Answer:
To factorize the expression 2√3x^2 + x - 5√3, you can look for factors that will allow you to write it as a product of two binomials. Here's how you can do it:
Start by looking at the quadratic term (2√3x^2) and see if it can be factored. In this case, you can factor out 2√3x from it:
2√3x^2 = 2√3x * x
Now, consider the constant term (-5√3). To factor this term, you can write it as -√3 * 5:
-5√3 = -√3 * 5
Now, rewrite the middle term (x) as the sum of two terms using the factors from steps 1 and 2:
x = 2√3x - √3 * 5 * x
Now, you have expressed the original expression as a sum of three terms:
2√3x^2 + x - 5√3 = 2√3x * x + 2√3x - √3 * 5 * x
Group the terms in pairs and factor by grouping:
(2√3x * x + 2√3x) - (√3 * 5 * x)
Factor out common factors from each group:
2√3x(x + 1) - √3 * 5 * x
Now, you can see that both terms have a common factor of √3x. Factor that out:
√3x(2(x + 1) - 5)
Simplify the expression inside the parentheses:
√3x(2x + 2 - 5)
Combine like terms inside the parentheses:
√3x(2x - 3)
So, the factorization of the expression 2√3x^2 + x - 5√3 is √3x(2x - 3).
Explanation: