help please

Question

Solve these polynomial equations:

 

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

 

B) x^2-3x=4

Answer 1

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

Answer 2

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

Answer 3

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.

 

x²-3x-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±√b²-4ac)/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.