Home > Algebra > Factorization of Quadratic Expressions

How do you factor the trinomial #7x^2-71x+10#?

Answer 1

Nathan Axel

#7x^2-71x+10 = (7x-1)(x-10)#

Look for a pair of factors of #AC=7*10 = 70# with sum #B=71#.

The pair #70, 1# works.

Use that to split the middle term and factor by grouping:

#7x^2-71x+10#

#=(7x^2-70x)-(x-10)#

#=7x(x-10)-1(x-10)#

#=(7x-1)(x-10)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Abigail Allen

To factor the trinomial 7x^2 - 71x + 10, you can use the factoring method by grouping or the quadratic formula.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Kennedy Adams

To factor the trinomial (7x^2 - 71x + 10), we can use the factoring by grouping method. Here's how to do it:

Multiply the coefficient of (x^2) (7) by the constant term (10) to get 70.
Find two numbers that multiply to 70 and add up to the coefficient of (x) (-71). The numbers -1 and -70 fit this criterion.
Rewrite the middle term (-71x) using these two numbers: (7x^2 - 1x - 70x + 10).
Group the terms and factor out the common factors from each group: (x(7x - 1) - 10(7x - 1)).
Factor out the common factor of (7x - 1): ((x - 10)(7x - 1)).

So, the factored form of (7x^2 - 71x + 10) is ((x - 10)(7x - 1)).

By signing up, you agree to our Terms of Service and Privacy Policy

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.