Question

(x² + 3x + 1)(x² + x + 2)
Help! Please!

Answer 1

Solution:
Step 1. Distribute sum groups


`x^(2) ( x^(2) +x+2)+3x( x^(2) +x+2)+ x^(2) +x+2`

Step 2. Distribute

`x^(4) + x^(3) + 2x^(2) +3x( x^(2) +x+2)+ x^(2) +x+2`

Step 3. Distribute

`x^(4) + x^(3) +2 x^(2) +3 x^(3) +3 x^(2) +6x+ x^(2) + x + 2`

Step 4. Gather like terms


`x^(4) + ( x^(3) + 3x^(3) ) + (2 x^(2) +3 x^(2) + x^(2) )+(6x+6)+2`

Step 5. Simplify and that's your answer


`x^(4) +4 x^(3) + 6 x^(2) +7x+2`

Done! :)

Answer 2

X ^ 4 + X ^3 + 2x^2 + 3x^3 + 3x^2 + 6x + x^2 + X + 2.

Then collect like terms and arrange the polynomial in descending order from the highest exponential value to the lowest.

X^4 + 4x^3 + 6x^2 + 7x + 2.

This is the final solution.