How do you factor the expression #x^2+ 2x -3#?

2 Answers
Jim G.
Feb 22, 2016

(x + 3 )(x - 1 )

Explanation:

To factor , consider the factors of the constant term - 3 which sum to give the coefficient of the x term +2

factors of - 3 are ± (1 , 3 )

The required factors are +3 and - 1 ,as they sum to +2.

#rArr x^2 + 2x - 3 = (x + 3 )(x - 1 )#

This may be confirmed by distributing the brackets.

Noah G
Feb 22, 2016

This is a trinomial of the form #y = ax^2 + bx + c#, which is factored as #(x + m)(x + n)#

Explanation:

We can find the value of m and n by finding two numbers that multiply to c and that add to b. Two numbers that multiply to -3 and that add to +2 are 3 and -1:

So, when factored, the expression is #(x + 3)(x - 1)#

Practice exercises:

  1. Find which of the following trinomials are factorable. For those that are, factor them completely.

a) #x^2 + 7x + 12#

b) #x^2 - 7x - 12#

c) #x^2 - 7x + 12#

d) #-x^2 + 7x - 12#

d) #x^2 + 8x + 16#

e) #x^2 + 8x - 16#

f) #x^2 - 8x + 16#

g) #x^2 + 16#

h) #x^2 - 16#

Good luck!

Related questions
See all questions in Factoring Completely
Impact of this question
26211 views around the world
You can reuse this answer
Creative Commons License