Question

Can anyone help me do the questions that are circled with red and you don't need to do the graphing calculator thing, please

Answer 1

There are six problems circled in red.

As requested, only the analytical solutions are shown.

Question 16. Factor the polynomial

• 
  `44+15h+h^2`

• Answer: (h + 4) (h + 11)

Question 17. Factor the polynomial

• 
  `40-22x+x^2`

• Answer: (x - 2) (x -20)

Question 18. Factor the polynomial

• 
  `-24-10x+x^2`

• Answer: (x - 12) (x + 2)

Question 19. Factor the polynomial

• 
  `-42-m+m^2`

• Answer: (m - 7) (m + 6)

Question 20. Solve the equation

• 
  `x^2-7x+12=0`

• Answer: x = 4 and x = 3

Question 22. Solve the equation

• 
  `x^2-6x=27`

• Answer: x = 9 and x = - 3.

Step-by-step explanation:

Question 16. Factor the polynomial

`44+15h+h^2`

1. Rearrange the terms:

• 
  `h^2+15h+44`

2. Open two parenthesis and place the common variable, h, as the first term of each.

• 
  `(h+a)(h+b)`

You are going to determine the values of a and b.

3. The values of a and b must satisfy that their product is 44 and their sum is 15.

• a + b = 15 and a × b = 44

• 11 and 4 meet those conditions: 11 + 4 = 15, and 11 × 4 = 44.

So, the factored polynomial is:

• 
  `(h+4)(h+11)`

Question 17. Factor the polynomial

`40-22x+x^2`

1. Rearrange the terms:

• 
  `x^2-22x+40`

2. Write two binomials; each with first term x

• (x-a)(x-b)

The negative sign for a comes from the negative sign before 22x; the negative sign of b comes from the product of the signs of -22x and + 40.

3. Find a and b such that a + b = 22 and a × b = 40

• 20 + 2 = 22 and 20 × 2 = 40, so the binomials are (x - 2) and (x - 20)

And the factored polynomial is:

• 
  `(x-2)(x-20)`

Question 18. Factor the polynomial

`-24-10x+x^2`

1. Rearrange the terms

• 
  `x^2-10x-24`

2. Sketch two binomials

• 
  `(x-a)(x+b)`

The negative sign for a corresponds to the negative sign for -10x, and the positive sign for b corresponds to the multplication of the signs of -10x and -4.

3. Find a and b such that their product is -24 and their aum is - 10.

Those numbers are - 12 and + 2:

• - 12 + 2 = - 10
• - 12 × (2) = - 24

Thus, the two factors are (x - 12) and (x +2).

And the factored polynomial is:

• 
  `(x-12)(x+2)`

Question 19. Factor the polynomial

`-42-m+m^2`

1. Rearrange the terms

• 
  `m^2-m-42`

2. Sketch the factors:

• 
  `(m-a)(m+b)`

The negative sign for a corresponds to the negative sign in front of m, the positive sign for b corresponds to the product of the signs of -m and -42.

3. Find two numbers, a and b, such that - a + b = - 1, and a × b = - 42

Those numbers are 6 and 7:

• - 7 + 6 = - 1
• -7 × 6 = - 42

Then, the factors are m - 7 and m + 6.

The factored polynomial is:

• 
  `(m-7)(m+6)`

Question 20. Solve the equation

`x^2-7x+12=0`

1. Factor the left side:

Find two numbers that sum -7 and their product is + 12. Those two numbers are - 4 and - 3.

• 
  `(x-4)(x-3)=0`

2. Use the zero product rule

• x - 4 = 0 or x - 3 = 0

• x = 4 or x = 3

Both, x = 4 and x = 3 are solutions.

Hence, the solutions are x = 4 and x = 3.

Question 22. Solve the equation

`x^2-6x=27`

1. Move 27 to the left side (using subtraction property of equalities):

• 
  `x^2-6x-27=0`

2. Factor the polynomial.

Find two numbers whose sum is - 6 and their product is - 27.

Those numbers are - 9 and + 3:

• - 9 + 3 = - 6
• - 9 × 3 = 27

• 
  `(x-9)(x+3)=0`

3. Zero product rule

`x-9=0\\ \\ x=9\\ \\ x+3=0\\ \\ x=-3`

The two solutions are: x = 9 and x = -3