2x^2-10x+8
2x^2-10x+8
=2(x²-5x+4)
Find numbers a and b such that
a*b=4, and a+b=-5
=2(x+a)(x+b)
=2(x-4)(x-1)
i.e. a=-4, b=-1
To simplify the expression 2x^2 - 10x + 8, we can factorize it if possible. Let's go through the steps:
Step 1: Check if common factors can be factored out.
In this case, there are no common factors that can be factored out from all the terms.
Step 2: Check if it is a quadratic trinomial that can be factored.
A quadratic trinomial is a trinomial with the highest power term being of the second degree (x^2).
Step 3: To factorize a quadratic trinomial, we look for two binomials in the form (ax + b)(cx + d) that multiply together to give the original trinomial.
In our case, we have 2x^2 - 10x + 8.
Step 4: Multiply the values of a and c from the binomial form. We need to find two numbers whose product is 2 * 8 = 16.
Step 5: Find two numbers whose product equals 16 and whose sum equals the coefficient of the x term -10.
After considering various possibilities, -2 and -8 are the numbers that satisfy these conditions since (-2) * (-8) = 16 and (-2) + (-8) = -10.
Step 6: Now, we rewrite the middle term (-10x) as the sum of the two values we found in Step 5: -2x - 8x.
So, our quadratic trinomial 2x^2 - 10x + 8 can be factored as follows:
2x^2 - 2x - 8x + 8.
Step 7: Group the terms and factor by grouping:
(2x^2 - 2x) - (8x - 8).
Step 8: Factor out the common factors from each group:
2x(x - 1) - 8(x - 1).
Step 9: Notice that (x - 1) is the common factor in both terms. Factor it out:
(2x - 8)(x - 1).
Therefore, the factored form of the expression 2x^2 - 10x + 8 is (2x - 8)(x - 1).