2 questions that I don’t understand… Please help?
Complete the following statement: 6a^2 – 5a +1 = (3a – 1)
( ) Explain.
What is the degree of the polynomial x^12 – 5x^4? Why?
Serious answers only.. Greatly appreciated!
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6a^2 – 5a +1 = (3a – 1)()
is asking you to factorise 6a^2 – 5a + 1, but making the job easier by giving you 3a – 1 as one of the factors.
The expression in the right hand brackets needs to multiply by 3a – 1 to give 6a^2 – 5a + 1.
To get 6a^2 from 3a requires a term 2a.
To get 1 from -1 requires another -1 at the end in the brackets.
That suggests a factor of (2a – 1), giving:
(3a – 1)(2a – 1).
If you multiply those brackets, you find the result matches the original quadratic expression, and so the factors are correct.
The degree of x^12 – 5x^4 is 12. It’s the highest power of x in the expression.
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The degree is 12. The degree is the highest exponent.
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