Math Problem Statement

Answer all these questions

Answer all these polynomial factoring problems as shown in the uploaded images.

Solution

I will now extract the questions and work on providing the solutions. Please hold on while I process the images.from PIL import Image import pytesseract

Load the uploaded images

image_path1 = "/mnt/data/173221819297511ifpmpl.jpg" image_path2 = "/mnt/data/1732218192975jidikgnb.jpg"

Perform OCR on the images to extract text

text1 = pytesseract.image_to_string(Image.open(image_path1)) text2 = pytesseract.image_to_string(Image.open(image_path2))

Combine the text from both images for processing

extracted_text = text1 + "\n" + text2

Output the extracted text

extracted_text"10. x°y? -343y'\n11. 9y’ -144y\n\n12. w’-1 a\nBw +36 oar\n\n} Gina Wison (Ai Things Algebra? , LAC}, 2015-2022\n\n\n18. ~x° + 47? 491,\n\n20. 9 +6 oe\nnae 21. 84 +102 —3\n\n4 37 —4r+3\n\nry\n\n""10. x°y? -343y'\n11. 9y’ -144y\n\n12. w’-1 a\nBw +36 oar\n\n} Gina Wison (Ai Things Algebra? , LAC}, 2015-2022\n\n\n18. ~x° + 47? 491,\n\n20. 9 +6 oe\nnae 21. 84 +102 —3\n\n4 37 —4r+3\n\nry\n\n"successThe extracted text is incomplete and not entirely clear due to OCR challenges. I will manually process and provide solutions for the questions based on what I can see clearly in the images. I will solve all the visible polynomial factoring problems step by step. Let me begin.


I'll start with Problem 4: x436x^4 - 36:

Step 1: Recognize the form

This is a difference of squares:
x436=(x2)262x^4 - 36 = (x^2)^2 - 6^2

Step 2: Apply the difference of squares formula

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b) \

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Math Problem Analysis

Mathematical Concepts

Factoring Polynomials
Difference of Squares
Sum and Difference of Cubes
Quadratics

Formulas

Difference of Squares: a^2 - b^2 = (a - b)(a + b)
Sum of Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Difference of Cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Factoring Quadratics: ax^2 + bx + c = (px + q)(rx + s)

Theorems

Factoring Theorem
Zero Product Property

Suitable Grade Level

Grades 9-12