Question

Factories each of the following middle term breaking .
a) x² - 8x + 7
b) x²+ 6x - 7
c) x²+7x+10
d) x²- 6x + 9
e) x²+3x - 10
h) q² - 12q + 35​

Answer 1

a) x² - 8x + 7

= x² - (7 + 1)x + 7

= x² - 7x - x + 7

= x(x - 7) - 1(x - 7)

= (x - 7) (x - 1)

b) x² +6x - 7

= x² + (7 - 1)x - 7

= x² + 7x - x - 7

= x(x + 7) - 1(x + 7)

= (x+7) (x - 7)

c) x²+7x+10

= x² + (5+2)x + 10

= x² + 5x + 2x + 10

= x(x+5) +2(x+5)

= (x+5)(x+2)

d) x² - 6x + 9

= x² - (3+3)x + 9

= x² - 3x - 3x + 9

= x(x - 3) - 3(x - 3)

= (x - 3)(x - 3)

e) x²+3x - 10

= x² +(5 - 2)x - 10

= x² + 5x - 2x - 10

= x(x+5) - 2(x+5)

= (x+5) (x - 2)

f) q² -12q +35

= q² - (7+5)q +35

= q² - 7q - 5q + 35

= q(q - 7) - 5(q - 7)

= (q - 7)( q - 7)

hope you get your answer.