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(6x3−25x2+2x+8)(2x+1) (6x^3-25x^2+2x+8)(2x+1)

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Full solution

Q. (6x3−25x2+2x+8)(2x+1) (6x^3-25x^2+2x+8)(2x+1)
  1. Distribute and Multiply: First, let's distribute (2x+1)(2x + 1) across the polynomial 6x3−25x2+2x+86x^3 - 25x^2 + 2x + 8.(6x3−25x2+2x+8)(2x)+(6x3−25x2+2x+8)(1)(6x^3 - 25x^2 + 2x + 8)(2x) + (6x^3 - 25x^2 + 2x + 8)(1)
  2. Multiply by 22x: Now, multiply each term in the polynomial by 2x2x.
    (6x3×2x)−(25x2×2x)+(2x×2x)+(8×2x)(6x^3 \times 2x) - (25x^2 \times 2x) + (2x \times 2x) + (8 \times 2x)
    12x4−50x3+4x2+16x12x^4 - 50x^3 + 4x^2 + 16x
  3. Multiply by 11: Next, multiply each term in the polynomial by 11.\newline(6x3×1)−(25x2×1)+(2x×1)+(8×1)(6x^3 \times 1) - (25x^2 \times 1) + (2x \times 1) + (8 \times 1)\newline6x3−25x2+2x+86x^3 - 25x^2 + 2x + 8
  4. Add Multiplications: Now, add the results from the two multiplications.\newline12x4−50x3+4x2+16x+6x3−25x2+2x+812x^4 - 50x^3 + 4x^2 + 16x + 6x^3 - 25x^2 + 2x + 8
  5. Combine Like Terms: Combine like terms.\newline12x4−(50x3+6x3)+(4x2−25x2)+(16x+2x)+812x^4 - (50x^3 + 6x^3) + (4x^2 - 25x^2) + (16x + 2x) + 8\newline12x4−56x3−21x2+18x+812x^4 - 56x^3 - 21x^2 + 18x + 8
  6. Check for Factoring: Check for any possible factoring of the resulting polynomial, but it seems that the polynomial is already in its factored form since we multiplied it by 2x+12x + 1.

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