Final answer:
The tabular method for multiplying the given polynomials involves creating a table, multiplying each term of the first polynomial by each term of the second, placing the products in cells, and then adding like terms to get the expanded form: x³ + 6x² + 11x + 12.
Step-by-step explanation:
The tabular method, also known as the grid method, is a way to multiply polynomials. For the expression (x²+2x+3)(x+4), we create a table where we list each term of the first polynomial on the left side and each term of the second polynomial on the top. Then we multiply each corresponding pair of terms and place the product in the corresponding cell of the table. Finally, we add up the products to find the expanded form of the polynomial.
Here's the step-by-step process:
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- Write down the first polynomial: x², 2x, and 3
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- Write down the second polynomial: x and 4
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- Multiply each term from the first polynomial with each term of the second. We get: x³, 4x², 2x², 8x, 3x, and 12.
Now, add the like terms: x³ + (4x² + 2x²) + (8x + 3x) + 12 which simplifies to x³ + 6x² + 11x + 12.