High School

Multiply these polynomials using the tabular method: [tex](2x + 5)(x^2 + 5x + 1)[/tex].

A. [tex]2x^3 + 15x^2 + 27x + 5[/tex]
B. [tex]2x^3 + 15x^2 + 11x + 5[/tex]
C. [tex]2x^3 + 25x^2 + 11x + 5[/tex]
D. [tex]2x^3 + 25x^2 + 27x + 5[/tex]

Answer :

Final answer:

To multiply the polynomials (2x + 5) and (x² + 5x + 1), the tabular method is used, resulting in the polynomial 2x³ + 15x² + 27x + 5 after addition of like terms.

Explanation:

To multiply the polynomials (2x + 5) and (x² + 5x + 1) using the tabular method, we construct a table with rows representing the terms of the first polynomial and columns representing the terms of the second polynomial.

Then, we multiply each term of the first polynomial with each term of the second polynomial and add up the products according to the powers of x.

  • The product of 2x and x² is 2x³.
  • The product of 2x and 5x is 10x².
  • The product of 2x and 1 is 2x.
  • The product of 5 and x² is 5x².
  • The product of 5 and 5x is 25x.
  • The product of 5 and 1 is 5.

Adding up the like terms, we get:

  • 2x³ from the 2x and x² product.
  • 10x² + 5x² = 15x² from the 2x and 5x and the 5 and x² products.
  • 2x + 25x = 27x from the 2x and 1 and the 5 and 5x products.
  • 5 from the 5 and 1 product.

So, the multiplication of (2x + 5) and (x² + 5x + 1) using the tabular method is 2x³ + 15x² + 27x + 5, which corresponds to option (a).

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