## RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.1
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.2
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.3
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.4
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.5
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.8
- RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9

**Factorize each of the following quadratic polynomials by using the method of completing the square.**

**Question 1.**

**p ^{2} + 6p + 8**

**Solution:**

p

^{2}+ 6p + 8

= p

^{2}+ 2 x p x 3 + 3

^{2}– 3

^{2}+ 8 (completing the square)

= (p

^{2}+ 6p + 3

^{2}) – 1

= (p + 3)

^{2}– 1

^{2}

= (P + 3)

^{2}– (1)

^{2}{ ∵ a

^{2}+ b

^{2}= (a+b) (a-b)}

^{ }= (p +3+1) (p + 3 -1)

= (p+4) (p+ 2)

**Question 2.
**

**q**

^{2}– 10q + 21**Solution:**

q

^{2}– 10q + 21

= (q)

^{2}– 2 x q x 5 + (5)

^{2}– (5)

^{2}+ 21 (completing the square)

= (q)

^{2}– 2 x q x 5 + (5)

^{2}-25+21

= (q)

^{2}-2 x q x 5 + (5)

^{2}– 25 +21

= (q)

^{2}-2 x q x 5 + (5)

^{2}– 4

= (q – 5)

^{2}– (2) {∵

^{ }a

^{2}– b

^{2}= (a + b) (a – b)}

= (q- 5 + 2) (q-5-2)

=(q- 3) (q-7)

**Question 3.
**

*4y*12y + 5^{2}+**Solution:**

4y

^{2 }+12y + 5

= (2y)

^{2}+ 2 x 2y x 3 + (3)

^{2}– (3)

^{2}+ 5 (completing the square)

= (2y + 3)

^{2}– 9 + 5

= (2y + 3)

^{2}– 4

= (2y + 3)

^{2}-(2)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (2y + 3 + 2) (2y + 3 – 2)

= (2y + 5) (2y+ 1)

**Question 4.
**

**p**

^{2}+ 6p-

**16****Solution:**

p

^{2}+ 6p – 16

= (p)

^{2}+ 2 x p x 3 + (3)

^{2}– (3)

^{2}– 16 (completing the square)

= (p)

^{2}+ 2 x p x 3 + (3)

^{2}– 9 – 16

= (p + 3)

^{2}– 25

= (p + 3)

^{2}– (5)

^{2 }{∵ a

^{2}-b

^{2}= {a + b) (a – b)}

= (p + 3 + 5)(p + 3-5)

= (p + 8) (p – 2)

**Question 5.
**

**x**

^{2}+ 12x + 20**Solution:**

x

^{2}+ 12x + 20

= (x)

^{2}+ 2 x x x 6 + (6)

^{2}– (6)

^{2}+ 20 (completing the square)

= (x)

^{2}+ 2 x x x6 + (6)

^{2}-36 + 20

= (x + 6)

^{2}-16

= (x + 6)

^{2}– (4)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (x + 6 + 4) (x + 6 – 4)

= (x + 10) (x + 2)

**Question 6.
**

**a**

^{2}– 14a – 51**Solution:**

a

^{2}– 14a-51

= (a)

^{2}– 2 x x 7 + (7)

^{2}– (7)

^{2}– 51 (completing the square)

= (a)

^{2}– 2 x a x 7 + (7)

^{2}– 49 – 51

= (a – 7)

^{2}– 100

= (a – 7)

^{2}– (10)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (a – 7 + 10) (a – 7 – 10)

= (a + 3) (a – 17)

**Question 7.
**

**a**

^{2}+ 2a – 3**Solution:**

a

^{2}+ 2a – 3

= (a)

^{2}+ 2 x a x 1 + (1)

^{2}– (1)2 – 3 (completing the square)

= (a)

^{2}+ 2 x a x 1 + (1)

^{2}– 1 – 3

= (a + 1)

^{2}– 4

= (a + 1)

^{2}– (2)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (a + 1 + 2) (a + 1 – 2)

= (a + 3) (a – 1)

**Question 8.
**

**4x**

^{2}– 12x + 5**Solution:**

4x

^{2}– 12x + 5

= (2x)

^{2}– 2 x 2x x 3 + (3)

^{2}– (3)

^{2}+ 5 (completing the square)

= (2x)

^{2}– 2 x 2x x 3 + (3)

^{2}-9 + 5

= (2x – 3)

^{2}– 4

= (2x – 3)

^{2}– (2)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (2x – 3 + 2) (2x – 3 – 2)

= (2x – 1) (2x – 5)

**Question 9.
**

**y**

^{2}– 7y +

**12****Solution:**

**Question 10.
**

**z**

^{2}-4z-12**Solution:**

z

^{2}– 4z – 12

= (z)

^{2}– 2 x z x 2 + (2)

^{2}– (2)

^{2}– 12 (completing the square)

= (z)

^{2}– 2 x z x 2 + (2)

^{2}– 4 – 12

= (z-2)

^{2}-16

= (z-2)

^{2}-(4)

^{2 }{∵ a

^{2}– b

^{2}= (a + b) (a – b)}

= (z – 2 + 4) (z – 2 – 4)

= (z + 2)(z-6)

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.9 are helpful to complete your math homework.

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