Factoring Perfect Square Trinomials Worksheet

PERFECT SQUARE TRINOMIALS WORKSHEET

Question 1 :

Cistron the following perfect foursquare trinomial.

x² + 12x + 36

Question two :

Find the factors of the following perfect square trinomial.

aⁱⁱ + 4a + 4

Question 3 :

Check whether the following trinomial is a perfect foursquare trinomial.

10² - 13x + 36

Question iv :

Check whether the following trinomial is a perfect square trinomial.

xⁱⁱ - 10x + 100

Question 5 :

Cheque whether the following trinomial is a perfect square trinomial.

2x² + 17x + 21

Question half-dozen :

Check whether the following trinomial is a perfect square trinomial.

4x^two + 8x + iv

Question 7 :

What value should exist added to the post-obit expression to go far as a perfect square?

x² + 6x

Question viii :

Solve :

x² - 8x + 16 = 0

Answers

i. Reply :

= x ² + 12x + 36

= x ^two + two(ten)(6) + half dozen ²

The trinomial 'x ⁱⁱ + 2(10)(six) + 6 ^two' is in the form of

a ⁱⁱ + 2ab + b ^two

Since a ² + 2ab + b ²= (a + b)ⁱⁱ ,

x ² + two(x)(6) + 6 ^two= (x + 6)²

Therefore, the factors of 'x ⁱⁱ + 12x + 36' are

(x + 6)(x + 6) or (x + 6)²

2. Answer :

= a ² + 4a + iv

= a ⁱⁱ + 2(a)(2) + 2 ²

The trinomial 'a ² + ii(a)(2) + two ²' is in the form of

a²+ 2ab + b²

Since a ⁱⁱ + 2ab + b ²= (a + b)^two ,

a² + 2(a)(ii) + ii²= (a + 2)ⁱⁱ

Therefore, the factors of 'a² + 4a + iv' are

(a + 2)(a + two) or (a + 2)²

3. Reply :

10 ² - 13x + 36

The given trinomial is in the grade of ax^two + bx + c.

Comparingax ² + bx + c and x ² - 13x + 36,

a = one, b = -13 and c = 36

b² = (-13)² = 169

4ac = 4(1)(36) = 144

Since b² ≠ 4ac, the given trinomial is not a perfect foursquare trinomial.

iv. Respond :

10² - 10x + 100

The given trinomial is in the grade of ax² + bx + c.

Comparisonax ^two + bx + c and 10 ² - 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 course of ax² + bx + c.

Comparisonax ^two + bx + c and 2x ⁱⁱ + 17x + 21,

a = 2, b = 17 and c = 21

b^two = 17² = 289

4ac = iv(two)(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 class of axⁱⁱ + bx + c.

Comparingax ^two + bx + c and 4x ⁱⁱ + 8x + 4 ,

a = iv, b = 8 and c = 4

b^two = eight² = 64

4ac = 4(4)(4) = 64

Since bⁱⁱ = 4ac, the given trinomial is a perfect square trinomial.

vii. Answer :

In ten ⁱⁱ + 6x, write 6x as a multiple of 2. That is, in the course of 2ab.

x² + 6x = x^two + 2(x)(3)

x² + 2(x)(3) is in the grade of a² + 2ab.

We know thata² + 2ab + b²is a perfect square trinomial.

Comparing

x² + 2(ten)(iii)

and

a ² + 2ab + b ²,

instead b², yous must have +3²in x² + 2(x)(3).

So, you take to add 3ⁱⁱ or ix to tenⁱⁱ + 6x to brand it every bit a perfect square.

8. Answer :

x² - 8x + 16 = 0

x² - ii(10)(4) + 16 = 0

ten² - 2(x)(4) + iv² = 0

(x - 4)²= 0

Take square root on both sides.

x - four= 0

Add 4 to both sides.

x = four

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