91Ó°ÊÓ

To help you factor the sum or difference of cubes, complete the following list of cubes. $$ 1^{3}= \text{____}$$ $$ 2^{3}= \text{____}$$ $$ \begin{aligned} &3^{3}=\\\ \end{aligned} \text{____}$$ $$ 4^{3}= \text{____}$$ $$ 5^{3}= \text{____}$$ $$ 6^{3}= \text{____}$$ $$ 7^{3}= \text{____}$$ $$ 8^{3}= \text{____}$$ $$ 9^{3}= \text{____}$$ $$ 10^{3}= \text{____}$$

list all pairs of integers with the given product. Then find the pair whose sum is given. Product: \(-24 ; \quad\) Sum: \(-5\)

The middle term of each trinomial has been rewritten. Now factor by grouping. $$ \begin{aligned} 15 z^{2}-19 z &+6 \\ =& 15 z^{2}-10 z-9 z+6 \end{aligned} $$

The following powers of \(x\) are all perfect cubes: \(x^{3}, x^{6}, x^{9}, x^{12}, x^{15} .\) On the basis of this observation, we may make a conjecture that if the power of a variable is divisible by ____ (with 0 remainder), then we have a perfect cube.

The middle term of each trinomial has been rewritten. Now factor by grouping. $$ \begin{aligned} 12 p^{2}-17 p+6 & \\ =12 p^{2}-9 p-8 p+6 \end{aligned} $$

In Exercises \(1-5,\) fill in the blank with the correct response. The equation \(x^{3}+x^{2}+x=0\) is not a quadratic equation, because _____.

list all pairs of integers with the given product. Then find the pair whose sum is given. Product: \(-36 ; \quad\) Sum: \(-16\)

Find the greatest common factor for each list of numbers. \(15,30,45,75\)

The middle term of each trinomial has been rewritten. Now factor by grouping. \begin{aligned} 8 s^{2}+2 s t-3 t^{2} & \\ =& 8 s^{2}-4 s t+6 s t-3 t^{2} \end{aligned}

Identify each monomial as a perfect square, a perfect cube, both of these, or neither of these. (a) \(64 x^{6} y^{12}\) (b) \(125 t^{6}\) (c) \(49 x^{12}\) (d) \(81 r^{10}\)