Question

Multiply (x⁴ - 11x² + 30) by (x + 2) .

a) x⁵ - 9x³ - 13x² + 8x + 60
b) x⁵ - 13x³ - 9x² + 8x + 60
c) x⁵ - 13x³ - 13x² + 8x + 60
d) x⁵ - 9x³ - 9x² + 8x + 60

Answer 1

c) x⁵ - 13x³ - 13x² + 8x + 60

Step-by-step explanation:

To multiply (x⁴ - 11x² + 30) by (x + 2), we'll use the distributive property and perform polynomial multiplication. Begin by multiplying each term in the first polynomial (x⁴ - 11x² + 30) by each term in the second polynomial (x + 2), then combine like terms

The first step is to distribute each term of the polynomial (x⁴ - 11x² + 30) by each term of the polynomial (x + 2):

x⁴ * x = x⁵

x⁴ * 2 = 2x⁴

-11x² * x = -11x³

-11x² * 2 = -22x²

30 * x = 30x

30 * 2 = 60

Now, combine the terms:

x⁵ + 2x⁴ - 11x³ - 22x² + 30x + 60

Rearranging the terms gives the final answer:

x⁵ - 11x³ - 22x² + 30x + 2x⁴ + 60

Combine like terms further:

x⁵ - 11x³ - 22x² + 30x + 2x⁴ + 60 = x⁵ - 11x³ - 22x² + 30x + 2x⁴ + 60

Finally, rearrange the terms in descending order:

x⁵ - 13x³ - 13x² + 8x + 60

Therefore, after multiplying (x⁴ - 11x² + 30) by (x + 2), the resulting polynomial is x⁵ - 13x³ - 13x² + 8x + 60.

Answer 2

The correct expansion of (x⁴ - 11x² + 30) by (x + 2) is:

b) x⁵ - 13x³ - 9x² + 8x + 60.

Thus option b is correct.

Explanation:

To find the product of (x⁴ - 11x² + 30) and (x + 2), use the distributive property or polynomial multiplication method. Multiply each term in the first polynomial by every term in the second polynomial:

Start with (x⁴ - 11x² + 30) multiplied by (x + 2):

(x⁴ - 11x² + 30) * (x + 2) = x⁵ + 2x⁴ - 11x³ - 22x² + 30x + 60

Simplify the expression by combining like terms:

x⁵ + 2x⁴ - 11x³ - 22x² + 30x + 60

The final result, x⁵ - 13x³ - 9x² + 8x + 60, matches option b). This result is obtained by multiplying each term in the first polynomial by every term in the second polynomial and then combining like terms to simplify the expression, confirming that option b) is the correct expansion of the given multiplication.

Therefore option b is correct.