Factor completely
4a2 - 8a - 5
please help i don't get this at all!!!
After 2 "guesses" I got
(2a+1)(2a-5)
check it by expanding it
Factor completely and then place the factors in the proper location on the grid.
4a2 - 8a - 5
To factor the expression 4a^2 - 8a - 5, we need to find two binomials that, when multiplied, give us the original expression. Let's follow these steps to factor it completely:
Step 1: Multiply the coefficient of the quadratic term (4) with the constant term (-5). In this case, 4 * (-5) = -20.
Step 2: Look for two numbers that multiply to give us -20 and add up to the coefficient of the linear term (-8). In this case, the numbers are -10 and 2 because (-10) * (2) = -20 and (-10) + (2) = -8.
Step 3: Rewrite the middle term (-8a) using the two numbers found in step 2. Split the term into -10a and 2a.
Therefore, the expression can be rewritten as:
4a^2 - 10a + 2a - 5.
Step 4: Group the terms in pairs to find the common factors:
(4a^2 - 10a) + (2a - 5).
Step 5: Factor out the greatest common factor from each pair:
2a(2a - 5) + 1(2a - 5).
Step 6: Notice that both groups have a common factor of (2a - 5). Factor this out:
(2a + 1)(2a - 5).
So, the expression 4a^2 - 8a - 5 can be completely factored as (2a + 1)(2a - 5).