Factor completely.
5x^2 + 49x - 10
To factorize the polynomial 5x^2 + 49x - 10, we need to find two numbers that multiply to give -10 and add up to 49.
The pairs of numbers that multiply to give -10 are: (-1,10) and (1,-10), (-2,5) and (2,-5), (-5,2) and (5,-2), (-10,1) and (10,-1).
From these pairs, the pair that adds up to 49 is (5,-2).
Therefore, we can factorize the polynomial as: (5x - 2)(x + 5).
Again
Apologies for the confusion. Upon reviewing the problem, it seems that I made an error in my previous response.
To factorize the polynomial 5x^2 + 49x - 10, we can use the quadratic formula or the method of factoring by grouping.
Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 5, b = 49, and c = -10:
x = (-49 ± √(49^2 - 4 * 5 * -10)) / (2 * 5)
x = (-49 ± √(2401 + 200)) / 10
x = (-49 ± √(2601)) / 10
x = (-49 ± 51) / 10
This gives us two possible values for x:
x1 = (-49 + 51) / 10 = 2 / 10 = 0.2
x2 = (-49 - 51) / 10 = -100 / 10 = -10
Therefore, the quadratic equation factors as (x - 0.2)(x + 10).