question\nfactor the trinomial:\n$3x^{2}+17x + 20$
question\nfactor the trinomial:\n$3x^{2}+17x + 20$
Answer
Explanation:
Step1: Multiply the coefficient of (x^{2}) and the constant term
For the trinomial (3x^{2}+17x + 20), (a = 3), (b=17), (c = 20). Calculate (a\times c=3\times20 = 60).
Step2: Find two numbers that multiply to (60) and add up to (17)
The numbers are (12) and (5) since (12\times5=60) and (12 + 5=17).
Step3: Rewrite the middle term
Rewrite (17x) as (12x+5x). So, (3x^{2}+17x + 20=3x^{2}+12x+5x + 20).
Step4: Group the terms
Group the terms as ((3x^{2}+12x)+(5x + 20)).
Step5: Factor out the common factors from each group
Factor out (3x) from the first group and (5) from the second group: (3x(x + 4)+5(x + 4)).
Step6: Factor out the common binomial factor
Factor out ((x + 4)), we get ((3x + 5)(x+4)).
Answer:
((3x + 5)(x + 4))