Daniel L. answered • 10/16/15

Certified in tutoring/academic coaching by the National Tutoring Assn.

Tom B.

asked • 10/16/15Solve these polynomial equations:

A) (2x-3)(3x-1)=0

B) x^2-3x=4

Follow
•
4

Add comment

More

Report

Daniel L. answered • 10/16/15

Tutor

5.0
(23)
Certified in tutoring/academic coaching by the National Tutoring Assn.

Hi Tom,

A) When you multiply two binomials (two terms in each expression), remember FOIL:

Multiply the First terms

Multiply the Outside terms

Multiply the Inside terms

Multiply the Last terms and combine everything:

First terms are 2X and 3X --> 6X^2

Outside terms are 2X and -1 --> -2X

Inside terms are -3 and 3X --> -9X

Last terms are -3 and -1 --> +3

6X^2-2X-9X+3 = 0

6X^2-11X+3=0

B) Subtract 4 from both sides to leave zero on the right side--> X^2 - 3X - 4 =0

Now you have to do a reverse FOIL . . . figure out what terms in two binomials will multiply to the above expression

The first term in each binomial is easy. . . X. . . because X times X is X^2 . . . F is done!

Now the second terms have to multiply to -4 (L) and also produce -3 when you do the O and the I

-4 times +1 equals -4

-4 plus +1 equals -3 so that looks good--> (X - 4) (X + 1)

Dan

Michael J. answered • 10/16/15

Tutor

5
(5)
Effective High School STEM Tutor & CUNY Math Peer Leader

For part B, you can factor using FOIL. There are two numbers that give a product of -4 and a sum of -3.

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

Set the factors equal to zero.

x - 4 = 0 and x + 1 = 0

x = 4 and x = -1

Sabrina R. answered • 10/16/15

Tutor

4.9
(148)
Available for Mathematics and Chemistry Tutoring!

For Part A:

You will get 2 answers because you need to solve for *x *in both parentheses.

2x-3 = 0

3x-1 = 0

So *x* = 3/2 and 1/3

For Part B:

First subtract the 4 to get it to the left side.

x^{2}-3x-4=0

Next use the quadratic equation to solve. So a, b, c in the quadratic equation are the coefficients of the polynomial.

a=1

b=-3

c=-4

The quadratic equation is (-b±√b^{2}-4ac)/4a

So you will have +3±{√[(-3)^{2}]-4(1)(-4)}/4(1)

Thus giving us 3±√{9+16}/4 ---> (3±5)/4

*Note that for quadratic equations you will always get 2 answers.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.