which expression is a factor of 10x² + 11x + 3?\no x - 3\no 2x + 1\no 5x - 3\no 10x + 3
which expression is a factor of 10x² + 11x + 3?\no x - 3\no 2x + 1\no 5x - 3\no 10x + 3
Answer
Explanation:
Step1: Factor the quadratic expression
We use the AC - method for factoring (ax^{2}+bx + c) (here (a = 10), (b=11), (c = 3)). Calculate (ac=10\times3 = 30). We need to find two numbers that multiply to (30) and add up to (11). The numbers are (5) and (6). Rewrite the middle - term: (10x^{2}+11x + 3=10x^{2}+5x+6x + 3). Group the terms: ((10x^{2}+5x)+(6x + 3)). Factor out the greatest common factor from each group: (5x(2x + 1)+3(2x + 1)). Then, (10x^{2}+11x + 3=(2x + 1)(5x+3)).
Answer:
B. (2x + 1)