Question

[ 5x² + 13x + 6 ]

Factor this trinomial. Please show your work.

a) (5x + 2)(x + 3)

b) (5x - 2)(x + 3)

c) (5x + 1)(x + 6)

d) (5x - 1)(x + 6)

Answer 1

`\sf\\\textsf{There is no correct answer in the options.}`

Step-by-step explanation:

`\sf\\5x^2+13x+6\\=5x^2+(10+3)x+6\\=5x^2+10x+3x+6\\=5x(x+2)+3(x+2)\\=(x+2)(5x+3)`

Answer 2

The correct factorization of the trinomial [ 5x² + 13x + 6 ] is (a) (5x + 2)(x + 3). Therefore the correct option is a). (5x + 2)(x + 3).

Step-by-step explanation:

To factorize the trinomial [ 5x² + 13x + 6 ], we look for two binomials whose product results in the given expression. The expression can be factored by breaking down the middle term (13x) into two terms whose coefficients multiply to give the product of the leading and trailing coefficients (5 * 6 = 30) and whose sum equals the middle coefficient (13). The pair that satisfies these conditions is (5x + 2)(x + 3).

The factorization process involves splitting the middle term as follows:

5x² + 13x + 6 = 5x² + 10x + 3x + 6

Now, group the terms:

(5x² + 10x) + (3x + 6)

Factor out the common factor from each group:

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

Now, factor out the common binomial factor (x + 2):

(5x + 3)(x + 2).

Therefore, the correct factorization is (5x + 2)(x + 3), which corresponds to option (a). Therefore the correct option is a). (5x + 2)(x + 3).