factor the following trinomial. 7c² - 4c - 20 (7c + ?)(c - )

Explanation:

Step1: Multiply leading - coefficient and constant

For the trinomial (7c^{2}-4c - 20), the leading - coefficient (a = 7) and the constant (c=-20). So (a\times c=7\times(-20)=-140).

Step2: Find two numbers

We need to find two numbers that multiply to (-140) and add up to the middle - coefficient (-4). The numbers are (10) and (-14) since (10\times(-14)=-140) and (10+( - 14)=-4).

Step3: Rewrite the middle term

Rewrite (-4c) as (10c-14c). So (7c^{2}-4c - 20=7c^{2}+10c-14c - 20).

Step4: Group the terms

((7c^{2}+10c)-(14c + 20)=c(7c + 10)-2(7c + 10)).

Step5: Factor out the common factor

((7c + 10)(c-2))

Answer:

The missing numbers are (10) and (2), so the factored form is ((7c + 10)(c - 2))