Yes😁
\((2x - 1)(x - 5)\) ### Problem 2: Factor \(5x^2 - 9x - 2\)
題目
Turn 1 Question
- $2x^2 - 11x + 5$
- $5x^2 - 9x - 2$
- $2x^2 + 13x + 7$
- $3x^2 + 5x + 2$
- $5x^2 - 6x + 1$
- $5x^2 + 9x - 2$
Turn 2 Question
For number 3 it’s a -7 not +7
Turn 3 Question
Yes😁
解題步驟
-
Understand the question
Turn 1 Question
- $2x^2 - 11x + 5$
- $5x^2 - 9x - 2$
- $2x^2 + 13x + 7$
- $3x^2 + 5x + 2$
- $5x^2 - 6x + 1$
- $5x^2 + 9x - 2$
Turn 2 Question
For number 3 it’s a -7 not +7
Turn 3 Question
Yes😁
-
Response
Turn 1 Answer
Problem 1: Factor \(2x^2 - 11x + 5\)
-
Explanation
Step 1: Find \(ac\) and split middle term
For \(ax^2+bx+c\), \(a = 2\), \(b=-11\), \(c = 5\). \(ac=2\times5 = 10\). Find two numbers that multiply to \(10\) and add to \(-11\): \(-10\) and \(-1\).
Rewrite the middle term: \(2x^2-10x - x + 5\)Step 2: Group and factor
Group first two and last two terms: \((2x^2 - 10x)+(-x + 5)\)
Factor out GCF from each group: \(2x(x - 5)-1(x - 5)\)
Factor out \((x - 5)\): \((2x - 1)(x - 5)\) -
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 5\), \(b=-9\), \(c=-2\). \(ac=5\times(-2)=-10\). Find two numbers that multiply to \(-10\) and add to \(-9\): \(-10\) and \(1\).
Rewrite the middle term: \(5x^2-10x+x - 2\)Step 2: Group and factor
Group: \((5x^2 - 10x)+(x - 2)\)
Factor out GCF: \(5x(x - 2)+1(x - 2)\)
Factor out \((x - 2)\): \((5x + 1)(x - 2)\) -
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 2\), \(b = 13\), \(c = 7\). \(ac=2\times7 = 14\). Find two numbers that multiply to \(14\) and add to \(13\): \(14\) and \(1\).
Rewrite the middle term: \(2x^2+14x+x + 7\)Step 2: Group and factor
Group: \((2x^2 + 14x)+(x + 7)\)
Factor out GCF: \(2x(x + 7)+1(x + 7)\)
Factor out \((x + 7)\): \((2x + 1)(x + 7)\) -
Final answer
\((2x - 1)(x - 5)\)
Problem 2: Factor \(5x^2 - 9x - 2\)
答案
Response
Turn 1 Answer
Problem 1: Factor \(2x^2 - 11x + 5\)
Explanation
Step 1: Find \(ac\) and split middle term
For \(ax^2+bx+c\), \(a = 2\), \(b=-11\), \(c = 5\). \(ac=2\times5 = 10\). Find two numbers that multiply to \(10\) and add to \(-11\): \(-10\) and \(-1\).
Rewrite the middle term: \(2x^2-10x - x + 5\)
Step 2: Group and factor
Group first two and last two terms: \((2x^2 - 10x)+(-x + 5)\)
Factor out GCF from each group: \(2x(x - 5)-1(x - 5)\)
Factor out \((x - 5)\): \((2x - 1)(x - 5)\)
Answer
\((2x - 1)(x - 5)\)
Problem 2: Factor \(5x^2 - 9x - 2\)
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 5\), \(b=-9\), \(c=-2\). \(ac=5\times(-2)=-10\). Find two numbers that multiply to \(-10\) and add to \(-9\): \(-10\) and \(1\).
