Pre-Calculus for Programmers

Expanding, the binomial theorem and factoring

Pre-Calculus for Programmers

Expanding, the binomial theorem and factoring

Medium0 of 15 parts

Half of these ask you to multiply out and half ask you to un-multiply. Both directions are marked by agreement, so an answer in any equivalent arrangement is accepted, and both directions can be checked by substituting a value before you submit.

1

Expand (3x−4)2(3x-4)^{2}.

in terms of x

2

Expand (2x+5)(2x−5)(2x+5)(2x-5).

in terms of x

3

Expand (x+2)3(x+2)^{3}.

in terms of x

4

What is the coefficient of x3x^{3} in the expansion of (x+2)5(x+2)^{5}?

5

What is the coefficient of x2x^{2} in the expansion of (2x−1)4(2x-1)^{4}?

6

Factor x2−7x+12x^{2}-7x+12.

in terms of x

7

Factor 6x2+7x−36x^{2}+7x-3.

in terms of x

8

Factor 27x3−827x^{3}-8.

in terms of x

9

Factor 2x3−18x2x^{3}-18x completely.

in terms of x

10

Factor x3+2x2−9x−18x^{3}+2x^{2}-9x-18 completely.

in terms of x

11

Expand (2x−3)3(2x-3)^{3}.

in terms of x

12

What is the coefficient of x5x^{5} in the expansion of (3x−2)7(3x-2)^{7}?

13

Factor 12x2−x−612x^{2}-x-6.

in terms of x

14

Factor 2x3−3x2−18x+272x^{3}-3x^{2}-18x+27 completely.

in terms of x

15

Factor 8x3+1258x^{3}+125.

in terms of x