Answer :
Final answer:
The sum of the given polynomials is 16x^3 + 9x^2 + 9x + 13. Adding the expression 3x - 2 to this sum gives a final result of 16x^3 + 9x^2 + 9x + 15.
Explanation:
To find the sum of the polynomials 6x3 + 8x2 – 2x + 4 and 10x3 + x2 + 11x + 9, we add the like terms. For example, the x^3 terms have coefficients of 6 and 10, so their sum is 16x^3. Similarly, we add the coefficients of the x^2 terms, the x terms, and the constants to get the final sum:
16x^3 + 9x^2 + 9x + 13
To add 3x - 2 to this sum, we combine the like terms again. The x^3, x^2, and x terms remain the same, and the constant terms become 15:
16x^3 + 9x^2 + 9x + 15
Answer:
[tex]16x^{3} +9x^{2} +9x+13[/tex]
[tex]16x^{3} +9x^{2} +12x+11[/tex]
Step-by-step explanation:
We are given two polynomials:
[tex]6x^{3} +8x^{2} -2x+4[/tex] and [tex]10x^{3} +x^{2}+11x+9[/tex]
Add these polynomials
[tex]6x^{3} +8x^{2} -2x+4+10x^{3} +x^{2}+11x+9[/tex]
[tex]16x^{3} +9x^{2} +9x+13[/tex]
Thus Option B of part a is correct
Now we are asked to add 3x-2 to this result :
[tex]16x^{3} +9x^{2} +9x+13+3x-2[/tex]
[tex]16x^{3} +9x^{2} +12x+11[/tex]
Thus the answer is [tex]16x^{3} +9x^{2} +12x+11[/tex]
Hence option B of part b is correct
