Polynomial Operations Quiz

Grade 10 · Math · Quiz

Test your skills adding, subtracting, multiplying, and dividing polynomials.

Questions

  1. What is the degree of 7x² - 3x⁴ + 2?

    1. 2
    2. 4
    3. 7
    4. 3
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    Answer: 4

    The term -3x⁴ has the highest exponent (4), so the degree is 4.

  2. (5x² - 3x + 2) - (2x² + x - 4) = 3x² - 4x + ___.

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    Answer: 6

    Constants: 2-(-4)=2+4=6. Full result: (5x²-2x²)+(-3x-x)+(2+4) = 3x²-4x+6.

  3. What is (x + 5)(x + 2) using FOIL?

    1. x² + 3x + 10
    2. x² + 7x + 10
    3. x² + 10x + 7
    4. x² + 7x + 7
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    Answer: x² + 7x + 10

    FOIL: x·x + x·2 + 5·x + 5·2 = x² + 2x + 5x + 10 = x² + 7x + 10.

  4. 3x² and 5x³ are like terms and can be combined.

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    Answer: False

    Like terms must have the same variable AND the same exponent. 3x² (exp 2) and 5x³ (exp 3) are different.

  5. If p(x) = x³ - 4x + 3, what is p(1)?

    1. 0
    2. 1
    3. 4
    4. -2
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    Answer: 0

    p(1) = (1)³ - 4(1) + 3 = 1 - 4 + 3 = 0.

  6. A polynomial with exactly two terms is called a ___.

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    Answer: binomial

    Mono=1 term, bi=2 terms (binomial), tri=3 terms (trinomial), poly=many terms.

  7. According to the Factor Theorem, if p(3) = 0, then which is a factor of p(x)?

    1. (x + 3)
    2. (x - 3)
    3. (3x)
    4. (x - 1)
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    Answer: (x - 3)

    The Factor Theorem: if p(c)=0, then (x-c) is a factor. p(3)=0 means (x-3) is a factor.

  8. The product of two polynomials always has degree equal to the sum of their degrees.

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    Answer: True

    When multiplying polynomials of degrees m and n, the highest-degree term is x^(m+n), so the product has degree m+n.

  9. Simplify: (3x³ + 2x - 5) + (-x³ + 4x + 1)

    1. 2x³ + 6x - 4
    2. 2x³ - 6x + 4
    3. 4x³ + 6x - 4
    4. 2x³ + 6x + 4
    Show answer

    Answer: 2x³ + 6x - 4

    Combine like terms: (3x³-x³)+(2x+4x)+(-5+1) = 2x³+6x-4.

  10. When multiplying a monomial by a polynomial, you only multiply the first term.

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    Answer: False

    The distributive property requires multiplying the monomial by EVERY term in the polynomial.

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