Perform division x^3+8/x+2

Question

1. factor the polynomial a^4+4a^3b-5a^2b^2

 

2. Perform division x^3+8/x+2

 

3. use the quadratic formula to solve the equation 5x^2-3x-7=0

Answer 1

1)

 

a⁴ + 4a³b - 5a²b²

 

 

Factor by taking out the GCF.  GCF is a².

 

a²(a² + 4ab - 5b²)

 

 

Next, we can factor out the term in parenthesis using FOIL.

 

a²(a + 5b)(a -  b)       

 

 

 

2)

 

(x³ + 8) / (x + 2)

 

 

We use long division when dividing by a polynomial.  Note that the coefficients of the x² and x terms in the numerator are zero.  We can write the division as

 

 

                      x² -  2x  + 4

            __________________

(x + 2) | x³ + 0x² + 0x + 8

             x³ + 2x²                                               subtract and bring down the next term.

            ___________

                   -2x² + 0x

                   -2x² - 4x                          subtract and bring down the next term.

                   ____________

                           4x    +  8

                           4x   + 8

                          ________

                                    0                        remainder

 

 

The quotient is (x² - 2x + 4)

 

 

3)

 

A quadratic equation is always in the form

 

ax² + bx + c = 0

 

 

Use the quadratic formula:

 

x = (-b ± √(b² - 4ac)) / 2a

 

 

where:

a = 5

b = -3

c = -7

 

 

Plug in these numbers into the formula.

 

 

Answer 2

1.  a^2*[(a+5*b) (a-b)] 3. r1=(3+sqrt(9-4*5*-7))=1.1957+1.3593i,

r2=(3-sqrt(9-4*5*-7))=1.1957-1.3593i,

2. (x^4+2*x+8)/x 

Apparently this should have been (x^3 + 8)/(x+2) instead (x^4+2*x+8)/x. The correct answer is excellently prouduced  above.  I failed to notice the denominator was parenthetical . 

Answer 3

Vivian,

 

1. In a^4+4a^3b-5a^2b^2 can you see that they all have a^2 in common?  (So, it would be on the outside of the parenthesis.)

 

2. In  x^3+8/x+2 do you know we subtract exponents when dividing?

 

3.  In 5x^2-3x-7=0 do you know how to find a,b, and c to plug them into the quadratic formula?

 

LMK if these ideas have put you on the right path!

Debra, This Generation Learning