8. Sometimes we can factor by grouping
pairs of terms with a common monomial
factor:
ra + rb + sa + sb = r(a + b) + s(a + b)
= (r + s)(a + b)
Example:
x3 – 2x2 – 9x + 18
11. An expression of the form
au2 + bu + c where u is any expression
in x is in quadratic form.
We can factor these like a quadratic.
Example:
Factor 81x4 - 16
14. Remember the zero product property?
If AB = 0 then A = 0 or B = 0
To solve, factor and set each factor equal
to zero. Then solve for x.
Only include real solutions.
May have up to n solutions. (where n is
the degree.)
15. Find the real number solutions of the
equation.
2x5 + 24x = 14x3
2x5 – 18x = 0
16. A large concrete block is discovered by
archaeologists with a volume of 330 cubic
yards. The dimensions are x yards high
by 13x – 11 yards long by 13x – 5 yards
wide. What is the height?
17. You are building a bin to hold mulch for
your garden. The bin will hold 162 cubic
feet of mulch. The dimensions are x ft
by 5x – 6 ft by 5x – 9 ft. How tall will the
bin be?