Rewrite the middle term: \(5x^2-10x+x - 2\)
Step 2: Group and factor
Group: \((5x^2 - 10x)+(x - 2)\)
Factor out GCF: \(5x(x - 2)+1(x - 2)\)
Factor out \((x - 2)\): \((5x + 1)(x - 2)\)
Answer
\((5x + 1)(x - 2)\)
Problem 3: Factor \(2x^2 + 13x + 7\)
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 2\), \(b = 13\), \(c = 7\). \(ac=2\times7 = 14\). Find two numbers that multiply to \(14\) and add to \(13\): \(14\) and \(1\).
Rewrite the middle term: \(2x^2+14x+x + 7\)
Step 2: Group and factor
Group: \((2x^2 + 14x)+(x + 7)\)
Factor out GCF: \(2x(x + 7)+1(x + 7)\)
Factor out \((x + 7)\): \((2x + 1)(x + 7)\)
Answer
\((2x + 1)(x + 7)\)
Problem 4: Factor \(3x^2 + 5x + 2\)
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 3\), \(b = 5\), \(c = 2\). \(ac=3\times2 = 6\). Find two numbers that multiply to \(6\) and add to \(5\): \(3\) and \(2\).
Rewrite the middle term: \(3x^2+3x+2x + 2\)
Step 2: Group and factor
Group: \((3x^2 + 3x)+(2x + 2)\)
Factor out GCF: \(3x(x + 1)+2(x + 1)\)
Factor out \((x + 1)\): \((3x + 2)(x + 1)\)
Answer
\((3x + 2)(x + 1)\)
Problem 5: Factor \(5x^2 - 6x + 1\)
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 5\), \(b=-6\), \(c = 1\). \(ac=5\times1 = 5\). Find two numbers that multiply to \(5\) and add to \(-6\): \(-5\) and \(-1\).
Rewrite the middle term: \(5x^2-5x - x + 1\)
Step 2: Group and factor
Group: \((5x^2 - 5x)+(-x + 1)\)
Factor out GCF: \(5x(x - 1)-1(x - 1)\)
Factor out \((x - 1)\): \((5x - 1)(x - 1)\)
Answer
\((5x - 1)(x - 1)\)
Problem 6: Factor \(5x^2 + 9x - 2\)
Explanation
Step 1: Find \(ac\) and split middle term
\(a = 5\), \(b = 9\), \(c=-2\). \(ac=5\times(-2)=-10\). Find two numbers that multiply to \(-10\) and add to \(9\): \(10\) and \(-1\).
Rewrite the middle term: \(5x^2+10x - x - 2\)
Step 2: Group and factor
Group: \((5x^2 + 10x)+(-x - 2)\)
Factor out GCF: \(5x(x + 2)-1(x + 2)\)
Factor out \((x + 2)\): \((5x - 1)(x + 2)\)
Answer
\((5x - 1)(x + 2)\)
Turn 2 Answer
Oops, my bad for misreading that! Let me fix problem 3 for you:
Problem 3: Factor \(2x^2 + 13x - 7\)
Explanation
- First, calculate \(ac\): \(a=2\), \(c=-7\), so \(ac = 2\times(-7) = -14\)
- Find two numbers that multiply to \(-14\) and add up to \(13\): those numbers are \(14\) and \(-1\)
- Split the middle term using these numbers: \(2x^2 + 14x - x - 7\)
- Group and factor:
- Group the first two and last two terms: \((2x^2 + 14x) + (-x - 7)\)
- Factor out the GCF from each group: \(2x(x + 7) - 1(x + 7)\)
- Factor out the common binomial: \((2x - 1)(x + 7)\)
Answer
\((2x - 1)(x + 7)\)
Did I get that right this time? 😅
Turn 3 Answer
Phew, crisis averted! 😂 Glad I could fix that for you. Want to go over any of these again, or is there something else you feel like chatting about?
Question Analysis
Subject
mathematics
Sub Subject
algebra
Education Level
high school
Difficulty
unspecified
Question Type
calculation
Multi Question
Yes
Question Count
3
Analysis Status
completed
Analyzed At
2026-02-06T00:44:53
OCR Text
Show OCR extraction
Yes😁
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