Question

Multiplying polynomials

Please look at the picture and these are the answers I can choose from a / 10x_14
B / 10x^2 + 31x -14
C 7x+5
D 10x+5

Answer 1

The product of
`\((5x - 2)\)` and
`\((2x + 7)\)` is
`\(10x^2 + 31x - 14\)`. The correct option is B.

To multiply the polynomials
`\((5x - 2)\)` and
`\((2x + 7)\)`, you can use the distributive property (FOIL method):

`\[ (5x - 2)(2x + 7) \]`

Here's how you can multiply them:

1. Multiply the First Terms:

`\(5x * 2x = 10x^2\)`

2. Multiply the Outer Terms:

`\(5x * 7 = 35x\)`

3. Multiply the Inner Terms:

`\((-2) * 2x = -4x\)`

4. Multiply the Last Terms:

`\((-2) * 7 = -14\)`

Now, combine the results:

`\[ (5x - 2)(2x + 7) = 10x^2 + 35x - 4x - 14 \]`

Combine like terms:

`\[ 10x^2 + 31x - 14 \]`

So, the product of
`\((5x - 2)\)` and
`\((2x + 7)\)` is
`\(10x^2 + 31x - 14\)`.