x^2-19x-120

Question

x^2-19x-120

anonymous · Answer

Factor -120, find a factor pair ab that adds to -19, use those to represent the trinomial as the product (x+a)(x+b).

anonymous · Answer

I understand the process but I am wracking my brain trying to figure out which pair I should use...

unklerhaukus · Answer

$$x^2-19x-120=(x+ a )(x+ b)=x^2+(a+b)x+ab$$
$$ab=-120$$
$$a+b=-19$$

unklerhaukus · Answer

$$-120=\pm1\times\mp120,\quad\pm2\times\mp60,\quad\pm3\times\mp40,\quad\pm4\times\mp30$$$$\qquad\qquad\pm5\times\mp24,\quad\pm 6\times\mp20,\quad \pm 8\times\mp15,\quad \pm10\times \mp12$$

unklerhaukus · Answer

which pair of factors add to give negative nineteen?

anonymous · Answer

Thank you unklerhaukus I just realized while looking at your pairing that I had left one out and that is why I was not getting my answer the factors are 5 & 24

unklerhaukus · Answer

which one is negative

anonymous · Answer

24

unklerhaukus · Answer

right,

so what does $x^2-19x-120$ look like in factored form ?

anonymous · Answer

(x+5)(x-24)

unklerhaukus · Answer

to check if your got it right , expand the brackets 

$$(x+5)(x-24)=x(x-24)+5(x-24)$$$$\quad\qquad\qquad\qquad=x^2-24x+5x-120$$$$\quad\qquad\qquad\qquad=x^2+(-24+5)x-120$$$$\color{orange}{BINGO}$$