Question

How do you factor the expression `5x^2+7x+2`?

Answer 1

(x + 1 )(5x + 2 )

Explanation:

The standard form of the quadratic function is `ax^2 + bx + c`

To factor , begin by considering the factors of the product ac , which also sum to give b , the coefficient of the x term.

in this question a = 5 , b = 7 and c = 2

hence: `ac = 5xx2 =10 " whose factors are ±(1,2,5,10)"`

The 'pair' are 5 and 2 as 5 + 2 = 7 = b

Now, rewrite the expression , replacing 7x by 5x + 2x

hence : `5x^2 + 7x + 2 = 5x^2 + 5x + 2x + 2`

Factor the pairs : `[5x^2 +5x ] " and " [2x + 2 ]`

`5x^2 + 5x = 5x(x + 1 ) " and " 2x + 2 = 2(x +1)`

Finally , 'take out' the common factor (x + 1)

hence: (x +1)(5x + 2 )

`rArr 5x^2 + 7x + 2 = (x + 1 )(5x + 2 )`