The product of a + 3 and - 2a² + 15a + 6 is - 2a³ + xa² + 51a + 18. What is the value of x?

Solution:

Let’s find the product of the LHS, then compare the coefficients of the variables with RHS.

Step 1: Simplify (- 2a² + 15a + 6) × (a + 3)

= - 2a³ + xa² + 51a + 18

Step 2: Add the like terms.

⇒ - 2a³ + 15a² + 6a - 6a² + 45a + 18

= - 2a³ + xa² + 51a + 18

⇒ - 2a³ + 9a² + 51a + 18

= 2a³ + xa² + 51a + 18

Step 3: Compare the coefficients of a³ = -2, a² = 9, a = 51, constant term = 18.

⇒ Thus, the value of x is 9.

The product of a + 3 and - 2a² + 15a + 6 is - 2a³ + xa² + 51a + 18. What is the value of x?

Summary:

If the product of a + 3 and - 2a² + 15a + 6 is - 2a³ + xa² + 51a + 18, then the value of x is 9.