Question 1 :
Factor the following perfect square trinomial.
x2 + 12x + 36
Question 2 :
Find the factors of the following perfect square trinomial.
a2 + 4a + 4
Question 3 :
Check whether the following trinomial is a perfect square trinomial.
x2 - 13x + 36
Question 4 :
Check whether the following trinomial is a perfect square trinomial.
x2 - 10x + 100
Question 5 :
Check whether the following trinomial is a perfect square trinomial.
2x2 + 17x + 21
Question 6 :
Check whether the following trinomial is a perfect square trinomial.
4x2 + 8x + 4
Question 7 :
What value should be added to the following expression to make it as a perfect square?
x2 + 6x
Question 8 :
Solve :
x2 - 8x + 16 = 0
1. Answer :
= x2 + 12x + 36
= x2 + 2(x)(6) + 62
The trinomial 'x2 + 2(x)(6) + 62' is in the form of
a2 + 2ab + b2
Since a2 + 2ab + b2 = (a + b)2,
x2 + 2(x)(6) + 62 = (x + 6)2
Therefore, the factors of 'x2 + 12x + 36' are
(x + 6)(x + 6) or (x + 6)2
2. Answer :
= a2 + 4a + 4
= a2 + 2(a)(2) + 22
The trinomial 'a2 + 2(a)(2) + 22' is in the form of
a2 + 2ab + b2
Since a2 + 2ab + b2 = (a + b)2,
a2 + 2(a)(2) + 22 = (a + 2)2
Therefore, the factors of 'a2 + 4a + 4' are
(a + 2)(a + 2) or (a + 2)2
3. Answer :
x2 - 13x + 36
The given trinomial is in the form of ax2 + bx + c.
Comparing ax2 + bx + c and x2 - 13x + 36,
a = 1, b = -13 and c = 36
b2 = (-13)2 = 169
4ac = 4(1)(36) = 144
Since b2 ≠ 4ac, the given trinomial is not a perfect square trinomial.
4. Answer :
x2 - 10x + 100
The given trinomial is in the form of ax2 + bx + c.
Comparing ax2 + bx + c and x2 - 13x + 36,
a = 1, b = -10 and c = 100
b2 = (-10)2 = 100
4ac = 4(1)(100) = 400
Since b2 ≠ 4ac, the given trinomial is not a perfect square trinomial.
5. Answer :
2x2 + 17x + 21
The given trinomial is in the form of ax2 + bx + c.
Comparing ax2 + bx + c and 2x2 + 17x + 21,
a = 2, b = 17 and c = 21
b2 = 172 = 289
4ac = 4(2)(21) = 168
Since b2 ≠ 4ac, the given trinomial is not a perfect square trinomial.
6. Answer :
4x2 + 8x + 4
The given trinomial is in the form of ax2 + bx + c.
Comparing ax2 + bx + c and 4x2 + 8x + 4,
a = 4, b = 8 and c = 4
b2 = 82 = 64
4ac = 4(4)(4) = 64
Since b2 = 4ac, the given trinomial is a perfect square trinomial.
7. Answer :
In x2 + 6x, write 6x as a multiple of 2. That is, in the form of 2ab.
x2 + 6x = x2 + 2(x)(3)
x2 + 2(x)(3) is in the form of a2 + 2ab.
We know that a2 + 2ab + b2 is a perfect square trinomial.
Comparing
x2 + 2(x)(3)
and
a2 + 2ab + b2,
instead b2, you must have +32 in x2 + 2(x)(3).
So, you have to add 32 or 9 to x2 + 6x to make it as a perfect square.
8. Answer :
x2 - 8x + 16 = 0
x2 - 2(x)(4) + 16 = 0
x2 - 2(x)(4) + 42 = 0
(x - 4)2 = 0
Take square root on both sides.
x - 4 = 0
Add 4 to both sides.
x = 4
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