How do you factor quadratic trinomials?

Updated: 4/28/2022
User Avatar

Wiki User

11y ago

Best Answer

ax2 + bx + c is the general formula for a quadratic trinomial.

If a = 1 it is easier. Find 2 integers whose product = c AND whose sum = b.

The 2 number must do both. call thos numbers m and n

The factors become (a+m)(a+n)

ex: x2 - x - 12

c = -12, has many factors -1 x 12, -2 x 6, -3 x 4, -4x3, -6x2, and -1x12

compare these to b = -1. the only ones that have a sum of -1 are -4 and 3

so the factors are (x-4)(x+3) --- answer

But if a is not equal to 1

step1. Multiply a and c find a new number, lets call it d. Use d instead of c like above to find factors and look for a sum equal to b. just like above but you are factoring d NOT c. lets call these factors m and n just like before.

step 2. Replace bx with mx + nx Now you have 4 terms instead of 3

ax2 + bx + c becomes ax2 + mx + nx + c group in twos using parenthesis

( ax2 + mx) + (nx + c)

step 3. Look at each group separately and get a GCF.

step 4, Look at the parenthesis after each above GCF. If they are not the same the original trinomial was prime (or you made a mistake). If they are the same then put the GCF's into a parenthesis multiplied by the parenthesis that was the same. This is the answer. This sounds complicated, but it is easier to do than to explain using a computer.

Ex: Factor 2x2 +11x +12

Step 1 --- 2x12 = 24, Factors are 1x24, 2x12, 3x8, 4x6 and some negatives which we don't need THIS TIME. Look for the sum that = b = 11 ... 3+8 = 11

Step 2 --- replace b ---- 2x2 +11x +12 = 2x2 + 8x + 3x +12

group ---- ( 2x2 + 8x) + ( 3x +12)

Step 3 --- GCF --- 2x(x + 4) + 3(x + 4) ----- notice parenthesis is same.

Step 4 ---- Both GCF's make a new group and same parenthesis is used once

(2x + 3)(x+4)

This is the answer.

User Avatar

Wiki User

11y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: How do you factor quadratic trinomials?
Write your answer...
Still have questions?
magnify glass
Related questions

What is the quadratic trinomials factor of 12xsquared-20x -8?

12x2-20x-8 = (12x+4)(x-2)

How To Factor Trinomials?

Find one factor by substituting in values, then use long division. You can then apply the quadratic formula to the result - or factorise it by sight, of course

What is difference between monic quadratic trinomials and general quadratic trinomials?

the difference between the two is that in quadratic u find the factors of the last term that when u add/subtract u get the answer of the middle term. while the general quadratic trinomial u find the factors of both first term and last term and proceed to trial and error. Welcome -Delin-shaw Guillermo

How do you Factor the trinomials of 12x2-32x-12?

12x ^2 -32x-12

Is it possible to apply the procedures in factoring quadratic trinomials to factoring the difference of two terms?

Yes, simply treat the middle coefficient as 0.

What is the quadratic equation used for?

It is used to solve quadratic equations that cannot be factored. Usually you would factor a quadratic equation, identify the critical values and solve, but when you cannot factor you utilize the quadratic equation.

Can a factor pair have an extra addition problem?

Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.

Why use quadratic formula?

Using the quadratic formula to solve any quadratic equation is the best way of getting around it because the quadratic formula is "the opposite of b plus or minus the square root of b squared minus 4ac all divided by 2a. This formula only works with trinomials and second degree equaitons. If the equation is a binomial, then put in a placeholer (0) and substitute them into the equation.

How do you solve a quadratic equation that will not factor?

How you solve an equation that doesn't factor is to plug a quadratic equation's format; ax2+bx+c into the quadratic formula which is x=-b+square root to (b2-4ac)/2a.

How do you solve Quadratic functions?

All you do is set the quadratic function to equal to 0. Then you can either factor or use the quadratic formula to solve for your unknown variable.

What is a common factor of the trinomials 2x2- x- 28 and 2x2 - 15x 28?

If that's +28, the answer is (x - 4)

What is the factor of 2x2-10x plus 3?

Doesn't factor evenly, use quadratic