complete.
6t to the 2nd power - 23t + 20=(3t - 4)(2t - .....)
What is 5?
To find the missing factor in the given quadratic expression, we can use the factoring method.
First, let's multiply the two binomial factors, (3t - 4) and (2t - x), together using the distributive property:
(3t - 4)(2t - x) = 6t^2 - 8t - 3xt + 4x
Now, we can compare the expanded form of the product to the original quadratic expression, 6t^2 - 23t + 20, and equate the corresponding terms:
6t^2 - 8t - 3xt + 4x = 6t^2 - 23t + 20
By comparing the coefficients of the like terms on both sides of the equation, we can determine the value of x.
-8t - 3xt = -23t (comparing the coefficients of t)
4x = 20 (comparing the constants)
From the first equation, we can solve for x by equating the coefficients and isolating x:
-8t - 3xt = -23t
-3xt = -23t + 8t
-3xt = -15t
x = (-15t) / (-3t)
x = 5
Therefore, the missing factor in the original quadratic expression is 2t - 5.
So, the complete factored form of the quadratic expression is:
6t^2 - 23t + 20 = (3t - 4)(2t - 5)