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What's the Standard Form of a Polynomial?

What's the standard form of a polynomial?

Summary

  1. 6x8-7x2-5x+8 is in standard form because all like terms are combined and the degree drops from 8 to 2, to 1, and to 0
  2. 7x2+6x8-5x+8 is in not in standard form because the degrees do not drop from left to right, 2 goes up to 8
  3. 6x8-3x2-4x2-5x+8 is not in standard form because all like terms are not combined
  4. There are two x2 terms

Notes

    1. 'x' is a variable
    1. Remember, to be in standard form all like terms must be combined, and the degree of each term must drop as we move from left to right
    1. Remember, to be in standard form all like terms must be combined, and the degree of each term must drop as we move from left to right
    1. These represent the type of terms in 6x8-7x2-5x+8
    2. 'x' is a variable
    3. There is only one x8 term
    4. There is only one x2 term
    5. There is only one 'x' term
    6. There is only one constant
    1. The degrees of 6x8-7x2-5x+8 go from 8, to 2, to 1, to 0
    1. Going from 8 to 2, to 1, and then to 0 satisfies the second criterion
    1. Going from 8 to 2, to 1, and then to 0 satisfies the second criterion
    1. Remember, to be in standard form all like terms must be combined, and the degree of each term must drop as we move from left to right
    1. 'x' is a variable
    1. Remember, to be in standard form all like terms must be combined, and the degree of each term must drop as we move from left to right
    1. Remember, to be in standard form all like terms must be combined, and the degree of each term must drop as we move from left to right
    1. These represent the type of terms in 7x2+6x8-5x+8
    2. 'x' is a variable
    3. There is only one x2 term
    4. There is only one x8 term
    5. There is only one 'x' term
    6. There is only one constant
    1. In standard form, the degrees can only go down from left to right, so this polynomial is not in standard form
    1. In standard form, the degrees can only go down from left to right, so this polynomial is not in standard form
    1. Remember, to be in standard form all like terms must be combined, and the degree of each term must drop as we move from left to right
    1. These represent the type of terms in 6x8-3x2-4x2-5x+8
    2. 'x' is a variable
    3. There is only one x8 term
    4. There are two x2 terms
    5. There is only one 'x' term
    6. There is only one constant
    1. The first criterion says that we cannot have like terms that are not combined in the polynomial
    2. -3x2 and -4x2 are like terms
    3. There are two x2 terms
    4. 'x' is a variable
    1. The first criterion says that we cannot have like terms that are not combined in the polynomial