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

Answer:

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.

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