Question

The product of a binomial and a trinomial is x 3 3 x 2 âÂ’ x 2 x 2 6 x âÂ’ 2. Which expression is equivalent to this product after it has been fully simplified? x3 5x2 5x â€"" 2 x3 2x2 8x â€"" 2 x3 11x2 â€"" 2 x3 10x2 â€"" 2.

Answer 1

The product of given binomial and trinomial is given by below polynomial:

$x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4$

Given polynomials:

• Trinomial : $x^3+3x^2-x+2$

• Binomial: $x^2+6x-2$

Explanation:

The expression formed by the sum of sub expressions which are product of constant integers with variables raised to some exponent is called polynomial.

Their product is given by:

$(x^3 + 3x^2 - x + 2) \times (x^2 + 6x -2)\\= x^5 + 6x^4 - 2x^3 + 3x^4 + 18x^3 - 6x^2 -x^3 -6x^2 + 2x +2x^2 + 12x - 4\\= x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4$

Thus the product of given binomial and trinomial is given by below polynomial:

$x^5 + 9x^4 + 15x^3 -10x^2 + 14x - 4$

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