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यदि \(x^2+11x+30\) को आयत क्षेत्र मॉडल से गुणनखंडित करना हो, तो कौन सी भुजाएं उचित हैं?
If \(x^2+11x+30\) is to be factorised using a rectangle area model, which sides are suitable?
#factorisation
#rectangle model
#quadratic area
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A (x+5) और (x+6) / (x+5) and (x+6)
B (x+3) और (x+10) / (x+3) and (x+10)
C (x+2) और (x+15) / (x+2) and (x+15)
D (x+1) और (x+30) / (x+1) and (x+30)
Explanation opens after your attempt
Correct Answer
A. (x+5) और (x+6) / (x+5) and (x+6)
Step 1
Concept
\(5\cdot6=30\) and (5+6=11). So the rectangle sides are (x+5) and (x+6).
Step 2
Why this answer is correct
The correct answer is A. (x+5) और (x+6) / (x+5) and (x+6). \(5\cdot6=30\) and (5+6=11). So the rectangle sides are (x+5) and (x+6).
Step 3
Exam Tip
\(5\cdot6=30\) और (5+6=11) है। इसलिए आयत की भुजाएं (x+5) और (x+6) होंगी।
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आयत मॉडल में \(x^2-13x+40\) को दो भुजाओं में लिखने के लिए कौन सा विकल्प सही है?
In a rectangle model, which option correctly writes \(x^2-13x+40\) as two sides?
#signed rectangle
#factorisation
#quadratic model
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A (x-5) और (x-8) / (x-5) and (x-8)
B (x+5) और (x+8) / (x+5) and (x+8)
C (x-4) और (x-10) / (x-4) and (x-10)
D (x+4) और (x+10) / (x+4) and (x+10)
Explanation opens after your attempt
Correct Answer
A. (x-5) और (x-8) / (x-5) and (x-8)
Step 1
Concept
((-5)+(-8)=-13) and ((-5)(-8)=40). Exam tip: with negative rectangles, the constant term can be positive.
Step 2
Why this answer is correct
The correct answer is A. (x-5) और (x-8) / (x-5) and (x-8). ((-5)+(-8)=-13) and ((-5)(-8)=40). Exam tip: with negative rectangles, the constant term can be positive.
Step 3
Exam Tip
((-5)+(-8)=-13) और ((-5)(-8)=40) है। परीक्षा में ऋण आयतों के साथ स्थिर पद धनात्मक हो सकता है।
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यदि \(x^2-2x-24\) का क्षेत्र मॉडल बनाना हो, तो कौन सा गुणनफल सही है?
If an area model for \(x^2-2x-24\) is to be made, which product is correct?
#area model
#factorisation
#signed tiles
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A ((x-6)(x+4))
B ((x+6)(x-4))
C ((x-8)(x+3))
D ((x+8)(x-3))
Explanation opens after your attempt
Correct Answer
A. ((x-6)(x+4))
Step 1
Concept
(-6+4=-2) and \(-6\cdot4=-24\). Exam tip: find factors of the constant term with opposite signs.
Step 2
Why this answer is correct
The correct answer is A. ((x-6)(x+4)). (-6+4=-2) and \(-6\cdot4=-24\). Exam tip: find factors of the constant term with opposite signs.
Step 3
Exam Tip
(-6+4=-2) और \(-6\cdot4=-24\) है। परीक्षा में स्थिर पद के विपरीत चिह्न वाले कारक खोजें।
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एक (12) भुजा वाले वर्ग में से (5) भुजा वाला वर्ग हटाया गया। बचे क्षेत्र को ((a-b)(a+b)) मॉडल से कैसे लिखेंगे?
A square of side (5) is removed from a square of side (12). How will the remaining area be written using the ((a-b)(a+b)) model?
#numeric difference
#square removal
#visual factorisation
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A \(7\cdot17\)
B \(12\cdot5\)
C \(12\cdot17\)
D \(7\cdot5\)
Explanation opens after your attempt
Correct Answer
A. \(7\cdot17\)
Step 1
Concept
(122 -52 =(12-5)(12+5)=7\cdot17). Exam tip: form sum and difference with the removed square.
Step 2
Why this answer is correct
The correct answer is A. \(7\cdot17\). (122 -52 =(12-5)(12+5)=7\cdot17). Exam tip: form sum and difference with the removed square.
Step 3
Exam Tip
(122 -52 =(12-5)(12+5)=7\cdot17) है। परीक्षा में घटाए गए वर्ग के साथ योग और अंतर बनाएं।
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यदि \(64x^2-81y^2\) को दृश्य रूप में वर्गों के अंतर की तरह देखें, तो सही गुणनखंड कौन सा है?
