What is the value of the remainder if 10x^4 – 6x^3 + 5x^2 – x + 1 is divided by x – 3?

691

Step-by-step explanation:

There are 3 different ways to find the remainder.  I am not sure which method you are supposed to use, so I will solve using all 3 methods.

Long Division:

         10x³ + 24x² + 77x + 230

x - 3 ) 10x⁴ -  6x³  + 5x²   - x  +  1

      - (10x⁴ - 30x³)   ↓       ↓      ↓

                   24x³ + 5x²     ↓      ↓

               - (24x³ - 72x²)   ↓      ↓

                              77x²  - x       ↓

                         -  (77x² - 231x)  ↓

                                        230x + 1

                                     - (230x - 690)

                                                    691 ← remainder

Synthetic Division:

x - 3 = 0   ⇒  x = 3

3  |  10     -6        5       -1        1

   |   ↓      30     72    231    690

      10      24     77    230   691 ← remainder

Remainder Theorem:

f(x) = 10x⁴ - 6x³ + 5x²  - x  +  1

f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3)  +  1

     =  810   - 162    + 45    -  3  +  1

     = 691

i dont know sorry

step-by-step explanation:

the two may have that, even a breakdown is probably offered