factor trinomial
This is what I have so far don't know where to go from here
4h^2 + 8h - 5
(4h^2-2h) + (10h-5)
2h(h-5) + -5(2h-1)
cant figure out what to do next
4h^2 + 8h - 5 is a quadratic, so do not factor by grouping. It has only 2 factors.
Try (2h + _)(2h - _). (The other possibility is (4h +/- _)(h +/- _).
(2h + 5)(2h - 1) gives the +8h we need.
4h^2 + 8h - 5.
Use the AC Method:
A*C = 4*-5 = -20 = -2*10.
4h^2 + (-2h + 10h) - 5,
Group the 4 terms into 2 factorable
pairss:
(4h^2 - 2h) + (10h - 5),
2h(2h - 1) + 5(2h - 1),
Factor out (2h - 1):
(2h - 1)(2h + 5).
To factor the trinomial 4h^2 + 8h - 5, you need to find two binomials that, when multiplied together, would result in the given trinomial.
Here's one way to factor it:
Step 1: Identify the coefficients of the trinomial: a = 4, b = 8, and c = -5.
Step 2: Multiply the coefficient of the quadratic term (a) by the constant term (c): 4 * (-5) = -20.
Step 3: Find two numbers that multiply to give -20 and add up to the coefficient of the linear term (b) = 8. In this case, the numbers are 10 and -2 (-10 * 2 = -20 and -10 + (-2) = 8).
Step 4: Rewrite the middle term (8h) using the two numbers found in step 3:
4h^2 + 10h - 2h - 5
Step 5: Group the terms and factor by grouping:
(4h^2 + 10h) + (-2h - 5)
2h(2h + 5) - 1(2h + 5)
Now, you can see that both terms have a common factor of (2h + 5).
Step 6: Combine the common factor to simplify:
(2h + 5)(2h - 1)
So, the factored form of the trinomial 4h^2 + 8h - 5 is (2h + 5)(2h - 1).