Question

Use synthetic division to solve (3 x Superscript 4 Baseline 6 x cubed 2 x squared 9 x 10) divided by (x 2). What is the quotient?.

Answer 1

The quotient is (2x²+10x-5).

Polynomial

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Given

$3x^4+6x^{2} +2x^{2} +9x+10$ and $x +2$ polynomials.

To find

The division of $3x^4+6x^{2} +2x^{2} +9x+10$ by $x +2$.

How to find the division?

$3x^4+6x^{2} +2x^{2} +9x+10$ and $x +2$ polynomials are given.

$3x^4+6x^{2} +2x^{2} +9x+10$ satisfied by $\rm x = -1,\ -2,\ 0.5,\ 0.5$ . then

Then the equation become

(x+1)(x+2)(x-0.5)(x0.5) then divide the polynomial by x - 3.

$\dfrac{3x^4+6x^{2} +2x^{2} +9x+10}{x+2} = \dfrac{(x+1)(x+2)(x-0.5)(x-0.5)}{x+2} \\\dfrac{3x^4+6x^{2} +2x^{2} +9x+10}{x+2} = (x+1)(x-0.5)(x-0.5)$

And on multiplication we have,

$(x+1)(x-0.5)(x-0.5) = (3^{3} +2x+5)$

Thus the quotient is $(3^{3} +2x+5)$.

More about the polynomial link is given below.

https://brainly.com/question/17822016