Question - Factoring Trinomials with Leading Coefficient Greater Than 1
Solution:
The trinomial given is $$ 7p^2 - 5p - 8 $$.To factor this trinomial, we look for two numbers that multiply to give $$ 7*(-8) = -56 $$ and add to give $$ -5 $$. These two numbers are -8 and 7 because $$ -8*7 = -56 $$ and $$ -8+7 = -1 $$.We can then rewrite the middle term $$ -5p $$ using -8 and 7:$$ 7p^2 - 8p + 7p - 8 $$Now, we can factor by grouping:$$ (7p^2 - 8p) + (7p - 8) $$Factor out the greatest common factor from each group:$$ p(7p - 8) + 1(7p - 8) $$Now, factor out the common binomial factor:$$ (p + 1)(7p - 8) $$Therefore, the completely factored form of the trinomial is $$ (p + 1)(7p - 8) $$, which is not one of the options provided in the image. There appears to be a mistake in the options given. None of the choices matches the correct factorization of the trinomial.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com