Factor the following polynomials.
1. 25x³-36x
25x³-36x
step1, common factor
= x(25x^2 - 36)
step2, recognize the difference of squares
= x(5x-6)(5x+6)
Sol:
Given
25x^3-36x
Factor out the common term x
=x(25x^2-36)
=x[(5x)^2-(6)^2]
We know that
a^2-b^2=(a+b)(a-b)
so,now
=x(5x+6)(5x-6)
Final answer:
=x(5x+6)(5x-6)
To factor the polynomial 25x³ - 36x, we can start by looking for any common factors. In this case, we notice that both terms have a common factor of x. So we can factor out an x from both terms:
25x³ - 36x = x(25x² - 36)
Next, we can focus on factoring the expression within the parentheses, 25x² - 36. This is a difference of squares since 25x² can be expressed as (5x)² and 36 can be expressed as (6)². The difference of squares formula states that a² - b² can be factored as (a + b)(a - b). Applying this to our expression, we have:
25x² - 36 = (5x + 6)(5x - 6)
Therefore, the fully factored form of 25x³ - 36x is:
25x³ - 36x = x(5x + 6)(5x - 6)