  and  and  is only multiplied to .

### Example Question #4 : How To Multiply Trinomials

What is ?

Explanation:

is distributed first to  and  is distributed to . This results in  and .  Like terms can then be added together. When added together, , , and . This makes the correct answer .