How to factor a variable - ACT Math
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Simplify:
Simplify:
factors to 
One 
cancels from the bottom, leaving 
One
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Two consecutive positive multiples of five have a product of 300. What is their sum?
Two consecutive positive multiples of five have a product of 300. What is their sum?
Define the variables as x = 1st number and x + 5 = 2nd number, so the product is given as x(x + 5) = 300, which becomes x2 + 5x – 300 = 0.
Factoring results in (x + 20)(x – 15) = 0, so the positive answer is 15, making the second number 20.
The sum of the two numbers is 35.
Define the variables as x = 1st number and x + 5 = 2nd number, so the product is given as x(x + 5) = 300, which becomes x2 + 5x – 300 = 0.
Factoring results in (x + 20)(x – 15) = 0, so the positive answer is 15, making the second number 20.
The sum of the two numbers is 35.
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Factor 12_x_3_y_4 + 156_x_2_y_3
Factor 12_x_3_y_4 + 156_x_2_y_3
The common factors are 12, x2, and y3.
So 12_x_2_y_3(xy + 13)
The common factors are 12, x2, and y3.
So 12_x_2_y_3(xy + 13)
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Factor: 
Factor:
In the form of 
you must find two numbers which add to give you 
and multiply to give you 
and then put them in the form of (
+ number) (
+ number)
Therefore 
is the answer.
To check, multiply the two expressions out and it should equal 
In the form of
Therefore
To check, multiply the two expressions out and it should equal
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Solve for all solutions of 
:
Solve for all solutions of
First move all of the variables to the left side of the equation. Combine similar terms, and set the equation equal to zero. Then factor the equation to get 
Thus the solutions of 
are 4 and 6.
First move all of the variables to the left side of the equation. Combine similar terms, and set the equation equal to zero. Then factor the equation to get
Thus the solutions of
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Factor the following expression:
Factor the following expression:
To factor an expression we look for the greatest common factor.
Remember that
Thus:
To factor an expression we look for the greatest common factor.
Remember that
Thus:
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Factor the following expression:
Factor the following expression:
To factor, you are looking for two factors of 40 that add to equal 13.
Factors of 40 include: (1, 40), (2, 20), (4, 10), (5, 8). Of these factors which two will add up to 13?
Also, since the first sign (-) and the second sign is (+) this tells us both binomials will be negative. This is because two negatives multiplied together will result in the positive third term, while two negatives added together will result in a larger negative number.
Thus,
To factor, you are looking for two factors of 40 that add to equal 13.
Factors of 40 include: (1, 40), (2, 20), (4, 10), (5, 8). Of these factors which two will add up to 13?
Also, since the first sign (-) and the second sign is (+) this tells us both binomials will be negative. This is because two negatives multiplied together will result in the positive third term, while two negatives added together will result in a larger negative number.
Thus,
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