Divide 26x^4 - 13x^3 - 74x^2 - 46x - 24 by 2x^2 - 3x -5 and verify the result by division algorithm

Step-by-step explanation:

Using long division:

                        13x^2 + 13x + 15   <Quotient

2x^2 - 3x - 5 )  26x^4 - 13x^3 -  74x^2 - 46x - 24

                        26x^4 - 39x^3 - 65x^2

                                     26x^3 -   9x^2  - 46x

                                     26x^3 -  39x^2 - 65x

                                                    30x^2 + 19x   - 24

                                                    30x^2  - 45x  - 75

                                                                   64x + 51  < Remainder.     Division algorithm:

a = bq + r

Here a = the original expression , b = the divisor (2x^2 - 3x - 5), q is the quotient and r = the remainder,

26x^4 - 13x^3 - 74x^2 - 46x - 24 = (2x^2 - 3x - 5)(13x^2 + 13x + 15) + 64x + 51

= 2x^2(13x^2 + 13x + 15) - 3x(13x^2 + 13x + 15) - 5(13x^2 + 13x + 15) + 64x + 51

= 26x^4 + 26x^3 + 30x^2 - 39x^3 - 39x^2 - 45x - 65x^2 - 65x - 75+64x+51

= 25x^4 - 13x^3 - 74x^2 - 46x - 24 which is the same as the above.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.