Dr. J's Maths.com
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Algebra - Factorisation - Cross method (non-monics).
Test Yourself 1.


 

Factorise each of the following expressions using the cross-method:

x
Type of question No.   No.  
Both signs positive. 1. 5k2 + 17k + 6
Answer.(5k + 2)(k + 3).		 2. 9x2 + 9x + 2
Answer.(3x + 2)(3x + 1).
  3. 3t2 + 17t + 10
Answer.(3t + 2)(t +5).		 4. 5m2 + 26m + 32
Answer.(5m + 16)(m +2).
Signs are negative then positive respectively. 5. 3x2 - 13x + 14
Answer.(3x - 7)(x - 2).		 6. 3x2 - 31xy + 50y2
Answer.(3x - 25y)(x - 2y).
  7. 10f2 - 13f + 4
Answer.(5f - 4)(2f - 1).		 8. 6n2 - 19n + 10
Answer.(3n - 2)(2n - 5).
Signs are positive then negative respectively. 9. 6x2 + 13x - 5
Answer.(2x + 5)(3x - 1).		 10. 5k2 + 2k - 7
Answer.(5k + 7)(k - 1).
  11. 7d2 + 48d - 7
Answer.(7d - 1)(d + 7).		 12. 2g2 + 13g - 24 Hint.The 2g squared only has one pair of factors. We need to create an odd number for the g coefficient so use a pair of numbers which multiply to get 24 but also which contain an odd number. There is only 1 pair!!!
Answer.(2g - 3)(g + 8).
Signs are both negative. 13. 6x2 - x - 1
Answer.(3x + 1)(2x - 1).		 14. 2w2 - 11w - 21
Answer.(2w + 3)(w - 7).
  15. 18z2 - 3z - 10
Answer.(6z - 5)(3z + 2).		 16. 7p2 - 55pq - 72q2 Hint.The 7p squared only has one pair of factors. We need to create an odd number for the pq coefficient so use a pair of numbers which multiply to get 72 but also which contain an odd number. There are 2 pairs!!!
Answer.(7p + 8q)(p - 9q).
Randoms. 17. 6a2 + 17a + 12
Answer.(3a + 4)(2a + 3).		 18. 16 - 8j - 3j2
Answer.(4 - 3j)(4 + j).
  19. 12p2 - 29pq + 15q2 Hint.The 15 for the q coefficient only has two pairs of factors and 15q/q can't work. Similarly a 12p/p factorisation for the first term results in a product which exceeds 29. So try factor pairs other than these.
Answer.(4p - 3q)(3p - 5q).		 20. 11g2 + 17g - 48
Answer.(11g - 16)(g + 3).