To factorize the expression 5x^2 - 6x - 8, we need to find two binomials such that when multiplied, the result is equal to the given expression.
First, we multiply the coefficient of x^2 (5) and the constant term (-8), which gives us -40.
Now, we need to find two numbers whose product is -40 and whose sum equals the coefficient of x (-6). The numbers that satisfy these conditions are -10 and 4.
Next, we split the middle term (-6x) using these two numbers:
-6x = -10x + 4x
Now we rewrite the original expression, substituting -6x with -10x + 4x:
5x^2 - 10x + 4x - 8
We can now group the terms:
(5x^2 - 10x) + (4x - 8)
Now, we factor out the greatest common factor from each group:
5x(x - 2) + 4(x - 2)
Notice that (x - 2) is common to both terms. We can factor it out:
(x - 2)(5x + 4)
Therefore, the expression 5x^2 - 6x - 8, in factored form, is (x - 2)(5x + 4).
30. What is the expression in factored form? show steps
5x2 − 6x − 8
1 answer