In maths what does the word factor mean?

Answer 1

In math, factor is a verb and is usually stated as 'to factor'. To factor something basically means to derive the smaller units that when multiplied together will equal that something. Some times it becomes a trial and error exercise.

To factor the number twelve (12) you would consider what numbers multiplied together equal 12. Such as (12x1, 6x2, 4x3, 3x4, 2x6, 1x12) are all factors of the number twelve. The reverse sets (3x4 is the reverse set of 4x3) are used in more advanced areas of math such as Algebra.

To factor the Algebraic expression: x² + x -12

Determine what expressions when multiplied together equal that expression.

In Algebra you learn the two expressions ( _ + _ )( _ +_ ) are the keys in this case.

First determine the coefficients (any constants in the expression):

The constant of x² is 1, the constant of x is 1 and lastly -12 is a constant.

The factor of the 1 constants are 1 because the only numbers that when multiplied together to equal one are 1s (1 times 1 = 1). The factors of -12 are

-12 times 1, -1 times 12, -6 times 2, -2 times 6, -4 times 3, -3 times 4

Next determine the variable factors:

The factors of x² are x times x, factors of x are x times 1.

Now substitute those here: ( _ + _ )( _ + _ )

Which will end up being: [x = (-3)](x+4) which simplifies to (x-3)(x+4).

Multiplying these two factors will demonstrate why (-3,4) are the factors of -12 used.

To multiply (x-3)(x+4), first you take the first quantity in the first expression (x) and multiply it times the first quantity in the second expression, also (x)

so x times x equals x²

giving x²

Then multiply the first quantity in the first expression (x) times the second quantity in the second expression (4) so x times 4 equals 4x

giving x² + 4x

Then multiply the second quantity in the first expression (-3) times the first quantity in the second expression (x) so -3 times x equals -3x

giving x² +4x -3x

Then multiply the second quantity in the first expression (-3) times the second quantity in the second expression (4) so (-3) times 4 equals -12

giving x² +4x -3x -12 which simplifies to x² +x -12

So your factors are (x-3)(x+4)

By some quick calculations you will find that the (-3) and (4) are the only factors of -12 that will work in this expression. The rule of thumb in this circumstance is determine the factors of -12 that when multiplied together will equal -12 and when combined will equal the coefficient of the middle term which in this case is 1. (x can be stated as 1 times x for such exercises which would make the initial expression look like 1x² + 1x -12.

Answer 2

A number or quantity that when multiplied with another produces a given number or expression.