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Polynomials and Rational Expressions Questions - All Grades

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Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 5th term in the expansion of [math](p + q)^9[/math].
  1. [math]126p^5q^4[/math]
  2. [math]126p^4q^5[/math]
  3. [math]84p^5q^4[/math]
  4. [math]70p^4q^5[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the middle term in the expansion of [math](x+1/x​)^6[/math].
  1. [math]15x^2[/math]
  2. 20
  3. [math]20x^3[/math]
  4. 15
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](x−5)^5[/math] using Pascal's Triangle.
  1. x⁵ − 25x⁴ + 250x³ − 1250x² + 3125x − 3125
  2. x⁵ − 5x⁴ + 50x³ − 250x² + 625x − 3125
  3. x⁵ − 25x⁴ + 200x³ − 1000x² + 2500x − 3125
  4. x⁵ − 25x⁴ + 250x³ − 1000x² + 2500x − 3125
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
To find the coefficient for any term in [math](p+q)^6[/math], which methods are valid? Select all that apply.
  1. Draw the first 7 rows of Pascal’s Triangle: 1, 6, 15, 20, 15, 6, 1
  2. Use the formula [math]{: :} _6^rC[/math] where r is the exponent of p
  3. Multiply the exponent of p by the exponent of q
  4. Recognize the coefficients are 1, 6, 15, 20, 15, 6, 1
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](a−1)^6[/math] using Pascal's Triangle.
  1. a⁶ − 6a⁵ + 15a⁴ − 20a³ + 15a² − 6a + 1
  2. a⁶ − 5a⁵ + 10a⁴ − 10a³ + 5a² − a + 1
  3. a⁶ − 6a⁵ + 12a⁴ − 16a³ + 12a² − 6a + 1
  4. a⁶ − 6a⁵ + 20a⁴ − 20a³ + 15a² − 6a + 1
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the coefficient of [math]x^3[/math] in the expansion of [math](2-x)^7[/math].
  1. -280
  2. 280
  3. -560
  4. 560
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the middle term in the expansion of [math](x+2y)^4[/math].
  1. [math]2x^2y^2[/math]
  2. [math]6x^2y^2[/math]
  3. [math]12x^2y^2[/math]
  4. [math]24x^2y^2[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 2nd term in the expansion of [math](1-4x)^7[/math].
  1. 28x
  2. -1792x
  3. -28
  4. -28x
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](x+2)^4[/math] using Pascal's Triangle.
  1. [math]x^4 + 4x^3 + 24x^2 + 32x + 16[/math]
  2. [math]x^4 + 8x^3 + 24x^2 + 32x + 16[/math]
  3. [math]x^4 + 8x^3 + 12x^2 + 8x + 16[/math]
  4. [math]x^4 + 8x^3 + 24x^2 + 16x + 8[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](x-1)^5[/math] using Pascal's Triangle.
  1. [math]x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1[/math]
  2. [math] x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1[/math]
  3. [math]x^5 - 5x^4 + 5x^3 - 5x^2 + 5x - 1[/math]
  4. [math]x^5 - 5x^4 + 15x^3 - 15x^2 + 5x - 1[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the term containing [math]x^5[/math] in the expansion of [math](x+3)^8[/math].
  1. [math] 1512x^5[/math]
  2. [math] 10206x^5[/math]
  3. [math] 20412x^5[/math]
  4. [math] 1702x^5[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the coefficient of [math]x^2y^3[/math] in the expansion of [math](3x-2y)^5[/math].
  1. -720
  2. 720
  3. -1080
  4. 360
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial [math](1−2x)^4[/math] using Pascal's Triangle.
  1. 1 − 4x + 12x² − 16x³ + 16x⁴
  2. 1 − 8x + 16x² − 32x³ + 16x⁴
  3. 1 − 8x + 24x² − 32x³ + 16x⁴
  4. 1 − 8x + 20x² − 32x³ + 16x⁴
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Which of the following are correct expressions for the coefficient of the term containing [math]x^(n-k)y^k[/math] in the expansion of [math](x+y)^n[/math]?
  1. C(n,k)
  2. P/(n,k)
  3. [math] (n!) / (k!(n-k)!)[/math]
  4. The nth row, kth entry of Pascal’s Triangle (counting from 0)
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 4th term in the expansion of [math](1 - x)^6[/math].
  1. [math]20x^2[/math]
  2. [math]-20x^3[/math]
  3. [math]-20x^2[/math]
  4. [math]15x^2[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 6th term in the expansion of [math](2a + b)^8[/math].
  1. [math]1120a^3b^5[/math]
  2. [math] 1792a^4b^4[/math]
  3. [math]1120a^4b^4[/math]
  4. [math]448a^3b^5[/math]
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