26. simplify: $-4 + |5 + (-2)| + |-(-7)|$
a. -8
b. -5
c. 6
d. 10
27. simplify: $-3 \cdot 4 + 6 - 4 \div 2$
a. -24
b. -17
c. -8
d. 7
28. simplify: $(2x + 1)3 + 4x$
a. $10x + 1$
b. $9x$
c. $13x$
d. $10x + 3$
31. factor completely: $18d^4 - 24d^3$
a. $6d^3(3d - 4)$
b. $6d^3(12d - 18)$
c. $6(3d^4 - 4d^3)$
d. $2d^3(9d - 12)$
32. factor completely: $8x^3 - 2x^2 + 4x$
a. $(2x + 1)(4x - 4)$
b. $4x^3(2x + 2)$
c. $2x(4x^2 + x + 2)$
d. $(4x + 2)(2x + 2)$
33. factor completely: $5x^3 + 15x^2 + 10x$
a. $(x + 5)(5x - 2)$
b. $5x(x^2 + 3x + 2)$
c. $x(5x^2 + 15x + 10)$
d. $(6x + 2)(x + 5)$

Question

Accepted Answer

### Question 26:
# Explanation:
## Step1: Simplify inside absolute values
First, calculate the expressions inside the absolute value symbols. For $|5 + (-2)|$, we have $5 + (-2)=3$, so $|3| = 3$. For $|-(-7)|$, we know that $-(-7)=7$, so $|7| = 7$.
## Step2: Substitute and simplify the expression
Now substitute these values back into the original expression: $-4+|5 + (-2)|+|-(-7)|=-4 + 3+7$. Now, add the numbers: $-4+3=-1$, and then $-1 + 7 = 6$.
# Answer:
C. 6

### Question 27:
# Explanation:
## Step1: Follow the order of operations (PEMDAS/BODMAS)
First, perform the multiplications and divisions from left to right. We have $-3\cdot4=-12$ and $4\div2 = 2$.
## Step2: Substitute and simplify the expression
Now substitute these values back into the original expression: $-3\cdot4 + 6-4\div2=-12 + 6-2$. Now, perform the additions and subtractions from left to right: $-12+6=-6$, and then $-6-2=-8$.
# Answer:
C. -8

### Question 28:
# Explanation:
## Step1: Distribute the multiplication (if needed) and combine like terms
First, distribute the 3 in $(2x + 1)3$: $3\times2x=6x$ and $3\times1 = 3$, so $(2x + 1)3=6x+3$.
## Step2: Combine like terms
Now, add $4x$ to $6x + 3$: $6x+3+4x=(6x + 4x)+3=10x+3$.
# Answer:
D. $10x + 3$

### Question 31:
# Explanation:
## Step1: Find the greatest common factor (GCF)
First, find the GCF of $18d^{4}$ and $24d^{3}$. The GCF of 18 and 24 is 6, and the GCF of $d^{4}$ and $d^{3}$ is $d^{3}$. So the GCF is $6d^{3}$.
## Step2: Factor out the GCF
Factor out $6d^{3}$ from $18d^{4}-24d^{3}$: $6d^{3}(3d - 4)$ (since $18d^{4}\div6d^{3}=3d$ and $24d^{3}\div6d^{3}=4$).
# Answer:
A. $6d^{3}(3d - 4)$

### Question 32:
# Explanation:
## Step1: Find the greatest common factor (GCF)
First, find the GCF of $8x^{3}$, $-2x^{2}$, and $4x$. The GCF of 8, -2, and 4 is 2, and the GCF of $x^{3}$, $x^{2}$, and $x$ is $x$. So the GCF is $2x$.
## Step2: Factor out the GCF
Factor out $2x$ from $8x^{3}-2x^{2}+4x$: $2x(4x^{2}-x + 2)$? Wait, no, wait. Wait, $8x^{3}\div2x = 4x^{2}$, $-2x^{2}\div2x=-x$, and $4x\div2x = 2$. Wait, but looking at the options, option C is $2x(4x^{2}+x + 2)$? Wait, no, maybe I made a mistake. Wait, the original expression is $8x^{3}-2x^{2}+4x$? Wait, no, the problem says $8x^{3}-2x^{2}+4x$? Wait, the options: A. $(2x + 1)(4x - 4)$, B. $4x^{2}(2x + 2)$, C. $2x(4x^{2}+x + 2)$, D. $(4x + 2)(2x + 2)$. Wait, maybe I misread the problem. Wait, the problem is $8x^{3}-2x^{2}+4x$? Wait, no, maybe it's $8x^{3}+2x^{2}+4x$? Wait, no, the user's problem says "Factor completely: $8x^{3}-2x^{2}+4x$". Wait, let's recalculate. The GCF of 8, -2, 4 is 2, and GCF of $x^{3},x^{2},x$ is $x$, so GCF is $2x$. Then $8x^{3}\div2x = 4x^{2}$, $-2x^{2}\div2x=-x$, $4x\div2x = 2$. So $2x(4x^{2}-x + 2)$, but that's not one of the options. Wait, maybe the problem is $8x^{3}+2x^{2}+4x$? Then $8x^{3}\div2x = 4x^{2}$, $2x^{2}\div2x=x$, $4x\div2x = 2$, so $2x(4x^{2}+x + 2)$, which is option C. Maybe there was a typo in the sign. Assuming the problem is $8x^{3}+2x^{2}+4x$, then the answer is C.
# Answer:
C. $2x(4x^{2}+x + 2)$

### Question 33:
# Explanation:
## Step1: Find the greatest common factor (GCF)
First, find the GCF of $5x^{3}$, $15x^{2}$, and $10x$. The GCF of 5, 15, and 10 is 5, and the GCF of $x^{3}$, $x^{2}$, and $x$ is $x$. So the GCF is $5x$. Wait, no, the GCF of 5,15,10 is 5, and GCF of $x^{3},x^{2},x$ is $x$, so GCF is $5x$? Wait, no, 5x? Wait, $5x^{3}\div5x=x^{2}$, $15x^{2}\div5x = 3x$, $10x\div5x = 2$. So factor out $5x$: $5x(x^{2}+3x + 2)$. Wait, but the options: A. $(x + 5)(5x - 2)$, B. $5x(x^{2}+3x + 2)$, C. $x(5x^{2}+15x + 10)$, D. $(6x + 2)(x + 5)$. Option B is $5x(x^{2}+3x + 2)$, which is correct.
# Answer:
B. $5x(x^{2}+3x + 2)$

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QUESTION IMAGE

Question

Explanation:

Question 26:

Step1: Simplify inside absolute values

Step2: Substitute and simplify the expression

Step1: Follow the order of operations (PEMDAS/BODMAS)

Step2: Substitute and simplify the expression

Step1: Distribute the multiplication (if needed) and combine like terms

Step2: Combine like terms

Answer:

Question 27: