Which of the following binomials is a factor of 3𝑥2+11𝑥−4 ?

To find out which binomial is a factor of the quadratic equation 3x² + 11x - 4, we need to factorize the equation.

The quadratic equation is in the form ax² + bx + c. We need to find two numbers that multiply to give ac (product) and add up to give b (sum).

Here, a = 3, b = 11, and c = -4.

So, ac = 3 * -4 = -12.

We need to find two numbers that multiply to -12 and add up to 11. These numbers are -1 and 12.

Now, we rewrite the middle term (11x) of the quadratic equation as the sum of -1x and 12x.

So, the equation 3x² + 11x - 4 becomes 3x² - 1x + 12x - 4.

Now, we group the terms and factor by grouping:

3x² - 1x + 12x - 4 = x(3x - 1) + 4(3x - 1)

Now, we can see that (3x - 1) is a common factor. So, the factored form of the equation is:

(3x - 1)(x + 4)

So, the binomials that are factors of the given quadratic equation are (3x - 1) and (x + 4).