How do you factor $n^{2} + 2 n - 15$ $n^2+2n-15$ ?

Question

How do you factor $n^{2} + 2 n - 15$ $n^2+2n-15$ ?

2 Answers

Impact of this question

3802 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-30T10:48:00

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

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

$N_{1} \cdot N_{2} = 1 \cdot - 15 = - 15$ $N_1*N_2 = 1*-15 = -15$
AND
$N_{1} + N_{2} = b = 2$ $N_1 +N_2 = b = 2$

After trying out a few numbers we get $N_{1} = 5$ $N_1 = 5$ and $N_{2} = - 3$ $N_2 =-3$
$5 \cdot - 3 = - 15$ $5*-3= -15$ , and $5 + (- 3) = 2$ $5+(-3)= 2$

$n^{2} + 2 n - 15 = n^{2} + 5 n - 3 n - 15$ $n^2+2n-15 = n^2 + 5n - 3n -15$

$= n (n + 5) - 3 (n + 5)$ $= n(n+5) - 3(n+5)$

$(n + 5)$ $(n+5)$ is a common factor to each of the terms

$= (n + 5) (n - 3)$ $=color(green)((n+5)(n-3)$

Answer 2 · 2015-05-30T10:50:42

$n^{2} + 2 n - 15$ $n^2+2n-15$

By factorization:

$n^{2} + 2 n - 15$ $n^2+color(red)2ncolor(blue)[-15$

working $\Rightarrow - 5 + 3 = 2, - 5 \times 3 = - 15$ $rArr -5+3=color(red)2, -5xx3=color(blue)[-15$

$n^{2} - 5 n + 3 n - 15$ $n^2-5n+3n-15$

$n (n - 5) + 3 (n - 5)$ $n(n-5)+3(n-5)$

Answer :
$(n + 3) (n - 5)$ $color(green)[(n+3)(n-5)$

Science

Math

Humanities

... and beyond

How do you factor $n^{2} + 2 n - 15$ $n^2+2n-15$ ?

2 Answers

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you factor n2+2n−15n^2+2n-15?

2 Answers

Related questions

Impact of this question

How do you factor $n^{2} + 2 n - 15$ $n^2+2n-15$ ?