Factorise using middle term splitting method: Q1 . q²-3q +2 Q2. x² + x - 20 Q3 . 6x² + 29x + 13 Q4 . 2p² - 23p-12 , Q5. 2a² - 5a -12 Q6. 7q² - 5q -12 ,
Q7. 3x² - 13x +12
Q8. x² +7x +12
Q9. q² - q -72
Q10. 2p² +5p -12
Answers
Answer:
1. q² - 3q + 2
= q² - q - 2q + 2
= q(q - 1) - 2(q - 1)
= (q - 2)(q - 1)
2. x² + x - 20
= x² + 5x - 4x - 20
= x(x + 5) - 4(x + 5)
= (x - 4)(x + 5)
3. 6x² + 29x + 13
= 6x² + 3x + 26x + 13
= 3x(2x + 1) + 13(2x + 1)
= (3x + 13)(2x + 1)
4. 2p² - 23p - 12
= 2p² + p - 24p - 12
= p(2p + 1) - 12(2p + 1)
= (p - 12)(2p + 1)
5. 2a² - 5a - 12
= 2a² - 8a + 3a - 12
= 2a(a - 4) + 3(a - 4)
= (2a + 3)(a - 4)
6. 7q² - 5q - 12
= 7q² + 7q - 12q - 12
= 7q(q + 1) - 12(q + 1)
= (7q - 12)(q + 1)
7. 3x² - 13x + 12
= 3x² - 9x - 4x + 12
= 3x(x - 3) - 4(x -3)
= (3x - 4)(x - 3)
8. x² + 7x + 12
= x² + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 4)(x + 3)
9. q² - q - 72
q² + 8q - 9q - 72
= q(q + 8) - 9(q - 8)
= (q - 9)(q - 8)
10. 2p² + 5p - 12
= 2p² + 8p - 3p - 12
= 2p(p + 4) - 3(p + 4)
= (2p - 3)(p + 4)
Hope this helps!
Answer: mhmm down
Step-by-step explanation:
1. q² - 3q + 2
= q² - q - 2q + 2
= q(q - 1) - 2(q - 1)
= (q - 2)(q - 1)
2. x² + x - 20
= x² + 5x - 4x - 20
= x(x + 5) - 4(x + 5)
= (x - 4)(x + 5)
3. 6x² + 29x + 13
= 6x² + 3x + 26x + 13
= 3x(2x + 1) + 13(2x + 1)
= (3x + 13)(2x + 1)
4. 2p² - 23p - 12
= 2p² + p - 24p - 12
= p(2p + 1) - 12(2p + 1)
= (p - 12)(2p + 1)
5. 2a² - 5a - 12
= 2a² - 8a + 3a - 12
= 2a(a - 4) + 3(a - 4)
= (2a + 3)(a - 4)
6. 7q² - 5q - 12
= 7q² + 7q - 12q - 12
= 7q(q + 1) - 12(q + 1)
= (7q - 12)(q + 1)
7. 3x² - 13x + 12
= 3x² - 9x - 4x + 12
= 3x(x - 3) - 4(x -3)
= (3x - 4)(x - 3)
8. x² + 7x + 12
= x² + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 4)(x + 3)
9. q² - q - 72
q² + 8q - 9q - 72
= q(q + 8) - 9(q - 8)
= (q - 9)(q - 8)
10. 2p² + 5p - 12
= 2p² + 8p - 3p - 12
= 2p(p + 4) - 3(p + 4)
= (2p - 3)(p + 4)