what is a simpler form of the expression?
19. $(2n^3 + 5n + 3)(4n - 5)$
a. $8n^3 + 10n^2 - 13n - 15$ c. $8n^3 - 10n^2 + 37n - 15$
b. $8n^3 + 30n^2 - 37n - 15$ d. $8n^3 + 13n^2 - 10n - 15$
what is the sum or difference?
20. $6x^7 + 8x^7$
a. $14x^7$ b. $-2x^7$ c. $14x^{14}$ d. $48x^7$
21. $2x^7 - 8x^7$
a. $-6x^{14}$ b. $10x^7$ c. $-16x^7$ d. $-6x^7$
simplify the sum.
22. $(2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6)$
a. $9 - 7u + 6u^2 + 4u^3$ c. $0u^3 - 7u^2 + 6u - 9$
b. $0u^3 + 6u^2 - 7u + 9$ d. $4u^3 + 6u^2 - 7u + 9$
simplify the difference.
23. $(4w^2 - 7w - 6) - (8w^2 + 2w - 3)$
a. $-4w^2 - 9w - 3$ c. $-4w^2 - 5w - 9$
b. $12w^2 + 9w + 3$ d. $12w^2 - 5w - 9$
simplify the product.
24. $2n(n^2 + 3n + 4)$
a. $2n^3 + 6n^2 + 8n$ c. $2n^3 + 6n + 8$
b. $2n^3 + 3n + 4$ d. $n^2 + 5n + 4$
multiply the polynomials.
25. $(3x + 4)(2x - 6)$
a. $6x^2 + 26x + 24$ c. $6x^2 - 26x + 24$
b. $6x^2 - 10x - 24$ d. $6x^2 + 10x - 24$
what are the zeros of the function? what are their multiplicities?
26. $f(x) = 4x^3 - 12x^2 - 16x$
a. the numbers 1, $-4$, and 0 are zeros of multiplicity 2
b. the numbers $-1$, 4, and 0 are zeros of multiplicity 2
c. the numbers $-1$, 4, and 0 are zeros of multiplicity 1
d. the numbers 1, $-4$, and 0 are zeros of multiplicity 1

Question

what is a simpler form of the expression?
19. $(2n^3 + 5n + 3)(4n - 5)$
   a. $8n^3 + 10n^2 - 13n - 15$   c. $8n^3 - 10n^2 + 37n - 15$
   b. $8n^3 + 30n^2 - 37n - 15$   d. $8n^3 + 13n^2 - 10n - 15$
what is the sum or difference?
20. $6x^7 + 8x^7$
   a. $14x^7$   b. $-2x^7$   c. $14x^{14}$   d. $48x^7$
21. $2x^7 - 8x^7$
   a. $-6x^{14}$   b. $10x^7$   c. $-16x^7$   d. $-6x^7$
simplify the sum.
22. $(2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6)$
   a. $9 - 7u + 6u^2 + 4u^3$   c. $0u^3 - 7u^2 + 6u - 9$
   b. $0u^3 + 6u^2 - 7u + 9$   d. $4u^3 + 6u^2 - 7u + 9$
simplify the difference.
23. $(4w^2 - 7w - 6) - (8w^2 + 2w - 3)$
   a. $-4w^2 - 9w - 3$   c. $-4w^2 - 5w - 9$
   b. $12w^2 + 9w + 3$   d. $12w^2 - 5w - 9$
simplify the product.
24. $2n(n^2 + 3n + 4)$
   a. $2n^3 + 6n^2 + 8n$   c. $2n^3 + 6n + 8$
   b. $2n^3 + 3n + 4$   d. $n^2 + 5n + 4$
multiply the polynomials.
25. $(3x + 4)(2x - 6)$
   a. $6x^2 + 26x + 24$   c. $6x^2 - 26x + 24$
   b. $6x^2 - 10x - 24$   d. $6x^2 + 10x - 24$
what are the zeros of the function? what are their multiplicities?
26. $f(x) = 4x^3 - 12x^2 - 16x$
   a. the numbers 1, $-4$, and 0 are zeros of multiplicity 2
   b. the numbers $-1$, 4, and 0 are zeros of multiplicity 2
   c. the numbers $-1$, 4, and 0 are zeros of multiplicity 1
   d. the numbers 1, $-4$, and 0 are zeros of multiplicity 1

