Question

Which represents factorization of the trinomial 10x^2 + 11x + 3 ?

(5x+3)(2x+1)

(5x+1)(2x+3)

(5x+1)(3x+3)

(5x+2)(3x+1)

Answer 1

`(5x+3)(2x+1)`

Explanation:

- Sum-product method

For a polynomial of the form
`ax^2+bx+c`

We rewrite the middle term as a sum of two terms whose product is

`a*c = 10*3 = 30` and whose sum is
`b = 11`

`10x^2 + 11x + 3`

`10x^2 + 6x + 5x + 3 -- > (3*10 = 6*5), (6+5 = 11)`

- Factor using the greatest common factors (GCF)

`2x(5x + 3) + 1(5x + 3)`

- Final Answer

`= (5x+3)(2x+1)`