Question

factorise the following by splitting the middle term:
1) 12x^2 - 7x + 1
2) 2x^2 + 7x +3
3) 6x^2 + 5x - 6
4) 3x^2 - x - 4
5) 6x^2 + 17x + 5​

Answer 1

Find the factors of each coefficient. It means to check every number before unknowns(x² and 1) and find the divisors.

Factors of:

12 → 1, 2, 3, 4, 6, 12

6 → 1, 2, 3, 6

The answers should be figured out by yourself.

1) 3+4=7

2) 1+6=7

3) 9-4=5

4) 3-4=-1

5) 15+2=17 (3×5+1×2=17)

Answer 2

Step-by-step explanation:

AnswEr:

$\bullet\:\large\sf\pink{12x^2 - 7x + 1}$

$\:\:\;\:\:\:\dag\:\footnotesize{\underline{\underline{\sf{\red{Using\: Splitting\: The\: Middle\:Term\;Method}}}}}$

$\implies\sf\; 12x^2 - 4x - 3x + 1 \\ \\ \implies\sf 4x(3x -1) -1 (3x -1)\\ \\ \implies\sf (3x -1) (4x -1) \\ \\ \implies\sf x = \dfrac{1}{3} \:\& x = \dfrac{1}{4}$

$\rule{120}2$

$\bullet\:\large\sf\pink{2x^2 + 7x + 3}$

$\implies\sf 2x^2 + 6x + x + 3 \\ \\ \implies\sf 2x(x +3) +1(x +3) \\ \\ \implies\sf (x + 3) (2x +1)\\ \\ \implies\sf x = -3 \:\& \: x = \dfrac{-1}{2}$

$\rule{120}2$

$\bullet\:\large\sf\pink{6x^2 + 5x -6}$

$\implies\sf 6x^2 + 9x - 4x - 6\\ \\ \implies\sf 3x(2x + 3) -2(2x +3) \\ \\ \implies\sf (2x +3) (3x -2)\\ \\ \implies\sf x = \dfrac{-3}{2} \:\&\: x = \dfrac{2}{3}$

$\rule{120}2$

$\bullet\;\large\sf\pink{3x^2 - x - 4}$

$\implies\sf 3x^2 - 4x + 3x -4 \\ \\ \implies\sf x(3x -4) +1(3x -4) \\ \\ \implies\sf (3x - 4) (x +1)\\ \\ \implies\sf x = \dfrac{4}{3} \:\&\: x = -1$