Question

Factorise and divide :-(x2 +7x+ 12) divide (x-3)​

Answer 1

Answer:

x+4

Step-by-step explanation:

Given,

x² + 7x + 12

By middle term splitting, we have

x² +(3+4)x + 12

x² + 3x + 4x + 12

x(x+3) +4(x+3)

(x+4)(x+3)

Dividing this with x+3, we get

x+4

Answer 2

Given,

• p(x) = x² + 7x + 12
• g(x) = x - 3

To Find,

• Factorise p(x).
• Divide p(x) by g(x).

Solution,

p(x) = x² + 7x + 12

p(x) = x² + 7x + 12 = x² + 7x + 12

p(x) = x² + 7x + 12 = x² + 4x + 3x + 12

p(x) = x² + 7x + 12 = x(x + 4) + 3(x + 4)

p(x) = x² + 7x + 12 = (x + 3)(x + 4)

x - 3 ) x² + 7x + 12 ( x + 10

•••••• x² - 3x

•••••• – +

•••••• 0 + 10x + 12

•••••••••••• 10x - 30

•••••••••••• — +

•••••••••••• 42

Verification,

Dividend = Divisor × Quotient + Remainder

x² + 7x + 12 = (x - 3)(x + 10) + 42

x² + 7x + 12 = (x + (-3))(x + 10) + 42

x² + 7x + 12 = x² + (-3 + 10)x - 30 + 42

x² + 7x + 12 = x² + 7x + 12

L.H.S. = R.H.S.

•••••••••••••••••Hence Proved,

Required Answer,

x² + 7x + 12 = (x + 3)(x + 4)

By dividing x² + 7x + 12 by x - 3,

Quotient = x + 10

Remainder = 42