Factoring Trinomials with Leading Coefficient Greater Than 1
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.
