Worksheet on Factoring Simple Quadratics

Practice the worksheet on factoring simple quadratics in the form of x² + bx + c.

The questions are based on how to factorize the simple quadratic expressions in the form of x² + bx + c by splitting their co-efficient of middle term.

1. Factorize the following expression:

(i) y² + 9y + 20

(ii) x² + 15x + 54

(iii) z² + 3z - 4

(iv) p² + 2p - 24

(v) a² – 5a + 4

(vi) p² - 15p + 14



2. Resolve into factors:

(i) m² + 3m - 10

(ii) x² – 18x - 63

(iii) x² + 6x + 8

(iv) x² + 12x + 32

(v) a² – 8a + 15

(vi) x² – 12x + 35



3. Factor the middle term:

(i) a² – 4a – 12

(ii) x² - 4x - 45

(iii) m² + 15m + 56

(iv) q² – 13q + 36

(v) p² + 5p - 24

(vi) t² + 17t - 84

(vii) x² - 15x + 44

(viii) x² - 5x - 24

(ix) m² - 4m – 77

(x) x² – 12x + 20

Answers for the worksheet on factoring simple quadratics are given below to check the exact answers of the factoring expression.

Answers:

1. (i) (y + 5) (y + 4)      

(ii) (x + 6) (x + 9)  

(iii) (z - 1) (z + 4 )        

(iv) (p + 6) (p - 4)

(v) (a - 1) (a - 4)          

(vi) (p - 1) (p - 14)   

2. (i) (m + 5) (m – 2)

(ii) (x + 3) (x – 21)

(iii) (x + 2) (x + 4)

(iv) (x + 4) (x + 8)

(v) (a – 3) (a – 5)

(vi) (x – 5) (x – 7)

3. (i) (a + 2) (a - 6)  

(ii) (x + 5) (x - 9)   

(iii) (m + 8) (m + 7)    

(iv) (q + 9) (q + 4)  

(v) (p - 3) (p + 8) 

(vi) (t + 21) (t - 4)

(vii) (x – 11) (x - 4)  

(viii) (x + 3) (x – 8)  

(ix) (m + 7) (m - 11)  

(x) (x – 10) (x – 2)

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