Solve the form ax2 - bx - c factoring polynomials, Mathematics

Assignment Help:

Solve the form ax2 - bx - c factoring polynomials ?

This tutorial will help you factor quadratics that look something like this:

2x2 -3x - 14

(Leading coefficient is not 1; the other two coefficients can be positive or negative.)

Step 1: Multiply the constant coefficient ( -14) by the leading coefficient (2). Don't forget the negative signs, if any! You get -28.
Step 2: Write down all the different ways to factor the result (which was -28) into two numbers

-28 = (-1)(+28)
-28 = (-2)(+14)
-28 = (-4)(+7)
-28 = (-7)(+4)
-28 = (-14)(+2)
-28 = (-28)(+1)

Step 3: Now, for each possible factorization, add together the two factors. You're looking for two that add up to the middle coefficient, which is -3.

-1 + 28 = 27
-2 + 14 = 12
-4 + 7 = 3
-7+4 = -3 ← found it
-14 + 2 = -4
-28 +1 = -1 Since you already found it you don't need to bother with these

Step 4. The factors you found, namely 4 and -7, add up to -3. Therefore, you can split apart the middle term, like this:

2x2 - 3x -14
= 2x2 + 4x - 7x - 14

By the way it doesn't matter in which order you put the two terms 4x and -7x.

Step 5: All your other terms are still in the correct order, right? Second degree term first, then the two first-degree terms, then the constant term. Now put parentheses around the first two and the last two terms.

(2x2 + 4x) + (-7x -14)

(If you have any negative signs, you have to be careful here. See how I've included the negative sign inside the parentheses?)

Step 6: Factor out common monomials in each of the two groups. (If you see any negative signs on the terms with variables, you should factor them out too.)

2x(x + 2) + -7(x + 2)

Step 7: If you haven't made any mistakes in the first 6 Steps, you should now see another common factor in each Term. In this example, you can see that (x + 2) is a Common factor. Factor it out using reverse distribution.

(x + 2)(2x - 7).

Step 8. Check your answer by multiplying out using FOIL.

(x + 2)(2x - 7) = 2x2 - 3x - 14 .


Related Discussions:- Solve the form ax2 - bx - c factoring polynomials

Calculate the regular monthly payments, A washing machine, cash price $ 850...

A washing machine, cash price $ 850 is available on the following terms: A deposit of $ 100 followed by equal payments at the end of each month for the next 18 months, if intere

Algebraic word problems, Algebraic Word Problems: Equations: 1....

Algebraic Word Problems: Equations: 1. The total electrical output of one nuclear facility is 200 megawatts more than that of another nuclear facility. Let L be the

Example of normal distribution, The mathematics results of 20 first-year un...

The mathematics results of 20 first-year university students are given, together with their results of their performances in the year 12 semester Test and Final Assignment:

Determine equation of tangent line, Determine equation of the tangent line ...

Determine equation of the tangent line to f (x) = 4x - 8 √x  at x = 16 . Solution : We already know that the equation of a tangent line is specified by,

Need some clarity?, THE % PARTICIPATION Feature in a major medical expense ...

THE % PARTICIPATION Feature in a major medical expense policy is 75% with a $100 deductible. how much of a $2,000 bill is the insured responsible for paying?

Relations, Suppose A and B be two non-empty sets then every subset of A Χ B...

Suppose A and B be two non-empty sets then every subset of A Χ B describes a relation from A to B and each relation from A to B is subset of AΧB. Normal 0 fals

Describe independent events in maths, Describe Independent Events in maths?...

Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event

Jason 10 two-point or 2 three-point how many points score, Jason made 10 tw...

Jason made 10 two-point baskets and 2 three-point baskets within Friday's basketball game. He did not score any other points. How many points did he score? Find out the number

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd