https://file.aiquickdraw.com/mathbot/file/17265359030256x4drakc.jpg

It seems like you've uploaded a math worksheet image, which contains polynomial factorization problems. I'll help you with questions 31-65, providing clear solutions for them.

Let's start with problem 31 and go through each one:

### 31. \( x^3 + 8x^2 - x - 8 \)
Factor by grouping:
\[
x^2(x + 8) - 1(x + 8) = (x^2 - 1)(x + 8)
\]
Now, \( x^2 - 1 \) is a difference of squares:
\[
(x - 1)(x + 1)(x + 8)
\]

### 32. \( p^2q - 25q + 3p^2 - 75 \)
Group terms:
\[
(p^2q + 3p^2) - (25q + 75)
\]
Factor out the common terms:
\[
p^2(q + 3) - 25(q + 3) = (p^2 - 25)(q + 3)
\]
Finally, factor \( p^2 - 25 \) as a difference of squares:
\[
(p - 5)(p + 5)(q + 3)
\]

### 33. \( 16x^2 + 2xy - y^2 \)
This is a quadratic in terms of \( x \):
\[
(4x - y)(4x + y)
\]

### 34. \( 2xy - x^2y - 6 + 3x \)
Group and factor:
\[
x(2y - xy) + 3(x - 2)
\]

### 35. \( 6x^2 + 23x + 20 \)
Factor the quadratic:
\[
(2x + 5)(3x + 4)
\]

### 36. \( 9x^2 + 15x + 4 \)
Factor the quadratic:
\[
(3x + 4)(3x + 1)
\]

### 37. \( 8m^2 - 6m - 9 \)
Factor:
\[
(4m + 3)(2m - 3)
\]

### 38. \( 16 - 10x + x^2 \)
This is a perfect square trinomial:
\[
(x - 5)(x - 2)
\]

### 39. \( 16 - w^2 + 2w \)
Factor by completing the square:
\[
(4 + w^2)(4w - 4)
\]

### 40. \( ay - yx - x^2 + ax \)
Factor:
\[
(a - x)(y + x)
\]

### 41. \( x^2 - 6x - 16 \)
Factor the quadratic:
\[
(x + 2)(x - 8)
\]

### 42. \( x^2 - 10xy + 24y^2 \)
Factor:
\[
(x - 4y)(x - 6y)
\]

### 43. \( x^2 + 3x + 2 \)
Factor:
\[
(x + 1)(x + 2)
\]

### 44. \( x^2 - 6x + 9 \)
This is a perfect square:
\[
(x - 3)^2
\]

### 45. \( x^2 + 7x - 6 \)
Factor:
\[
(x - 6)(x + 1)
\]

### 46. \( x^2 + 7x - 8 \)
Factor:
\[
(x + 8)(x + 7)
\]

### 47. \( x^2 + 8x - 7 \)

### Let me know

Math worksheet involving polynomial factorization from questions 31-65.

Learn how to factor polynomials step-by-step with solutions for questions 31-65. Topics covered include polynomial factorization, difference of squares, and quadratic equations. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation