# Determine if a Polynomial 3x(7x^4+8)-5(7x^4+8) 3x(7×4+8)-5(7×4+8)
A polynomial is a combination of terms separated using + or – signs. Polynomials cannot contain any of the following:
1. Variables raised to a negative or fractional exponent. (2x-2,x12,…).
2. Variables in the denominator. (1x,1×2,…).
3. Variables under a radical. (x,x3,…).
4. Special features. (trig functions, absolute values, logarithms, …).
Simplify each term.
Apply the distributive property.
3x(7×4)+3x⋅8-5(7×4+8)
Rewrite using the commutative property of multiplication.
3⋅7(x⋅x4)+3x⋅8-5(7×4+8)
Multiply 8 by 3.
3⋅7(x⋅x4)+24x-5(7×4+8)
Simplify each term.
Multiply x by x4 by adding the exponents.
Multiply x by x4.
Raise x to the power of 1.
3⋅7(x1x4)+24x-5(7×4+8)
Use the power rule aman=am+n to combine exponents.
3⋅7×1+4+24x-5(7×4+8)
3⋅7×1+4+24x-5(7×4+8)
Add 1 and 4.
3⋅7×5+24x-5(7×4+8)
3⋅7×5+24x-5(7×4+8)
Multiply 3 by 7.
21×5+24x-5(7×4+8)
21×5+24x-5(7×4+8)
Apply the distributive property.
21×5+24x-5(7×4)-5⋅8
Multiply 7 by -5.
21×5+24x-35×4-5⋅8
Multiply -5 by 8.
21×5+24x-35×4-40
21×5+24x-35×4-40
Determine if the expression breaks any of the rules.
Does not break any of the rules
Determine if the expression is a polynomial.
Polynomial
Determine if a Polynomial 3x(7x^4+8)-5(7x^4+8)   ## Download our App from the store

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