How do you factor #-5k^{2}-22k+15#?

Answer 1

#(+5+k)(3-5k)#

#"using the a-c method of factoring"#
#"the factors of "-5xx15=-75"#
#"which sum to - 22 are - 25 and + 3"#
#"split the middle term using these factors"#
#=-5k^2-25k+3k+15larrcolor(blue)"factor by grouping"#
#=color(red)(-5k)(k+5)color(red)(+3)(k+5)#
#"take out the "color(blue)"common factor "(k+5)#
#=(k+5)(color(red)(-5k+3))#
#rArr-5k^2-22k+15=(5+k)(3-5k)#
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Answer 2

#=-(5k-3)(k+5)#

Or with re-arranging:

#(3-5k)(5+k)#

#-5k^2-22k+15#

The negative at the front is not comfortable foe factorising. Divide it out as a common factor. All the signs will change.

#=-(5k^2+22k-15)#

The factors of a quadratic trinomial are two brackets.

The negative in front of #15# tells you two things:
A quick thought is that #5xx5 = 25# which is close to #22#
#" "5 and 15# #" "darr" "darr# #" "5" "3" "rarr 1 xx 3 = 3# #" "1" "5" "rarr 5 xx 5 = ul25# #color(white)(xxxxxxxxxxxxxxxxx)22" "(larr 25-3=22)#
We have the correct factors, now include the signs to get #-22#
#" "5 and 15# #" "darr" "darr# #" "5" "-3" "rarr 1 xx color(red)(-3 = -3)# #" "1" "+5" "rarr 5 xx color(blue)(+5 = ul(+25))# #color(white)(xxx.xxxxxxxxxxxxxxxx)color(blue)(+22)" "(larr +25-3=+22)#

The top row gives the first bracket and the bottom row gives the second bracket:

#=-(5k-3)(k+5)#
You could also solve the sign issue by re-arranging the terms:
#15-22k -5k^2#

This leads to the factors:

#(3-5k)(5+k)#
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Answer 3

To factor the quadratic expression (-5k^2 - 22k + 15), you can use the factoring by grouping method. First, multiply the leading coefficient (-5) by the constant term (15), resulting in (-5 \times 15 = -75). Next, find two numbers that multiply to (-75) and add to the coefficient of the linear term (-22). These numbers are (-25) and (3). Rewrite the middle term (22k) using these numbers, resulting in (-5k^2 - 25k + 3k + 15). Group the terms, factor by grouping, and then factor out the greatest common factor from each pair of terms. This will yield the factored form of the quadratic expression.

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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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