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### Question 1
# Explanation:
## Step 1: Factor each term
Factor $8x^2 = 2 \times 4 \times x^2$, $ -14x = 2 \times (-7) \times x$, $32 = 2 \times 16$.
## Step 2: Identify GCF
The greatest common factor (GCF) is the largest factor common to all terms. The common factor here is $2$. Wait, no, wait: Wait, $8x^2 = 2\times4x^2$, $-14x = 2\times(-7x)$, $32 = 2\times16$. Wait, but wait, $8x^2 = 2\times4x^2$, $-14x = 2\times(-7x)$, $32 = 2\times16$. But wait, actually, let's check again: $8x^2 = 2\times4x^2$, $-14x = 2\times(-7x)$, $32 = 2\times16$. Wait, but the options are $2x$, $2$, $4$, $8$. Wait, no, wait, maybe I made a mistake. Wait, $8x^2 = 2\times4x^2$, $-14x = 2\times(-7x)$, $32 = 2\times16$. So the GCF of the coefficients $8$, $-14$, $32$ is $2$, and there is no common $x$ term (since $32$ has no $x$). So the GCF is $2$. Wait, but the options: (a) $2x$, (b) $2$, (c) $4$, (d) $8$. So the answer should be (b) 2? Wait, no, wait, wait: Wait, $8x^2 = 2\times4x^2$, $-14x = 2\times(-7x)$, $32 = 2\times16$. So the GCF is $2$. So the answer is (b) 2. Wait, but let me check again. Wait, $8x^2 = 2\times4x^2$, $-14x = 2\times(-7x)$, $32 = 2\times16$. So the greatest common factor is $2$. So the answer is (b) 2.

# Answer: (b) 2

### Question 2
# Explanation:
We need to check which expression is $2x(4x - 3)+5(4x - 3)$ fully factored. Factoring by grouping, we can factor out $(4x - 3)$ from both terms: $(4x - 3)(2x + 5)$. Let's check the options: (a) $(4x - 3)(2x + 5)$, (b) $8x^2 - 6x + 20x - 15$ (this is expanded, not factored), (c) $8x^2 + 14x - 15$ (also expanded), (d) $(4x - 3)(2x - 5)$ (incorrect sign). So the fully factored form is $(4x - 3)(2x + 5)$, which is option (a).

# Answer: (a) $(4x - 3)(2x + 5)$

### Question 3
# Explanation:
We need to find the missing factor of $6x^2 - 11x + 4=(3x - 4)(\quad)$. Let's perform polynomial division or use factoring. Let the missing factor be $ax + b$. Then $(3x - 4)(ax + b)=3ax^2+(3b - 4a)x - 4b$. Set equal to $6x^2 - 11x + 4$. So $3a = 6$ ⇒ $a = 2$. Then $3b - 4a=-11$ ⇒ $3b - 8=-11$ ⇒ $3b=-3$ ⇒ $b = -1$. So the missing factor is $2x - 1$, which is option (b).

# Answer: (b) $(2x - 1)$

### Question 4
# Explanation:
In a quadratic equation, to solve it by factoring (or using other methods), one side of the equation must be zero (so we can use the zero - product property: if $ab = 0$, then $a = 0$ or $b = 0$). So the answer is (b) zero.

# Answer: (b) zero

### Question 5
# Explanation:
The quadratic formula is used to solve quadratic equations of the form $ax^2+bx + c = 0$ ($a
eq0$). The quadratic formula is $x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$. Let's check the options: (a) $x=\frac{b\pm\sqrt{b^2 - 4ac}}{2a}$ (incorrect sign of $b$), (b) $x=-b\pm\frac{\sqrt{b^2 - 4ac}}{2a}$ (incorrect format), (c) $x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$ (correct), (d) $x=\frac{-b\pm\sqrt{b - 4ac}}{2a}$ (missing square root on $b^2$). So the answer is (c).

# Answer: (c) $x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

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QUESTION IMAGE

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Explanation:

Question 1

Step 1: Factor each term

Step 2: Identify GCF

Answer:

Question 2