CHOOSE ANY BLOCK AND FACTORISE

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CHOOSE ANY BLOCK AND FACTORISE 2x² + 7x +3 2x² – 12x + 10 1) 2x² + 5x + 2 3x² + 23x + 14 3x² – 7x + 2 2) 2x² + 11x + 12 2x² + 14x + 20 3x² + 8x – 3 3) 6x² + 7x + 2 5x² + 29x + 36 3x² – 5x – 2 4) 3x² – 7x + 2

The Correct Answer and Explanation is:

Of the blocks provided, the third block is selected for factorization. This block contains four quadratic trinomials of the form ax² + bx + c.

Introduction to Factorising Quadratic Trinomials

Factorising a quadratic trinomial is the process of expressing it as a product of two linear binomials. The most common method for trinomials where the leading coefficient ‘a’ is not 1 is the ‘ac method’, also known as factoring by grouping or splitting the middle term.

The procedure involves these steps:

  1. Identify the coefficients a, b, and c in the expression ax² + bx + c.
  2. Calculate the product of a and c (ac).
  3. Find two numbers that multiply to give the value ‘ac’ and add to give the value ‘b’.
  4. Rewrite the middle term ‘bx’ as the sum of two terms using the numbers found in the previous step.
  5. Factor the resulting four-term polynomial by grouping the terms into two pairs and extracting the common factors.

Solutions for Block 3

1) Factorise 2x² + 5x + 2

  • Here, a = 2, b = 5, and c = 2.
  • The product ac = 2 × 2 = 4.
  • Two numbers that multiply to 4 and add to 5 are 4 and 1.
  • Rewrite the expression: 2x² + 4x + 1x + 2
  • Factor by grouping: (2x² + 4x) + (x + 2) = 2x(x + 2) + 1(x + 2)
  • The factored form is (2x + 1)(x + 2).

2) Factorise 2x² + 11x + 12

  • Here, a = 2, b = 11, and c = 12.
  • The product ac = 2 × 12 = 24.
  • Two numbers that multiply to 24 and add to 11 are 8 and 3.
  • Rewrite the expression: 2x² + 8x + 3x + 12
  • Factor by grouping: (2x² + 8x) + (3x + 12) = 2x(x + 4) + 3(x + 4)
  • The factored form is (2x + 3)(x + 4).

3) Factorise 6x² + 7x + 2

  • Here, a = 6, b = 7, and c = 2.
  • The product ac = 6 × 2 = 12.
  • Two numbers that multiply to 12 and add to 7 are 4 and 3.
  • Rewrite the expression: 6x² + 4x + 3x + 2
  • Factor by grouping: (6x² + 4x) + (3x + 2) = 2x(3x + 2) + 1(3x + 2)
  • The factored form is (2x + 1)(3x + 2).

4) Factorise 3x² – 7x + 2

  • Here, a = 3, b = -7, and c = 2.
  • The product ac = 3 × 2 = 6.
  • Two numbers that multiply to 6 and add to -7 are -6 and -1.
  • Rewrite the expression: 3x² – 6x – 1x + 2
  • Factor by grouping: (3x² – 6x) – (x – 2) = 3x(x – 2) – 1(x – 2)
  • The factored form is (3x – 1)(x – 2).

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