Simplify each expression. Show as much work as possible for each question for full credit. Write all answers in standard form

Step-by-step explanation:

3)

a) (- 5 + x)(x + 4)

We would apply the distributive property by expanding the brackets, it becomes

- 5x + 4 × - 5 + x² + 4 × x

- 5x - 20 + x² + 4x

x² - 5x + 4x - 20

x² - x - 20

b) the product of 5 + x and x - 4 is

(5 + x)(x - 4) = 5x - 20 + x² - 4x

= x² + 5x - 4x - 20

= x² + x - 20

Therefore,

(- 5 + x)(x + 4) and (5 + x)(x - 4) are not equal.

c) (2x + 5)(3x² + 4x - 3)

Expanding the brackets, it becomes

6x³ + 8x² - 6x + 15x² + 20x - 15

Collecting like terms, it becomes

6x³ + 8x² + 15x² + 20x - 6x - 15

= 6x³ + 23x² + 14x - 15

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer is 33

step-by-step explanation: