Pedagogy of Mathematics (Part II) - Algebra, Algebra, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy, Mathematics, Factorization using synthetic division

1. PEDAGOGY OF
MATHEMATICS – PART II
BY
Dr. I. UMA MAHESWARI
Principal
Peniel Rural College of Education,Vemparali,
Dindigul District
iuma_maheswari@yahoo.co.in

2. STD IX
CHAPTER 3 – ALGEBRA
Ex – 3.8

10. (i) x3 – 3x² – 10x + 24
Solution:
p(x) – x3 – 3x² – 10x + 24
p(1) = 13 – 3(1)² – 10(1) +
24
= 1 – 3 – 10 + 24
= 25 – 13
≠ 0
x – 1 is not a factor
p(-1) = (-1)3 – 3(-1)² – 10(-1) +
24
= – 1 – 3(1) + 10 + 24
= -1 – 3 + 10 + 24
= 34 – 4
= 30
≠ 0
x + 1 is not a factor

11. p(2) = 23 – 3(2)² – 10(2) + 24
= 8 – 3(4) – 20 + 24
= 8 – 12 – 20 + 24
= 32 – 32
= 0
∴ x – 2 is a factor
x² – x – 12 = x² – 4x + 3x – 12
= x(x – 4) + 3 (x – 4)
= (x – 4) (x + 3)
∴ The factors of x3 – 3x² – 10x + 24 = (x – 2) (x – 4)
(x + 3)

12. (ii) 2x3 – 3x² – 3x + 2
Solution:
p(x) = 2x3 – 3x² – 3x + 2
P(1) = 2(1)3 – 3(1)² – 3(1) +
2
= 2 – 3 – 3 + 2
= 2 – 6
= -4
≠ 0
x – 1 is not a factor
P(-1) = 2(-1)3 – 3(-1)² – 3(-1)
+ 2
= -2 – 3 + 3 + 2
= 5 – 5
= 0
∴ x + 1 is a factor

13. 2x² – 5x + 2 = 2x² – 4x – x + 2
= 2x(x – 2) – 1 (x – 2)
= (x – 2) (2x – 1)
∴The factors of 2x3 – 3x² – 3x + 2 = (x + 1) (x – 2) (2x – 1)

14. (iii) – 7x + 3 + 4x3
Solution:
p(x) = – 7x + 3 +
4x3
= 4x3 – 7x + 3
P(1) = 4(1)3 – 7(1)
+ 3
4 – 7 + 3
= 7 – 7
= 0
∴ x – 1 is a factor
4x² + 4x – 3 = 4x² + 6x – 2x – 3
= 2x(2x + 3) – 1 (2x + 3)
= (2x + 3) (2x – 1)
∴ The factors of – 7x + 3 + 4x3 = (x – 1) (2x + 3)

15. (iv) x3 + x² – 14x – 24
Solution:
p(x) = x3 + x² – 14x – 24
p(1) = (1)3 + (1)2 – 14 (1) –
24
= 1 + 1 – 14 – 24
= -36
≠ 0
x + 1 is not a factor.
p(-1) = (-1)3 + (-1)² – 14(-1) –
24
= -1 + 1 + 14 – 24
= 15 – 25
≠ 0
x – 1 is not a factor.

16. = x(x – 4) + 3 (x – 4)
= (x – 4) (x + 3)
This (x + 2) (x + 3) (x – 4) are the
factors.
x3 + x2 – 14x – 24 = (x + 2) (x + 3) (x
– 4)

17. (v) x3 – 7x + 6
Solution:
p(x) = x3 – 7x + 6
P( 1) = 13 – 7(1) + 6
= 1 – 7 + 6
= 7 – 7
= 0
∴ x – 1 is a factor

18. (vi) x3 – 10x² – x + 10
p(x) = x3 – 10x2 – x + 10
= 1 – 10 – 1 + 10
= 11 – 11
= 0
∴ x – 1 is a factor
x2 – 9x – 10 = x2 – 10x + x
– 10
= x(x – 10) + 1 (x – 10)
= (x – 10) (x + 1)
This (x – 1) (x + 1) (x – 10) are the factors.
∴ x3 – 10x2 – x + 10 = (x – 1) (x – 10) (x +
1)