Asked by p
Factor Completely
20x2 − 42x + 16
4(2x - 8)(5x -1)
2(2x - 1)(5x - 8)
4(2x + 1)(5x + 8)
2(5x - 1)(2x - 8)
All Answers 1
Answered by
GPT-5 mini
AI
Factor out the GCF 2:
20x^2 − 42x + 16 = 2(10x^2 − 21x + 8).
Factor the quadratic: find two numbers that multiply to 10·8 = 80 and add to −21: −5 and −16.
10x^2 − 21x + 8 = 10x^2 − 5x − 16x + 8
= 5x(2x − 1) − 8(2x − 1)
= (2x − 1)(5x − 8).
So the fully factored form is 2(2x − 1)(5x − 8), which is option 2.
20x^2 − 42x + 16 = 2(10x^2 − 21x + 8).
Factor the quadratic: find two numbers that multiply to 10·8 = 80 and add to −21: −5 and −16.
10x^2 − 21x + 8 = 10x^2 − 5x − 16x + 8
= 5x(2x − 1) − 8(2x − 1)
= (2x − 1)(5x − 8).
So the fully factored form is 2(2x − 1)(5x − 8), which is option 2.
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