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Algebra · real student question

Perform the indicated operation and state the degree: (-3x^3 + 4x^2 - 6x + 6) + (2x^3 + 4x^2 - 9x - 10).

Question

Perform the indicated operation and indicate the resulting polynomial's degree, writing the answer in standard form: (−3x3+4x2−6x+6)+(2x3+4x2−9x−10).\left(-3x^{3}+4x^{2}-6x+6\right)+\left(2x^{3}+4x^{2}-9x-10\right).

Step-by-step solution

  1. Note that addition needs no sign changes. Unlike subtraction, adding polynomials leaves every term as it is, so the brackets can simply be dropped and matching powers lined up.

  2. Add the cubic and quadratic coefficients. −3x3+2x3=−x3,4x2+4x2=8x2.-3x^{3}+2x^{3}=-x^{3},\qquad 4x^{2}+4x^{2}=8x^{2}.

  3. Add the linear and constant terms. −6x−9x=−15x,6+(−10)=−4.-6x-9x=-15x,\qquad 6+(-10)=-4 .

  4. Write the sum in standard form. −x3+8x2−15x−4.-x^{3}+8x^{2}-15x-4 .

  5. Determine the degree and check a value. The leading term is −x3-x^{3} with nonzero coefficient, so the degree is 33. At x=1x=1: the two originals give 11 and −13-13, summing to −12-12, and the answer gives −1+8−15−4=−12-1+8-15-4=-12.

Answer

−x3+8x2−15x−4,degree 3-x^{3}+8x^{2}-15x-4,\qquad \text{degree } 3

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