Factor the Quadratic for 4x^2+11x-3

Factor the quadratic
4x2+11x-3

We have our a, b, and c values:
a = 4, b = 11, c = -3

Factor the quadratic 4x2 + 11x - 3

Build factor pairs:

Since a = 4 ≠ 1, find all factor pairs:
a x c = 4 x -3 = -12
These must have a sum = 11

Factor Pairs of -12	Sum of Factor Pair
1,-12	1 - 12 = -11
2,-6	2 - 6 = -4
3,-4	3 - 4 = -1
4,-3	4 - 3 = 1
6,-2	6 - 2 = 4
12,-1	12 - 1 = 11

We want {12,-1}
Rewrite 11x as the sum of factor pairs:
12x - 1x
Our equation becomes
x2( + 12x - 1x) - 3 = 0

Group terms

GCF of 4 and 12 = 4
GCF of 4 and -1 = 1
Our first GCF is an integer
Group the terms below:
4x2 and 12x and -1x and -3

This can be written as:
(x2 + 12x) + (-1x - 3) = 0

Factor out terms:

Factor out 4x from the first group
Factor out 1 from the second group
4x(x + 3) + 1(-x - 3) = 0

Our common term is (x + 3)
Write this as (4x + 1)(x + 3) = 0

Use the Zero Product Principal

If A x B = 0, then either A = 0 or B = 0
Set each factor to 0 and solve

What is the Answer?

(4x + 1)(x + 3) = 0

How does the Quadratic Equations and Inequalities Calculator work?

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the squarea technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + kequationa statement declaring two mathematical expressions are equalfactora divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.interceptparabolaa plane curve which is approximately U-shapedquadraticPolynomials with a maximum term degree as the second degreequadratic equations and inequalitiesrational rootvertexHighest point or where 2 curves meet

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