Question

62. Factorise :
1. x2 - 17x + 16
2. x2 – 23x + 42
3. y2 + 10y + 24
4. Z2 + 122+27
5. x2 + 15x + 56
6. p2 + 6p + 8
7. x2 + 5x+6​

Answer 1

1)x^2-17x+16

x^2-16x-1x+17

x(x-16)-1(x-16)

(x-1) (x-16)

factors of this equation are (x-16) and (x-1)

2)x^2 – 23x + 42

x^2-21x-2x+42

x(x-21) -2(x-21)

(x -2) (x -21)

factors of this equation are (x-2) and (x-21)

3)y^2 + 10y + 24

y^2+6y+4y+24

y(y+6)+4(y+6)

(y + 6) (y + 4)

factors of this equation are (y+6) and (y+4)

4)Z^2 + 12z+27

z^2 + 9z + 3z + 27

z (z + 9 ) + 3 ( z + 9 )

(z + 3) ( z + 9)

factors of this equation are (z+3) and (z+9)

5)x^2 + 15x + 56

x^2 + 8x + 7x + 56

x( x + 8 ) + 7 ( x + 8)

(x +7) ( x +8)

factors of this equation are ( x + 8) and (x + 7)

6)p^2 + 6p + 8

p^2 + 4p + 2p + 8

p(p + 4) + 2(p + 4)

(p+2) (p+4)

factors of this equation are (p + 2) and (p + 4)

7) x^2 + 5x+6

x^2 + 3x + 2x + 6

x (x + 3 ) + 2 (x + 3)

(x + 3) (x + 2)

factors of this equation are (x +3) and (x + 2)

⚫In these above quadratic equations we can find the factors of the equation by splitting the middle term.