How do you factor #2x^2-21x-11#?

Answer 1

#2x^2-21x-11 = (x-11)(2x+1) #

We want to factorise #2x^2-21x-11#
We look for two numbers which add to give the coefficient of #x#; so we seek two numbers which add to give #-21#.
However, as the coefficient of #x^2# is not #1# then instead of looking for two numbers which multiply to give #−11# we must look for two numbers which multiply to give #−22#, (that is, the coefficient of #x^2# multiplied by the constant term, #2 × −11#.

a × b = -22 a + b = -21

By inspection (or trial ad error) we can find two numbers a=-22 and b=1

So we have, # 2x^2-21x-11 = 2x^2-22x + x-11 # # :. 2x^2-21x-11 = 2x(x-11) + x-11 # (by factorising the first two terms) # :. 2x^2-21x-11 = 2x(x-11) + (x-11) # (collecting common terms) # :. 2x^2-21x-11 = (x-11)(2x+1) # (by factorising the last two terms)
We can check this by multiplying out: # (x-11)(2x+1) = 2x^2 + x -22 x -11 = 2x^2-21x-11 # QED
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Answer 2

To factor the quadratic expression 2x^2 - 21x - 11, we need to find two numbers that multiply to give us (2 * -11) = -22 and add to give us -21. These numbers are -22 and 1. Then, we rewrite the middle term using these numbers, which gives us 2x^2 - 22x + x - 11. Now, we factor by grouping, taking out the common factors from the first two terms and the last two terms separately. This gives us 2x(x - 11) + 1(x - 11). Finally, we factor out the common factor (x - 11), which leaves us with the factored form: (2x + 1)(x - 11).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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