# How do I factor this problem?14x^2-56

Asked on by amgurly120

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to decompose the coefficients such that:

`14 = 1*2*7`

`56 = 1*2^3*7`

You need to write the expression using the factored form of coefficients, such that:

`2*7x^2 - 2^3*7`

You should notice that there exists the common factor `2*7` , hence, you may factor out `2*7` , such that:

`2*7(x^2 - 2^2)`

You need to convert the difference of squares `x^2 - 2^2` into a product, using the following formula, such that:

`a^2 - b^2 = (a-b)(a+b)`

Reasoning by analogy yields:

`x^2 - 2^2 = (x - 2)(x + 2)`

Hence, evaluating the factored form of the given expression, yields `14x^2 - 56 = 14(x - 2)(x + 2).`

violy | High School Teacher | (Level 1) Associate Educator

Posted on

First factor out the gcf (greatest common factor) which is 14:

14x^2 - 56 = 14(x^2 - 4)

We use the Difference of Two Squares Formula, for x^2 - 4:

a^2 - b^2 = (a - b)(a + b)

So,

x^2 - 4 = (x - 2)(x + 2)

We will now have,

14x^2 - 56 = 14(x^2 - 4) = 14(x - 2)(x + 2)

Hence, factored form of 14x^2 - 56 = 14(x - 2)(x + 2).

jovona | (Level 1) Salutatorian

Posted on

14x^2-56 =

14(x^2-4) =

14(x-2)(x+2)

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

14x^2-56

both 14 and 56 have a common factor of 14 so factor out 14

14 ( x^2 - 4 )

x^2 - 4 is known as the difference of 2 squares

difference of 2 squares =  (a - b)(a + b)

14 (x-2)(x+2)

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