How can I express x^2 - 7*x + 2 as (x - p)^2 + q ?

o One way to approach this question is to expand the right expression (x - p)2 + q.
As we know from binomial expansions this gives us x2 - 2px + p2 + q.

o Now we need to ensure that we choose values for p and q such that the above expression is equal to x2 - 7*x + 2. To find these values we can use the method of equating the coefficients which means that we look separately at the coefficients for x2, x and the last part without x and equate these three parts in both terms.

o For x2, the coefficients are luckily both times already 1, otherwise the example would not be solvable
o For x, the number 7 needs to be equal to 2p, hence p = 7/2
o For the term without x, 2 needs to be equal to (p2 + q). p is already chosen to be 7/2, hence q = 2 - (7/2)2 = 2 - 49/4 = -41/4 o This way we found that x2 - 7
x + 2 = (x - 7/2)2 - 41/4

SK
Answered by Simon K. HTML and CSS tutor

1945 Views

See similar HTML and CSS Mentoring tutors

Related HTML and CSS Mentoring answers

All answers ▸

What is the behaviourism?


What are main tags for text?


What's the difference between por and para in Spanish?


What is CSS used for?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning