Explanation: 3 x 2 + 10 x + 3 We can Split the Middle Term of this expression to factorise it. In this technique, if we have to factorise an expression like a x 2 + b x + c , we need to think of 2 numbers such that: N 1 ⋅ N 2 = a ⋅ c = 3 ⋅ 3 = 9 and, N 1 + N 2 = b = 10 After trying out a few numbers we get: N 1 = 9 and N 2 = 1 9 ⋅ 1 = 9 , and 9 + ( 1 ) = 10 3 x 2 + 10 x + 3 = 3 x 2 + 9 x + 1 x + 3 = 3 x ( x + 3 ) + 1 ( x + 3 ) ( 3 x + 1 ) ( x + 3 ) is the factorised form for the expression.
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
3
⋅
3
=
9
and,
N
1
+
N
2
=
b
=
10
After trying out a few numbers we get:
N
1
=
9
and
N
2
=
1
9
⋅
1
=
9
, and
9
+
(
1
)
=
10
3
x
2
+
10
x
+
3
=
3
x
2
+
9
x
+
1
x
+
3
=
3
x
(
x
+
3
)
+
1
(
x
+
3
)
(
3
x
+
1
)
(
x
+
3
)
is the factorised form for the expression.
<h2>
Answer with explanation:</h2>
The given function : 
Using completing the squares, we have
[∵ 
]
(1)
Comparing (1) to the standard vertex form 
, the vertex of function is at (h,k)=(-1,-4)
For x-intercept, put f(x)=0 in (1), we get
Square root on both sides, we get
∴ x intercepts : x= (-3,0) and (1,0)
For y-intercept put x=0 in (1), we get
∴ y intercept : (0,-3)
Axis of symmetry : 
In , a=1 and b=2
Axis of symmetry=
Answer:
Step-by-step explanation:
(A)
A=hw, h=1.5w
A=1.5w^2
(B)
A=(h+8)(w+8), h=1.5w
A=(1.5w+8)(w+8)
A=1.5w^2+12w+8w+64
A=1.5w^2+20w+64
