10t^2 +34t-2410t2+34t−24
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like at^2 + bt + cat2+bt+c, we need to think of 2 numbers such that:
N_1*N_2 = a*c = 10*(-24) = -240N1⋅N2=a⋅c=10⋅(−24)=−240
AND
N_1 +N_2 = b = 34N1+N2=b=34
After trying out a few numbers we get N_1 = 40N1=40 and N_2 =-6N2=−6
40*(-6) = -24040⋅(−6)=−240, and 40+(-6)= 3440+(−6)=34
10t^2 +34t-24 =10t^2 +40t-6t-24 10t2+34t−24=10t2+40t−6t−24
= 10t (t+4) - 6(t+4)=10t(t+4)−6(t+4)
(t+4)(t+4) is a common factor to each of the terms
= (10t-6) (t+4)=(10t−6)(t+4)
color(blue)( (10t-6) (t+4)(10t−6)(t+4) is the factorised form of the expression.
