Special Product Rules
Multiply:
(x-2)(x+2)
x2-4
What is the coefficient of the 2nd term of the expansion (x+y)3
3
What is the 1st term of the expansion (x+y)4?
3x2+5x+2 / (x+1)
3x+2
When f(x)=3x5 − 2x3 + x −4 is divided by x+1, what is the remainder?
-6
Multiply:
(2x-3)(2x+3)
4x2-9
What is the coefficient of the 1st term of the expansion (2x+1)4?
16
What is the 3rd term of the expansion (x+y)5?
10x3y2
3x2-3 / (x-1)
3x+3
Determine if x-2 divides evenly into f(x)=x3-4x+6. Why or why not?
No, because f(2) = 8, but not 0.
Multiply (x-3)2
x2-6x+9
Find the coefficient of the 4th term of (x-y)5
-10
Find the first term of the expansion (2x+3)4
16x4
Divide x4−6x3+11x2−6x by x−3
x3-3x2+2x
Find the remainder of the polynomial f(x) when divided by (x-2) if f(2) = 5.
5
Multiply (3x+2)2
9x2+12x+4
Find the coefficient of the x3 term of (x+2)5
Find the 2nd term of (y-2x)4
-8y3x
Divide 4x3+8x2-9x+3 by x+3
4x2−4x+3+(6/[x+3])
Determine if the divisor divides completely into the polynomial. If it is, factor it once and write the answer as 2 factors.
2x3 - 5 / (x-2)
(x-2) is not a factor.
Multiply (5x-2y)2
25x2-20xy+4y2
Find the coefficient of x4 in the expansion of (3x2−2)4
216
Find the 4th term of the expansion (3x-2y)5
-720x2y3
Divide x4+3x2-6 by (x-2)
x3+2x2+7x+14+(22/[x-2])
Determine if the divisor divides completely into the polynomial. If it is, factor it once and write the answer as 2 factors.
x3-x2-x+1 / (x+1)
(x+1)(x2-2x+1)