Question

Will give the brainliest! (with the right answers)

1.) Use synthetic division to divide 4x^3 - 6x^2 - 23x+10 by x+2.

2.) Divide (x^4 - 3x^2 - 55) divide (x-3).

Answer 1

(4x³ - 6x² - 23x + 10)/(x + 2) =

= (4x² + 8x² - 14x² - 28x + 5x + 10)/(x + 2)

= [4x²(x + 2) - 14x(x + 2) + 5(x + 2)]/(x + 2)

= (x + 2)(4x² - 14x + 5)/(x + 2)

= (4x² - 14x + 5)

Answer 2

Answer:

1.4 x² - 14 x + 5

2.x^3 + 3x^2 +6x +18 -1

Step-by-step explanation:

Question No 1:

4 x^3 - 6 x^2 - 23 x+10 / x+2

Factorize:

(4 x^3 + 8 x² - 14 x² - 28 x + 5 x + 10)/(x + 2)

= [4 x²(x + 2) - 14 x(x + 2) + 5(x + 2)]/(x + 2)

= (x + 2)(4 x² - 14 x + 5)/(x + 2)

cancel out x+2 then we get

=4 x² - 14 x + 5

and

by using synthetic equation we get the equation that i have attach a file where i did it by using synthetic equation you can see it.

After completing table getting the following coefficients: 4 ,-14 , 5 , 0.

4x^3 - 6x^2 - 23x+10/ x+2

x

=  4x^3– 14 x^2  -5 x

taking x common

x=x( 4x^3– 14 x^2  -5 x )

Cancel out x on both sides we get

=  4x^2– 14 x -5  

Question no 2:

= x^4 - 3 x^2 - 55 /x-3

Using synthetic equation we get the equation that i have attach a file where i did it by using synthetic equation you can see it.

We complete the table an get the coffiecnt  1, 3, 6 , 18 , -1

= x^4 - 3x^2 – 55/x-3

x= x^4 +3x^3+6x^2 +18x-1

taking x common , we get

x= x(x3 + 3x2 +6x +18 -1

)

cancel out both x we get

Answer = x3 + 3x2 +6x +18 -1