Polynomial Terminology
How many terms are in a monomial?
1
(4x^2+2x) + (x^2+6x)
5x2+8x
(y^2-10xy) - (2y^2+3xy)
-y^2-13xy
(6x2)(5x)
30x3
(x + 4)(x - 2)
x2 + 2x - 8
What is the constant term of
4x-5+3x^2+77x^9
-5
(-3y^2+y) + (4y^2+6y)
y2 +7y
(2x^2 + 5x - 3) - (3x^3 + 2x - 5)
-3x3 + 2x2 +3x + 2
(x2yz)(x2y4)
x4y5z
(a + 3)(a − 2)
a2 + 1a − 6
Is this a polynomial?
3x^2+4x^-1-6
No, because one of the terms has a negative exponent.
x^-1=1/x
which is division by a variable. A polynomial can have constants, variables and exponents,
but never division by a variable.
(2a^2 - 7a + 10) + (a^2 + 4a + 7)
3a2 -3a +17
(-3a^2-2a) - (4a^2-4)
-7a2 - 2a + 4
(3x2y)(5xyz)
15x3y2z
(4m + 2)(4m + 5)
16m2 + 28m + 10
What is the leading term of the polynomial:
5x^2+6x^9-5x
6x^9
because it is the term with the highest degree (biggest exponent on the variable). If you were going to write the polynomial in standard form, it would be written first.
(2r^2-5r+7)+(3r^3-6r)
3r^3 + 2r^2 -11r + 7
(4x^3+5x+2) - (1+2x-3x^2)
4x3 + 3x2 +3x + 1
Simplify 2x(3xy) - 10x2y
-4x2y
(x - 2)2
x2 - 4x + 4
Write the following polynomial in standard form AND state the leading coefficient:
9x-4+7x^3-2x^2
7x^3-2x^2+9x-4
The leading coefficient is 7 (the number in front of the variable with the largest power of x)
(5r^3-6r^2+3r) + (r^2-2r-3)
5r^3 - 5r^2 + r - 3
(4-x-2x^2) - (-2+3x-x^3)
x3 - 2x2 - 4x + 6
(5x3y2)(x3y)(-2y)
-10x6y4
(5b−6)(5b2+4b−2)
25b3 − 10b2 − 34b + 12