ACT Math › Factoring Polynomials
Which of the following is a factor of the polynomial 3y2+14y-24?
3y+4
y-6
4y-3
y+6
3y-6
The polynomial factors to (3y-4)(y+6). (y+6) is the only one of those two options available as an answer.
Which of the following is equivalent to ?
This cannot be factored.
You have two options for a problem like this. On the one hand, you can merely FOIL the answers until you find one that equals the value given in the equation. The other option is to factor it adequately from the beginning. For a question like this, it is a bit harder, given that there is a number in front of the first term. Now, given the signs in the original problem, you know that your groups will look like the following:
Now, you can do a little trick to make your life easier. Factor out the common :
The latter is very easy to factor:
Now, you have:
You can distribute the into either group. For the answers given, the only correct value is:
Which of the following is a factor of the polynomial 3y2+14y-24?
3y+4
y-6
4y-3
y+6
3y-6
The polynomial factors to (3y-4)(y+6). (y+6) is the only one of those two options available as an answer.
Which of the following expressions is a factor of this polynomial?
The polynomial factors into the following expression:
Therefore, the answer is
Which of the following is equivalent to ?
This cannot be factored.
You have two options for a problem like this. On the one hand, you can merely FOIL the answers until you find one that equals the value given in the equation. The other option is to factor it adequately from the beginning. For a question like this, it is a bit harder, given that there is a number in front of the first term. Now, given the signs in the original problem, you know that your groups will look like the following:
Now, you can do a little trick to make your life easier. Factor out the common :
The latter is very easy to factor:
Now, you have:
You can distribute the into either group. For the answers given, the only correct value is:
Which of the following expressions is a factor of this polynomial?
The polynomial factors into the following expression:
Therefore, the answer is
Which of the following is a factor of the polynomial ?
Factor the polynomial by choosing two values that when FOILed will sum to the middle coefficient, 3, and multiply to 2. These two numbers are 1 and 2.
Only (x +1) is one of the choices listed.
Which of the following is a factor of the polynomial ?
Factor the polynomial by choosing two values that when FOILed will sum to the middle coefficient, 3, and multiply to 2. These two numbers are 1 and 2.
Only (x +1) is one of the choices listed.
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 not present, 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 -81 & 1, 81 & -1, and -9 & 9 are the possible pairs. Now we can look and see which one adds up to make 0.
This gives us the pair -9 & 9 and we plug that into the equation as a and b to get our final answer.
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 not present, 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 -81 & 1, 81 & -1, and -9 & 9 are the possible pairs. Now we can look and see which one adds up to make 0.
This gives us the pair -9 & 9 and we plug that into the equation as a and b to get our final answer.