Question

Drag the numbers to the correct locations on the image. Not all numbers will be used. Complete the synthetic division to find the quotient of 3x3 - 25x2 + 12x - 32 and x - 8

Answer 1

Answer:

quotient of 3x3 - 25x2 + 12x - 32 and x - 8 is 3x^2-x+4

Answer 2

The quotient of the polynomial is 3x^2 + x + 4.

What is synthetic division?

Synthetic division is used when a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

For the given situation,

The polynomial is 3x^3 - 25x^2 + 12x - 32.

The divisor is x - 8.

The quotient can be found by using synthetic division method as,

Step 1: Write the coefficients of the polynomial. Here x - 8 is a binomial, which divides the polynomial. So x = 8, write the division as

⇒ $8 | 3 - 25 + 12 - 32$

⇒          $24-8+32$

       $--------$

        $3-1+4$    $|0$

Step 2: On dividing we get the quotient as $3x^{2} -x+4$

Hence we can conclude that the quotient of the polynomial is             3x^2 - x + 4.

Learn more about synthetic division here

https://brainly.com/question/4372468

#SPJ2