How to factor a trinomial - ACT Math
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Find the 
-intercepts:
Find the
-intercepts occur when 
.
1. Set the expression equal to 
and rearrange:
2. Factor the expression:
3. Solve for 
:
and...
4. Rewrite the answers as coordinates:
becomes 
and 
becomes 
.
1. Set the expression equal to
2. Factor the expression:
3. Solve for
and...
4. Rewrite the answers as coordinates:
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Solve for 
when 
.
Solve for
1. Factor the expression:
2. Solve for 
:
and...
1. Factor the expression:
2. Solve for
and...
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Factor the following expression:
Factor the following expression:
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 
Remember that when you factor a trinomial in the form
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
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Factor the expression completely
Factor the expression completely
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, 
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
List out the factors of
Thus,
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Which expression is equivalent to the polynomial 
.
Which expression is equivalent to the 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 +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.
This question calls for us to factor the polynomial into two binomials. Since the first term is
To find a and b we look at the second and third term. Since the second term is
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Which expression is equivalent to the following polynomial: 
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.
This question calls for us to factor the polynomial into two binomials. Since the first term is
To find a and b we look at the second and third term. Since the second term is
Compare your answer with the correct one above
Which expression is equivalent to the following polynomial:
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.
This question calls for us to factor the polynomial into two binomials. Since the first term is
To find a and b we look at the second and third term. Since the second term is
Compare your answer with the correct one above