Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
2.0k views
in Factorisation of Algebraic expressions by (48.7k points)
closed by

Factorize: 

i. x2 + 9x + 18 

ii. x2 – 10x + 9 

iii. y2 + 24y + 144 

iv. 5y2 + 5y – 10 

v. p2 – 2p – 35 

vi. p2 – 7p – 44 

vii. m2 – 23m + 120 

viii. m2 – 25m + 100 

ix. 3x2 + 14x + 15 

x. 2x2 + x – 45 

xi. 20x2 – 26x + 8 

xii. 44x2 – x – 3

1 Answer

+2 votes
by (49.4k points)
selected by
 
Best answer

i. x2 + 9x + 18 

= x2 + 6x + 3x + 18 

= x(x + 6) + 3(x + 6) 

= (x + 6) (x + 3)

ii. x2 – 10x + 9 

= x2 – 9x – x + 9 

= x(x – 9) – 1(x – 9) = (x – 9)(x – 1)

iii. y2 + 24y + 144 

= y2 + 12y + 12y + 144 

= y(y + 12) + 12(y + 12) = (y + 12)(y + 12)

iv. 5y2 + 5y – 10 

= 5(y2 + y – 2) … [Taking out the common factor 5] 

= 5(y2 + 2y – y – 2) 

= 5[y(y + 2) – 1(y + 2)] = 5(p + 2)(y- 1)

v. p2 – 2p – 35 

= p2 – 7p + 5p – 35 

= p(p – 7) + 5(p – 7) = (p – 7)(p + 5)

vi. p2 – 7p – 44 

= p2 – 11p + 4p – 44 

= p(p – 11) + 4(p – 11) = (p – 11)(p + 4)

vii. m2 – 23m + 120 

= m2 – 15m – 8m + 120 

= m(m – 15) – 8 (m – 15) = (m – 15) (m – 8)

viii. m2 – 25m + 100

= m2 – 20m – 5m + 100 

= m(m – 20) – 5(m – 20) = (m – 20) (m – 5)

ix. 3x2 + 14x + 15 

= 45 = 3x2 + 9x + 5x + 15 

= 3x(x + 3) + 5(x + 3) = (x + 3) (3x + 5)

x. 2x2 + x – 45 

= 2x+ 10x – 9x – 45 

= 2x(x + 5) – 9 (x + 5) = (x + 5) (2x – 9)

xi. 20x2 – 26x + 8 

= 2(10x2 – 13x + 4) … [Taking out the common factor 2] 

= 2(10x2 – 8x – 5x + 4) 

= 2[2x(5x – 4) – 1(5x – 4)] = 2(5x – 4) (2x – 1)

xii. 44x2 – x – 3 44 × (-3) = -132 

= 44x– 12x + 11x – 3 

= 4x(11x – 3) + 1(11x – 3) = (11x – 3) (4x + 1)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...