Let’s go step by step to understand what the problem is asking and how to solve it.
The image shows an example polynomial:
2x⁴ – 5x² + 3x – 7
It breaks down each term into its
coefficient and
exponent, and then tells us:
> “The degree of a polynomial is the largest exponent in the polynomial.”
So, we need to find the
degree of this polynomial.
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Step 1: Look at each term and identify its exponent.
- First term:
2x⁴ → exponent =
4
- Second term:
–5x² → exponent =
2
- Third term:
+3x → this is the same as
3x¹ → exponent =
1
- Fourth term:
–7 → this is the same as
–7x⁰ (since any number to the power 0 is 1) → exponent =
0
Step 2: Find the largest exponent among these.
Exponents are: 4, 2, 1, 0
The biggest one is
4.
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That means the degree of the polynomial is
4.
We double-check: yes, no other term has a higher exponent than 4. The definition says “largest exponent,” so we’re good.
Final Answer:
4
Parent Tip: Review the logic above to help your child master the concept of simplifying polynomial expressions worksheet.
