Complete the factored form.3x4 + 16x + 21 = (3x + 7)( )
1 answer:
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Answer:
There are six problems circled in red.
As requested, only the analytical solutions are shown.
Question 16. Factor the polynomial
- Answer: (h + 4) (h + 11)
Question 17. Factor the polynomial
- Answer: (x - 2) (x -20)
Question 18. Factor the polynomial
- Answer: (x - 12) (x + 2)
Question 19. Factor the polynomial
- Answer: (m - 7) (m + 6)
Question 20. Solve the equation
- Answer: x = 4 and x = 3
Question 22. Solve the equation
- Answer: x = 9 and x = - 3.
Explanation:
Question 16. Factor the polynomial
1. Rearrange the terms:
2. Open two parenthesis and place the common variable, h, as the first term of each.
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:
Question 17. Factor the polynomial
1. Rearrange the terms:
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:
Question 18. Factor the polynomial
1. Rearrange the terms
2. Sketch two binomials
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:
Question 19. Factor the polynomial
1. Rearrange the terms
2. Sketch the factors:
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:
Question 20. Solve the equation
1. Factor the left side:
Find two numbers that sum -7 and their product is + 12. Those two numbers are - 4 and - 3.
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
1. Move 27 to the left side (using subtraction property of equalities):
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
3. Zero product rule
The two solutions are: x = 9 and x = -3