Factor completely 4x² + 25x + 6.
(4x + 1)(x + 6), (4x + 6)(x + 1), (2x + 3)(2x + 2), (2x + 6)(2x + 1)

Solution:

Given is a quadratic polynomial.

Step 1: Identify the values of a, b and c.

In the above equation, a is the coefficient of x² = 4,

b is the coefficient of x = 25, and

c is the constant term = 6.

Step 2: Solve for x by factoring polynomial 

Multiply a and c and find the factors that add up to b.

4 × (6) = 24 

⇒ 1 and 24 are the factors of 24 that add up to b.

Step 3: Let's split the middle term

Split bx into two terms.

4x² + 24x + 1x + 6

Step 4: Take out the common factors by grouping.

4x(x + 6) +1(x + 6)

(4x + 1) (x + 6) 

Therefore, the The factors of the given polynomial 4x² + 25x + 6 are (4x + 1)(x + 6)

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Factor completely 4x² + 25x + 6.
(4x + 1)(x + 6), (4x + 6)(x + 1), (2x + 3)(2x + 2), (2x + 6)(2x + 1)

Summary:

The factors of the equation 4x² + 25x + 6 are (4x + 1)(x + 6).