what are the factors of 2x² + 3x - 54? select two options.\n□2x - 9\n□2x - 6\n□2x + 6\n□x - 6\n□x + 6
what are the factors of 2x² + 3x - 54? select two options.\n□2x - 9\n□2x - 6\n□2x + 6\n□x - 6\n□x + 6
Answer
Explanation:
Step1: Factor the quadratic expression
For a quadratic expression (ax^{2}+bx + c) (here (a = 2), (b=3), (c=- 54)), we need to find two numbers that multiply to (ac=2\times(-54)=-108) and add up to (b = 3). The numbers are (12) and (-9) since (12\times(-9)=-108) and (12+( - 9)=3). Then we rewrite the middle - term: (2x^{2}+3x - 54=2x^{2}+12x-9x - 54).
Step2: Group the terms
Group the terms as ((2x^{2}+12x)-(9x + 54)). Factor out the greatest common factor from each group: (2x(x + 6)-9(x + 6)).
Step3: Factor out the common binomial factor
Factor out ((x + 6)) to get ((2x-9)(x + 6)).
Answer:
A. (2x - 9), E. (x + 6)