Factoring by Grouping
factor each expression
(with solution)
1. 10p³ - 25p² + 4p - 10
2. 36x⁴ - 48x³ + 9x² - 12x
3. 16a³ - 24a² + 12a - 18
4. 24h² + 10h - 6
5. A rectangular prism has a volume of
36x³ + 51x² + 18x. Factor to find the possible expressions for length, width, and height of the prism.
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Answer:
1. 10p³-25p²+4p-10
= (10p³-25p²) + (4p-10)
= 5p²(2p-5) + 2(2p-5)
= (2p-5)(5p²+2)
2. 36x⁴-48x³+9x²-12x
= (36x⁴-48x³)+(9x²-12x)
= 12x³(3x-4)+3x(3x-4)
= (3x-4)(12x³+3x)
3. 16a³-24a²+12a-18
= (16a³-24a²)+(12a-18)
= 8a²(2a-3)+6(2a-3)
= (2a-3)(8a²+6)
4. 24h²+ 10h-6
= 2(12h²+5h-3)
= 2(4h+3)(3h-1)
5. 36x³+51x²+18x
= 3x(12x²+17x+6)
= 3x(4x+3)(3x+2)
v= l×w×h
length = 3x
width = 4x+3
height = 3x+2