How do you factor #7k^2+19k+10#?

Answer 1

Look for factor pairs of #7# and of #10# which when cross multiplied equal #19#.
This should allow you to find:
#color(white)("XXX")(k+2)(7k+5)#

Note that since all terms in the given expression are positive, we only need to consider positive factors.

Factors of #7# #color(white)("XXX"){color(red)(color(white)("")(1,7))}# Factors of #10# #color(white)("XXX"){color(blue)(color(white)("")(1,10),(2,5))}#

Using #" X "# to indicate cross multiplication: Since #color(red)(1)xxcolor(blue)(5)+color(red)(7)xxcolor(blue)(2) = 19#

#color(white)("XXX"){:(color(red)(1)),(color(red)(7)):}" X "{:(color(blue)(2)),(color(blue)(5)):}=19#

The required factors are #color(white)("XXX")(color(red)(1)k+color(blue)(2))(color(red)(7)k+color(blue)(5))#

Note that this method only works since the coefficients are integer.

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Answer 2

Nathan Axel

To factor $7k^2 + 19k + 10$ , you would find two numbers that multiply to $7 \times 10 = 70$ and add to $19$ . These numbers are $14$ and $5$ . Then, you can rewrite the expression as $(7k^2 + 14k) + (5k + 10)$ . Next, factor out the greatest common factor from each pair of terms, which is $7k$ from the first pair and $5$ from the second pair. This gives you $7k(k + 2) + 5(k + 2)$ . Finally, factor out the common binomial factor $k + 2$ , resulting in $(7k + 5)(k + 2)$ .

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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.