Accepted Answer

### Question 19
# Explanation:
## Step1: Distribute each term
Multiply $2n^2$ by $(4n - 5)$: $2n^2\times4n=8n^3$, $2n^2\times(-5)=-10n^2$
Multiply $5n$ by $(4n - 5)$: $5n\times4n = 20n^2$, $5n\times(-5)=-25n$
Multiply $3$ by $(4n - 5)$: $3\times4n = 12n$, $3\times(-5)=-15$
## Step2: Combine like terms
For $n^3$: $8n^3$
For $n^2$: $-10n^2 + 20n^2=10n^2$
For $n$: $-25n+12n=-13n$
Constant term: $-15$
So the expression is $8n^3 + 10n^2-13n - 15$
# Answer:
a. $8n^3 + 10n^2-13n - 15$

### Question 20
# Explanation:
## Step1: Combine like terms
Since $6x^7$ and $8x^7$ have the same variable and exponent, add their coefficients: $6 + 8 = 14$
## Step2: Write the result
The sum is $14x^7$
# Answer:
a. $14x^7$

### Question 21
# Explanation:
## Step1: Combine like terms
Subtract the coefficients of $2x^7$ and $8x^7$: $2-8=-6$
The variable and exponent remain $x^7$
## Step2: Write the result
The difference is $-6x^7$
# Answer:
d. $-6x^7$

### Question 22
# Explanation:
## Step1: Remove parentheses
$(2u^3+6u^2 + 3)+(2u^3-7u + 6)=2u^3+6u^2 + 3+2u^3-7u + 6$
## Step2: Combine like terms
For $u^3$: $2u^3+2u^3 = 4u^3$
For $u^2$: $6u^2$
For $u$: $-7u$
Constant term: $3 + 6=9$
So the expression is $4u^3+6u^2-7u + 9$
# Answer:
d. $4u^3+6u^2-7u + 9$

### Question 23
# Explanation:
## Step1: Distribute the negative sign
$(4w^2-7w - 6)-(8w^2+2w - 3)=4w^2-7w - 6-8w^2-2w + 3$
## Step2: Combine like terms
For $w^2$: $4w^2-8w^2=-4w^2$
For $w$: $-7w-2w=-9w$
Constant term: $-6 + 3=-3$
So the expression is $-4w^2-9w - 3$
# Answer:
a. $-4w^2-9w - 3$

### Question 24
# Explanation:
## Step1: Distribute $2n$
Multiply $2n$ by $n^2$: $2n\times n^2 = 2n^3$
Multiply $2n$ by $3n$: $2n\times3n=6n^2$
Multiply $2n$ by $4$: $2n\times4 = 8n$
## Step2: Write the result
The product is $2n^3+6n^2 + 8n$
# Answer:
a. $2n^3+6n^2 + 8n$

### Question 25
# Explanation:
## Step1: Distribute each term
Multiply $3x$ by $(2x - 6)$: $3x\times2x = 6x^2$, $3x\times(-6)=-18x$
Multiply $4$ by $(2x - 6)$: $4\times2x = 8x$, $4\times(-6)=-24$
## Step2: Combine like terms
For $x^2$: $6x^2$
For $x$: $-18x + 8x=-10x$
Constant term: $-24$
So the product is $6x^2-10x - 24$
# Answer:
b. $6x^2-10x - 24$

### Question 26
# Explanation:
## Step1: Factor the function
First, factor out $4x$: $f(x)=4x(x^2-3x - 4)$
Then factor the quadratic: $x^2-3x - 4=(x - 4)(x + 1)$
So $f(x)=4x(x - 4)(x + 1)$
## Step2: Find the zeros
Set $f(x)=0$: $4x = 0$ gives $x = 0$; $x - 4=0$ gives $x = 4$; $x + 1=0$ gives $x=-1$
Each factor has an exponent of $1$, so multiplicity is $1$ for each zero.
# Answer:
c. the numbers $-1$, $4$, and $0$ are zeros of multiplicity $1$

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QUESTION IMAGE

Question

Explanation:

Question 19

Step1: Distribute each term

Step2: Combine like terms

Step1: Combine like terms

Step2: Write the result

Step1: Combine like terms

Step2: Write the result

Answer:

Question 20