(x^4+11x^3+33x^2+24x+32)(x+6)

Question

i need to see them step by step so i can learn how to do them, is alot of work can you please help me do the first 8?

1) (x^4+11x^3+33x^2+24x+32)(x+6)

2) (6v^3+42v^2-50v-20)/(v+8)

3) (6b^4+53b^2-61b+19)/(b+8)

4) (4n^3-9n^2+9n+3)(n-1)

5) (6a^3+20a^2-15a+9)/(a+4)

6) (n^4-6n^3-10n^2+20n+15)/(n+2)

7) (p^5+8p^4+2p^2+19p+16)/(p+8)

8) (x^4-2x^3-16x^2+28x+9)/(x-4)

9) (r^5+6r^4-13r^3-5r^2-8r+14)/(r-2)

10) (8v^5+32v^4+5v+20)/(v+4)

 

HELP PLEASEEEEE!

 

Answer 1

REVISED

 

x⁴ + 11x³ + 33x² + 24x +23              (Called the dividend.)
                   x+6                            (Called the divisor.)

            _______x³ + 5x² +   3x  + 6        
   x + 6 |x⁴ + 11x³ + 33x² + 24x +23   
2.        -(x⁴ +  6x³)    |          |      |    
3.                  5x³ + 33x^{2        |        |}      
4.                -(5x³ + 30x²)    |      |   
5.                                      3x² + 24x    |    
6.                           -(3x² + 18x)  |    
7.                                      6 x + 23   
8.                                     -(6x + 36)  
9.                                             -13    

You have an x4 expression divided by an x expression.
1. What multiplied by x will give x⁴? -> x³. Write x³ up top above the x³ term in the dividend.
2. Multiply x³ times (x + 6) and write below the corresponding terms -> x⁴ + 6x³
3. Subtract the terms-you are left w/5x³. Bring down 33x².  Now you have 5x³ + 33x².
4. What multiplied by x will give 5x³? 5x². Put 5x² on & top multiply it by x + 6 = 5x² + 30x².  Write it below the 5x³ + 33x².
5. Subtract the terms-you're left w/3x². Bring down 24x.  Now you have 3x² + 24x.
6. What multiplied by x will give 3x²? Put 3x on & top multiply it by x + 6 = 3x² + 18x.  Write this below the 3x² + 24x.
7. Subtract the terms-you're left w/6x. Bring down 23.  Now you have 6x + 23.
8. What multiplied by x will give 6x? 6.  Put 6 on & top multiply by x + 6 = 6x + 36.  Write this under 6x + 23.
9. Subtract the terms-you're left w/-13. This is your remainder.
10. Your answer is x³ + 5x² + 3x + 6 R -13  

(x³ + 5x² + 3x + 6 is called the quotient and -13 is the remainder.)

It helps to write all of this down yourself while you follow along with the reasoning.  

 

I've numbered each step in the problem and numbered each step.  These should match up.  Let me know if you can follow it this way.