118 Part 2: Into the Unknown
CHECK POINT
Give the degree of each polynomial.- -3a^3 + 5a^2 – 3a + 12
- 6 + 3b -4b^2
- 2t – 9 + 7t^2 +4t^3
24. 11y – 7y^4 + 5y^2 – 3
25. 6 – 4x^2 + 3x
When you write a polynomial, no matter how many terms it has, it’s traditional to write it in
standard form. Standard form means that you write the terms of the polynomial in order from the
highest degree monomial to the lowest. The polynomial 8x^5 + -6x^3 + x^2 + 2x + 3 is in standard
form because the monomials start with the fifth degree, then the third degree, then the second,
first, and finally the zero degree term.WORLDLY WISDOM
The standard form of a polynomial writes the terms in order from highest degree to
the lowest.The polynomial 4t^3 – 6t^9 + 11t – 5t^2 + 8t^7 is not in standard form. To put it in standard form, you
need to first locate the highest degree term. In this case, that’s -6t^9. That has to be first, so move
it around to the front. The 4t^3 that was in front is positive, so you can put a plus between the
ninth degree term and the 4t^3. -6t^9 + 4t^3 + 11t – 5t^2 + 8t^7.
There’s no eighth degree term, but there’s a seventh degree, so that should be next.
-6t^9 + 8t^7 + 4t^3 + 11t – 5t^2.
There are no sixth, fifth, or fourth degree terms, and the third degree term is already next in
line. You just need to swap the last two terms. -6t^9 + 8t^7 + 4t^3 – 5t^2 + 11t is in standard form.CHECK POINT
Put each polynomial in standard form.- a^3 + 10a^4 – 11a + 9
- 2b^3 – 9b + 12b^2 – 5
- 3k^4 + 8k^5 – 13k – 7
29. 4 – 7m^2 + 14m^4 + 2m^3
30. 5p – 3 + 6p^2 – 15p^3