Use synthetic division to divide x^2-9 divide x-7

Question

1.Use synthetic division to divide x^2-9 divide x-7

 

2.solve the absolve value equation |10n+3|=0

Answer 1

1)

 

Synthetic division uses the coefficients of the polynomials.  Since (x - 7) is a factor of (x² - 9), 7 is a root.  We divide the coefficients of the (x² - 9) by the root.

 

 

7 | 1      0     -9

         

             7     49

______________

     1      7      40

 

 

This number under the line here is the quotient.  Since the degree of the polynomial we used to divide is 2, the degree of the polynomial in our quotient will be 1.  The last digit under this line is the remainder.

 

Quotient = x + 7

Remainder = 40

 

To check, we multiply the quotient by the divisor then add the remainder.  We should get back (x² - 9).

 

(x + 7)(x - 7) + 40 =

 

x² - 49 + 40 =

 

x² - 9

 

This checks out.

 

 

2)

 

The absolute value of a negative number is positive.  The absolute value of positive value is positive.

Since the absolute value of zero is zero, we can take out the absolute value symbol.

 

10n + 3 = 0

 

Solve for n.  I leave this part to you.

 

 

 

 

Answer 2

1. Place a 7 near the top left and draw a rectangle after that.  Near the top write the coefficients in a row: 1, 0, -9.

Drop the 1 to be bottom row.  Multiply this by 7 and write it under 0.  Take 0-7.  Jot -7 at the bottom just below.  Multiply this by 7 to get -49.  Jot -49 under -9.  Take -9-(-49)=40.  Jot this underneath at the bottom.

 

2. 10n+3=0.  Solve for n.