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Byju's Answer
Standard VIII
Mathematics
Factorisation by Regrouping Terms
Factorise.1 x...
Question
Factorise.
(1) x
2
+ 9x + 18
(2) x
2
− 10x + 9
(3) y
2
+ 24y + 144
(4) 5y
2
+ 5y − 10
(5) p
2
− 2p − 35
(6) p
2
− 7p − 44
(7) m
2
− 23m + 120
(8) m
2
− 25m + 100
(9) 3x
2
+ 14x + 15
(10) 2x
2
+ x − 45
(11) 20x
2
− 26x + 8
(12) 44x
2
− x − 3
Open in App
Solution
1
x
2
+
9
x
+
18
=
x
2
+
6
x
+
3
x
+
18
=
x
x
+
6
+
3
x
+
6
=
x
+
3
x
+
6
2
x
2
-
10
x
+
9
=
x
2
-
9
x
-
x
+
9
=
x
x
-
9
-
1
x
-
9
=
x
-
1
x
-
9
3
y
2
+
24
y
+
144
=
y
2
+
12
y
+
12
y
+
144
=
y
y
+
12
+
12
y
+
12
=
y
+
12
y
+
12
4
5
y
2
+
5
y
-
10
=
5
y
2
+
10
y
-
5
y
-
10
=
5
y
y
+
2
-
5
y
+
2
=
5
y
-
5
y
+
2
=
5
y
-
1
y
+
2
5
p
2
-
2
p
-
35
=
p
2
-
7
p
+
5
p
-
35
=
p
p
-
7
+
5
p
-
7
=
p
+
5
p
-
7
6
p
2
-
7
p
-
44
=
p
2
-
11
p
+
4
p
-
44
=
p
p
-
11
+
4
p
-
11
=
p
+
4
p
-
11
7
m
2
-
23
m
+
120
=
m
2
-
15
m
-
8
m
+
120
=
m
m
-
15
-
8
m
-
15
=
m
-
8
m
-
15
8
m
2
-
25
m
+
100
=
m
2
-
20
m
-
5
m
+
100
=
m
m
-
20
-
5
m
-
20
=
m
-
5
m
-
20
9
3
x
2
+
14
x
+
15
=
3
x
2
+
9
x
+
5
x
+
15
=
3
x
x
+
3
+
5
x
+
3
=
3
x
+
5
x
+
3
10
2
x
2
+
x
-
45
=
2
x
2
+
10
x
-
9
x
-
45
=
2
x
x
+
5
-
9
x
+
5
=
2
x
-
9
x
+
5
11
20
x
2
-
26
x
+
8
=
20
x
2
-
16
x
-
10
x
+
8
=
4
x
5
x
-
4
-
2
5
x
-
4
=
4
x
-
2
5
x
-
4
=
2
2
x
-
1
5
x
-
4
12
44
x
2
-
x
-
3
=
44
x
2
+
11
x
-
12
x
-
3
=
11
x
4
x
+
1
-
3
4
x
+
1
=
11
x
-
3
4
x
+
1
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12
Similar questions
Q.
Factorize:
(i)
y
2
+
24
y
+
144
(ii)
p
2
−
7
p
−
44
(iii)
3
x
2
+
14
x
+
15
(iv)
44
x
2
−
x
−
3
Q.
Simplify :
(i)
y
2
+
24
y
+
144
(ii)
p
2
−
7
p
−
44
(iii)
3
x
2
+
14
x
+
15
(iv)
44
x
2
−
x
−
3
Q.
lf the curves
x
2
a
2
+
y
2
b
2
=
1
and
x
2
p
2
−
y
2
m
2
=
1
cut each other orthogonally, then
Q.
Solve the following quadratic equations by factorisation.
(1) x
2
– 15x + 54 = 0
(2) x
2
+ x – 20 = 0
(3) 2y
2
+ 27y + 13 = 0
(4) 5m
2
= 22m + 15
(5) 2x
2
– 2x +
1
2
= 0
(6)
6
x
-
2
x
=
1
(7)
2
x
2
+
7
x
+
5
2
=
0
to solve this quadratic equation by factorisation, complete the following activity.
(8)
3
x
2
-
2
6
x
+
2
=
0
(9)
2
m
m
-
24
=
50
(10)
25
m
2
=
9
(11)
7
m
2
=
21
m
(12)
m
2
-
11
=
0
Q.
Divide and write the quotient and the remainder.
(1) (y
2
+ 10y + 24) Ć· (y + 4)
(2) (p
2
+ 7p ā 5) Ć· (p + 3)
(3) (3x + 2x
2
+ 4x
3
) Ć· (x ā 4)
(4) (2m
3
+ m
2
+ m + 9) Ć· (2m ā 1)
(5) (3x ā 3x
2
ā 12 + x
4
+ x
3
) Ć· (2 + x
2
)
(6) (a
4
ā a
3
+ a
2
ā a + 1) Ć· (a
3
ā 2)
(7) (4x
4
ā 5x
3
ā 7x + 1) Ć· (4x ā 1)