Question

factorise the quadratic trinomials :
${x}^{2} - 10x + 24$
​

Answer 1

Answer:

factorise it

In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that:

N1⋅N2=a⋅c=1⋅24=24

AND

N1+N2=b=−10

After trying out a few numbers we get N1=−6 and N2=−4

−6⋅−4=24, and (−6)+(−4)=−10

x2−10x+24=x2−6x−4x+24

=x(x−6)−4(x−6)

(x−6) is a common factor to each of the terms

=(x−6)(x−4)

Answer 2

ANSWER:

• Required Factorisation = (x-4)(x-6)

GIVEN:

• x²-10x+24

TO FIND:

• Factorise the above expression.

SOLUTION:

= x²-10x+24

= x²-4x-6x+24

= (x²-4x)+(-6x+24)

= x(x-4)-6(x-4)

= (x-4)(x-6)

Required Factorisation = (x-4)(x-6)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab