How do you factor the trinomial $5 t - 50 + t^{2}$ $5t-50+t^2$ ?

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Answer 1 · 2015-12-12T14:48:56

$(t - 5) (t + 10)$ $color(blue)( (t-5) (t+10)$ is the factorised form of the expression.

$5 t - 50 + t^{2}$ $5t-50+t^2$

$t^{2} + 5 t - 50$ $t^2 +5t-50$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a t^{2} + b t + c$ $at^2 + bt + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot - 50 = - 50$ $N_1*N_2 = a*c = 1*-50 = -50$

AND

$N_{1} + N_{2} = b = 5$ $N_1 +N_2 = b = 5$

After trying out a few numbers we get $N_{1} = 10$ $N_1 = 10$ and $N_{2} = - 5$ $N_2 =-5$

$10 \cdot (- 5) = - 50$ $10*(-5) = -50$ , and $10 + (- 5) = 5$ $10+(-5)= 5$

$t^{2} + 5 t - 50 = t^{2} + 10 t - 5 t - 50$ $t^2 +color(blue)(5t)-50 = t^2 +color(blue)(10t-5t)-50$

$t (t + 10) - 5 (t + 10)$ $t(t+10) -5(t+10)$

$= (t - 5) (t + 10)$ $=color(blue)( (t-5) (t+10)$

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