All ACT Math Resources
Example Questions
Example Question #1 : How To Factor A Trinomial
Which expression is equivalent to the following polynomial:
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 : Trinomials
Which expression is equivalent to the following polynomial:
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 : How To Multiply Trinomials
Simplify the following:
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 #1 : How To Multiply Trinomials
Solve:
The is distributed and multiplied to each term , , and .
Example Question #2 : How To Multiply Trinomials
Which of the following is equal to ?
is multiplied to both and and is only multiplied to .
Example Question #661 : Algebra
What is ?
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 .
Example Question #1 : How To Add Trinomials
Add and .
To add the trinomials, simply eliminate the parentheses and add like terms.
Example Question #661 : Algebra
Like terms can be added together: is added to , is added to , and is added to . The resulting answer choice that is correct is .
Example Question #1 : How To Add Trinomials
Choose the answer which best simplifies the following expression:
To solve this problem simply remove the parentheses and add the like terms:
Example Question #3 : How To Add Trinomials
Choose the answer which best simplifies the following expression:
To simplify, remove parentheses and combine like terms: