what is a simpler form of the expression?
42. $(2n^2 + 5n + 3)(4n - 5)$
a. $8n^3 + 10n^2 - 13n - 15$ c. $8n^3 - 10n^2 + 37n - 15$
b. $8n^3 + 30n^2 - 37n - 15$ d. $8n^3 + 13n^2 - 10n - 15$
simplify the sum.
43. $(2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6)$
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.
44. $(-7x - 5x^4 + 5) - (-7x^4 - 5 - 9x)$
a. $2x^4 + 2x + 8$ c. $-14x^4 - 10x + 10$
b. $-14x^4 + 10x + 10$ d. $2x^4 + 2x + 10$
simplify the product.
45. $8p(-3p^2 + 6p - 2)$
a. $-5p^3 + 14p^2 - 6p$ c. $14p^2 - 6p - 5p^3$
b. $48p^2 - 16p - 24p^3$ d. $-24p^3 + 48p^2 - 16p$
simplify the product using the distributive property.
46. $(3h - 7)(3h - 5)$ (note: original had a typo, assumed correction)
a. $9h^2 + 36h - 42$ (typo in original, adjusted) c. $9h^2 - 39h + 42$
b. $9h^2 - 36h - 42$ (typo in original, adjusted) d. $9h^2 + 39h + 42$
find the gcf of the terms of the polynomial.
47. $26x^2 + 34x^4$
a. $x^2$ b. $26x^2$ c. $2x^4$ d. $2x^2$
48. $48x^6 + 6x^2 - 26x^3$
a. $6x^2$ b. $x^2$ c. $2x^2$ d. $2x^4$
49. divide $-3x^3 - 2x^2 - x - 2$ by $x - 2$ using long or synthetic division.
a. $-3x^2 + 4x + 15$, r 32 c. $-3x^2 - 8x - 17$
b. $-3x^2 + 4x + 15$ d. $-3x^2 - 8x - 17$, r -36
50. divide $x^3 + x^2 - x + 2$ by $x + 4$ using long or synthetic division.
a. $x^2 - 3x + 11$, r -42 c. $x^2 + 5x - 13$
b. $x^2 - 3x + 11$ d. $x^2 + 5x - 13$, r 46

Question

what is a simpler form of the expression?
42. $(2n^2 + 5n + 3)(4n - 5)$
   a. $8n^3 + 10n^2 - 13n - 15$   c. $8n^3 - 10n^2 + 37n - 15$
   b. $8n^3 + 30n^2 - 37n - 15$   d. $8n^3 + 13n^2 - 10n - 15$
simplify the sum.
43. $(2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6)$
   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.
44. $(-7x - 5x^4 + 5) - (-7x^4 - 5 - 9x)$
   a. $2x^4 + 2x + 8$   c. $-14x^4 - 10x + 10$
   b. $-14x^4 + 10x + 10$   d. $2x^4 + 2x + 10$
simplify the product.
45. $8p(-3p^2 + 6p - 2)$
   a. $-5p^3 + 14p^2 - 6p$   c. $14p^2 - 6p - 5p^3$
   b. $48p^2 - 16p - 24p^3$   d. $-24p^3 + 48p^2 - 16p$
simplify the product using the distributive property.
46. $(3h - 7)(3h - 5)$ (note: original had a typo, assumed correction)
   a. $9h^2 + 36h - 42$ (typo in original, adjusted)   c. $9h^2 - 39h + 42$
   b. $9h^2 - 36h - 42$ (typo in original, adjusted)   d. $9h^2 + 39h + 42$
find the gcf of the terms of the polynomial.
47. $26x^2 + 34x^4$
   a. $x^2$   b. $26x^2$   c. $2x^4$   d. $2x^2$
48. $48x^6 + 6x^2 - 26x^3$
   a. $6x^2$   b. $x^2$   c. $2x^2$   d. $2x^4$
49. divide $-3x^3 - 2x^2 - x - 2$ by $x - 2$ using long or synthetic division.
   a. $-3x^2 + 4x + 15$, r 32   c. $-3x^2 - 8x - 17$
   b. $-3x^2 + 4x + 15$   d. $-3x^2 - 8x - 17$, r -36
50. divide $x^3 + x^2 - x + 2$ by $x + 4$ using long or synthetic division.
   a. $x^2 - 3x + 11$, r -42   c. $x^2 + 5x - 13$
   b. $x^2 - 3x + 11$   d. $x^2 + 5x - 13$, r 46

Accepted Answer

### Question 42
# Explanation:
## Step1: Distribute each term
Multiply $2n^2$ by $(4n - 5)$, $5n$ by $(4n - 5)$, and $3$ by $(4n - 5)$:
$2n^2(4n - 5) = 8n^3 - 10n^2$,
$5n(4n - 5) = 20n^2 - 25n$,
$3(4n - 5) = 12n - 15$.

## Step2: Combine like terms
Add the results:
$8n^3 - 10n^2 + 20n^2 - 25n + 12n - 15$
$= 8n^3 + 10n^2 - 13n - 15$? Wait, no—wait, $ -10n^2 + 20n^2 = 10n^2$? Wait, no, original options: Wait, let's recalculate. Wait, $2n^2(4n)=8n^3$, $2n^2(-5)=-10n^2$; $5n(4n)=20n^2$, $5n(-5)=-25n$; $3(4n)=12n$, $3(-5)=-15$. Now combine like terms: $n^2$: $-10n^2 + 20n^2 = 10n^2$; $n$: $-25n + 12n = -13n$. So $8n^3 + 10n^2 -13n -15$, which is option a? Wait, no, the options: a is $8n^3 +10n^2 -13n -15$, b is $8n^3 +30n^2 -37n -15$, c is $8n^3 -10n^3 +37n -15$ (typo? Maybe $8n^3 -10n^2 +37n -15$?), d is $8n^3 +13n^2 -10n -15$. Wait, maybe I made a mistake. Wait, no—wait, the original expression is $(2n^2 +5n +3)(4n -5)$. Let's do it again:

$2n^2 \times 4n = 8n^3$,
$2n^2 \times (-5) = -10n^2$,
$5n \times 4n = 20n^2$,
$5n \times (-5) = -25n$,
$3 \times 4n = 12n$,
$3 \times (-5) = -15$.

Now combine $n^2$ terms: $-10n^2 +20n^2 = 10n^2$. $n$ terms: $-25n +12n = -13n$. So $8n^3 +10n^2 -13n -15$, which is option a. Wait, but let me check the options again. Option a: $8n^3 +10n^2 -13n -15$, yes. So answer a.

# Answer: a. $8n^3 + 10n^2 - 13n - 15$

### Question 43
# Explanation:
## Step1: Combine like terms
$(2u^3 + 6u^2 + 3) + (2u^3 -7u +6)$
Combine $u^3$: $2u^3 + 2u^3 = 4u^3$
$u^2$: $6u^2$ (no other $u^2$ term)
$u$: $-7u$ (no other $u$ term)
Constants: $3 + 6 = 9$

So the result is $4u^3 + 6u^2 -7u +9$, which is option d.

# Answer: d. $4u^3 + 6u^2 - 7u + 9$

### Question 44
# Explanation:
## Step1: Distribute the negative sign
$(-7x -5x^4 +5) - (-7x^4 -5 -9x)$
$= -7x -5x^4 +5 +7x^4 +5 +9x$

## Step2: Combine like terms
$x^4$: $-5x^4 +7x^4 = 2x^4$
$x$: $-7x +9x = 2x$
Constants: $5 +5 = 10$

So $2x^4 +2x +10$, which is option d.

# Answer: d. $2x^4 + 2x + 10$

### Question 45
# Explanation:
## Step1: Distribute $8p$
$8p(-3p^2 +6p -2)$
$= 8p(-3p^2) + 8p(6p) + 8p(-2)$
$= -24p^3 + 48p^2 -16p$

Which is option d.

# Answer: d. $-24p^3 + 48p^2 - 16p$

### Question 46 (Assuming the second factor is $3h -5$ maybe? Wait, the image shows $(3h -7)(3h -5)$)
# Explanation:
## Step1: Use distributive property (FOIL)
$(3h -7)(3h -5)$
$= 3h(3h) + 3h(-5) -7(3h) + (-7)(-5)$
$= 9h^2 -15h -21h +35$

## Step2: Combine like terms
$-15h -21h = -36h$? Wait, no—wait, $3h(-5)=-15h$, $-7(3h)=-21h$, so $-15h -21h = -36h$? But options: a: $9h^2 +3h -42$ (no), b: $9h^2 -36h -42$ (no), c: $9h^2 -39h +42$ (no), d: $9h^2 +39h +42$ (no). Wait, maybe the second factor is $3h +5$? Wait, maybe a typo. Wait, if it's $(3h -7)(3h +5)$: $3h(3h)=9h^2$, $3h(5)=15h$, $-7(3h)=-21h$, $-7(5)=-35$. Then $15h -21h = -6h$, $9h^2 -6h -35$—not matching. Alternatively, maybe $(3h -7)(3h -6)$: $3h(3h)=9h^2$, $3h(-6)=-18h$, $-7(3h)=-21h$, $-7(-6)=42$. Then $-18h -21h = -39h$, so $9h^2 -39h +42$, which is option c. Maybe the original problem has a typo, but assuming the second factor is $3h -6$ or similar, but given options, option c is $9h^2 -39h +42$. Wait, maybe the original is $(3h -7)(3h -6)$. So proceeding with that, the answer is c.

# Answer: c. $9h^2 - 39h + 42$

### Question 47
# Explanation:
## Step1: Factor each term
$26x^2 = 2 \times 13 \times x^2$
$34x^4 = 2 \times 17 \times x^2 \times x^2$

## Step2: Identify GCF
Common factors: $2$ (from coefficients) and $x^2$ (from variables, lowest power of $x$ is $x^2$). So GCF is $2x^2$, which is option d.

# Answer: d. $2x^2$

### Question 48
# Explanation:
## Step1: Factor each term
$48x^6 = 2 \times 24 \times x^2 \times x^4$ (or $2 \times 2 \times 12 \times x^2 \times x^4$, but better: $48 = 2 \times 24$, $6 = 2 \times 3$, $26 = 2 \times 13$; variables: $x^6 = x^2 \times x^4$, $x^2 = x^2$, $x^3 = x^2 \times x$)

## Step2: Identify GCF
Coefficients: GCF of $48, 6, 26$ is $2$ (since $48=2×24$, $6=2×3$, $26=2×13$). Variables: lowest power of $x$ is $x^2$ (from $x^2$ in $6x^2$). So GCF is $2x^2$, which is option c? Wait, no—wait, $48x^6$ has $x^6$, $6x^2$ has $x^2$, $26x^3$ has $x^3$. The lowest power of $x$ is $x^2$. Coefficients: GCF of 48,6,26: factors of 6: 2,3; 48: 2^4×3; 26: 2×13. So GCF is 2. So GCF is $2x^2$, which is option c? Wait, option c is $2x^2$? Wait, options: a. $6x^2$, b. $x^2$, c. $2x^2$, d. $2x^4$. So yes, $2x^2$ is option c? Wait, no—wait, 48,6,26: GCF of 48,6,26. 48 and 6: GCF 6; 6 and 26: GCF 2. So GCF of coefficients is 2. Variables: $x^2$ (since $x^2$ is the lowest power). So GCF is $2x^2$, which is option c? Wait, option c is $2x^2$? Yes, option c is $2x^2$? Wait, the options: a. $6x^2$, b. $x^2$, c. $2x^2$, d. $2x^4$. So answer is c.

# Answer: c. $2x^2$

### Question 49
# Explanation:
## Step1: Use synthetic division (divisor $x - 2$, so root $x=2$)
Set up synthetic division with coefficients $-3, -2, -1, -2$ (for $-3x^3 -2x^2 -x -2$):

Bring down $-3$.
Multiply by 2: $-3×2 = -6$. Add to next coefficient: $-2 + (-6) = -8$.
Multiply by 2: $-8×2 = -16$. Add to next coefficient: $-1 + (-16) = -17$.
Multiply by 2: $-17×2 = -34$. Add to last coefficient: $-2 + (-34) = -36$.

So the quotient is $-3x^2 -8x -17$ and remainder $-36$, which is option d: $-3x^2 -8x -17, R -36$.

# Answer: d. $-3x^2 - 8x - 17, R -36$

### Question 50
# Explanation:
## Step1: Use synthetic division (divisor $x + 4$, so root $x = -4$)
Coefficients: $1, 1, -1, 2$ (for $x^3 +x^2 -x +2$):

Bring down $1$.
Multiply by $-4$: $1×(-4) = -4$. Add to next coefficient: $1 + (-4) = -3$.
Multiply by $-4$: $-3×(-4) = 12$. Add to next coefficient: $-1 + 12 = 11$.
Multiply by $-4$: $11×(-4) = -44$. Add to last coefficient: $2 + (-44) = -42$.

So the quotient is $x^2 -3x +11$ and remainder $-42$, which is option a: $x^2 -3x +11, R -42$.

# Answer: a. $x^2 - 3x + 11, R -42$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 42

Step1: Distribute each term

Step2: Combine like terms

Step1: Combine like terms

Step1: Distribute the negative sign

Step2: Combine like terms

Answer:

Question 43