how do you factor 4x^2-35x-9=0?

The terms are in descending order, so a = 4, b = -35, and c = -9.

find 2 numbers that when multiplied give you a * c (which is 4 * -9 = -36) and when added give you b (which is -35).

Try -36 and 1. When multiplied they equal -36, and when added they equal -35. Voila!

So split the middle term using the two numbers just found.

4x^2 + (-36x + 1x) - 9 = 0
Now factor by grouping. Remove the parentheses and factor out the GCF from the first 2 and the last 2 terms.

4x(x - 9) + 1(x - 9) = 0
Now factor out the GCF of the two terms.

(4x + 1)(x - 9) = 0
If 2 numbers multiplied together equal 0, then one or both of the numbers must equal 0.

4x + 1 = 0 and/or x = 9 = 0

take it from there.

ok thanks..

To factor the quadratic equation 4x^2 - 35x - 9 = 0, we can use the factoring or the quadratic formula method.

Let's explain the factoring method:

Step 1: Ensure that the equation is in the standard quadratic form, ax^2 + bx + c = 0.
In this case, the equation is already in the standard form.

Step 2: Multiply the coefficient of the x^2 term by the constant term. (ac)
In this case, (4)(-9) = -36.

Step 3: Find two numbers that multiply to give ac and add up to give the coefficient of the x term (bx).

In this case, we need to find two numbers that multiply to give -36 and add up to -35.
The numbers are -36 and 1, because -36 * 1 = -36 and -36 + 1 = -35.

Step 4: Rewrite the middle term (-35x) using the two numbers found in step 3.
So, the equation becomes: 4x^2 - 36x + x - 9 = 0

Step 5: Group the terms and factor by grouping.
Group the first two terms and the last two terms: (4x^2 - 36x) + (x - 9)
Factor out the greatest common factor from each group: 4x(x - 9) + 1(x - 9)
Notice that (x - 9) appears in both terms.

Step 6: Factor out the common binomial factor (x - 9)
(x - 9)(4x + 1) = 0

Step 7: Set each factor to zero and solve for x.
x - 9 = 0 or 4x + 1 = 0

Solving these equations:
x = 9 or x = -1/4

Therefore, the factored form of the quadratic equation 4x^2 - 35x - 9 = 0 is (x - 9)(4x + 1) = 0, and the solutions are x = 9 or x = -1/4.