Factorise: (i) 12x² - 7x + 1 (ii) 2x² + 7x + 3 (iii) 6x² + 5x - 6 (iv) 3x² - x - 4

Solution:

By the splitting of the middle term, we can find factors using the following method.

Find two numbers p, q such that,

p + q = co-efficient of x

p × q = product of the co-efficient of x² and the constant term.

(i) 12x² - 7x + 1

p + q = -7 (co-efficient of x)

p × q = 12 × 1 = 12 (co-efficient of x² and the constant term)

By trial and error method, we get p = -4, q = -3

Now splitting the middle term of the given polynomial,

12x² - 7x + 1 = 12x² - 4x - 3x + 1

= 4x(3x - 1) - 1(3x - 1)

= (3x - 1) (4x - 1) [taking (3x - 1) as a common term]

(ii) 2x² + 7x + 3

p + q = 7 (co-efficient of x)

p × q = 2 × 3 = 6 (product of co-efficient of x² and the constant term)

By trial and error method, we get p = 6, q = 1.

Now splitting the middle term of the given polynomial,

2x² + 7x + 3 = 2x² + 6x + x + 3

= 2x(x + 3) + 1(x + 3)

= (2x + 1) (x + 3)

(iii) 6x² + 5x - 6

p + q = 5 (co-efficient of x)

p × q = 6 × (-6) = -36 (product of co-efficient of x² and the constant term)

By trial and error method, we get p = 9, q = -4.

Now splitting the middle term of the given polynomial,

6x² + 5x - 6 = 6x² + 9x - 4x - 6

= 3x(2x + 3) - 2(2x + 3)

= (3x - 2) (2x + 3)

(iv) 3x² - x - 4

p + q = -1 (co-efficient of x)

p × q = 3 × (-4) = -12 (product of co-efficient of x² and the constant term.)

By trial and error method, we get p = -4, q = 3.

Now splitting the middle term of the given polynomial,

3x² - x - 4 = 3x² - 4x + 3x - 4

= 3x² + 3x - 4x - 4

= 3x(x + 1) - 4(x + 1)

= (3x - 4) (x +1)

☛ Check: NCERT Solutions Maths Class 9 Chapter 2

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Video Solution:

Factorise: (i) 12x² - 7x + 1  (ii) 2x² + 7x + 3  (iii) 6x² + 5x - 6  (iv) 3x² - x - 4

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.4 Question 4:

Summary:

The factorized form of 12x² - 7x + 1, 2x² + 7x + 3, 6x² + 5x - 6, 3x² - x - 4 are (3x - 1)(4x - 1), (2x + 1)(x + 3), (3x - 2)(2x + 3), (3x - 4)(x + 1)

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☛ Related Questions:

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