If \(64x^2-81y^2\) is viewed visually as a difference of squares, which factorisation is correct?
#difference of squares
#visual factorisation
#area model
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A ((8x-9y)(8x+9y))
B ((64x-81y)(x+y))
C ((8x+9y)2 )
D ((8x-9y)2 )
Explanation opens after your attempt
Correct Answer
A. ((8x-9y)(8x+9y))
Step 1
Concept
(64x-2 =(8x)2 ) and (81y-2 =(9y)2 ). So the factorisation is ((8x-9y)(8x+9y)).
Step 2
Why this answer is correct
The correct answer is A. ((8x-9y)(8x+9y)). (64x-2 =(8x)2 ) and (81y-2 =(9y)2 ). So the factorisation is ((8x-9y)(8x+9y)).
Step 3
Exam Tip
(64x-2 =(8x)2 ) और (81y-2 =(9y)2 ) है। इसलिए अंतर का गुणनखंड ((8x-9y)(8x+9y)) है।
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यदि \(a^2+6a+9-b^2\) को दृश्य रूप से गुणनखंडित करें, तो सही रूप क्या होगा?
If \(a^2+6a+9-b^2\) is factorised visually, what is the correct form?
#visual factorisation
#complete square
#difference of squares
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A ((a+3-b)(a+3+b))
B ((a-3-b)(a-3+b))
C ((a+3)2 +b-2 )
D ((a+b+3)2 )
Explanation opens after your attempt
Correct Answer
A. ((a+3-b)(a+3+b))
Step 1
Concept
(a-2 +6a+9=(a+3)2 ) and \(b^2\) is subtracted from it. So use difference of squares.
Step 2
Why this answer is correct
The correct answer is A. ((a+3-b)(a+3+b)). (a-2 +6a+9=(a+3)2 ) and \(b^2\) is subtracted from it. So use difference of squares.
Step 3
Exam Tip
(a-2 +6a+9=(a+3)2 ) है और उससे \(b^2\) घटता है। इसलिए अंतर के वर्ग का प्रयोग करें।
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एक क्षेत्र मॉडल में \(2x^2+7x+3\) के लिए सही भुजाएं पहचाननी हैं। कौन सा विकल्प वास्तव में सही है?
In an area model for \(2x^2+7x+3\), the correct sides must be identified. Which option is actually correct?
#area factorisation
#quadratic model
#visual grid
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A (2x+1) और (x+3) / (2x+1) and (x+3)
B (2x+3) और (x+1) / (2x+3) and (x+1)
C (x+2) और (2x+3) / (x+2) and (2x+3)
D (2x-1) और (x-3) / (2x-1) and (x-3)
Explanation opens after your attempt
Correct Answer
A. (2x+1) और (x+3) / (2x+1) and (x+3)
Step 1
Concept
((2x+1)(x+3)=2x-2 +6x+x+3=2x-2 +7x+3). Exam tip: split the middle term into two parts.
Step 2
Why this answer is correct
The correct answer is A. (2x+1) और (x+3) / (2x+1) and (x+3). ((2x+1)(x+3)=2x-2 +6x+x+3=2x-2 +7x+3). Exam tip: split the middle term into two parts.
Step 3
Exam Tip
((2x+1)(x+3)=2x-2 +6x+x+3=2x-2 +7x+3) है। परीक्षा में मध्य पद को दो भागों में तोड़ें।
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दृश्य क्षेत्रफल \(x^2+2x-35\) वाले आयत की उपयुक्त भुजाएं कौन सी होंगी?
What are suitable sides of a rectangle whose visual area is \(x^2+2x-35\)?
#signed area
#rectangle factorisation
#visual model
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A (x+7) और (x-5) / (x+7) and (x-5)
B (x-7) और (x+5) / (x-7) and (x+5)
C (x+35) और (x-1) / (x+35) and (x-1)
D (x-2) और (x+35) / (x-2) and (x+35)
Explanation opens after your attempt
Correct Answer
A. (x+7) और (x-5) / (x+7) and (x-5)
Step 1
Concept
(7+(-5)=2) and (7\cdot(-5)=-35). Exam tip: check the sum of opposite-sign factors.
Step 2
Why this answer is correct
The correct answer is A. (x+7) और (x-5) / (x+7) and (x-5). (7+(-5)=2) and (7\cdot(-5)=-35). Exam tip: check the sum of opposite-sign factors.
Step 3
Exam Tip
(7+(-5)=2) और (7\cdot(-5)=-35) है। परीक्षा में विपरीत चिह्न वाले कारकों का योग देखें।
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