Factor 10x^2+13x-3

Problem

10⁢x2+13⁢x−3 10 x squared plus 13 x minus 3

Solution

  1. Identify the coefficients of the quadratic expression a⁢x2+b⁢x+c a x squared plus b x plus c where a=10 a equals 10 b=13 b equals 13 and c=−3 c equals negative 3

  2. Find two numbers that multiply to a⁢c=10⋅(−3)=−30 a c equals 10 times negative 3 equals negative 30 and add to b=13 b equals 13

  3. Determine the pair of numbers, which are 15 15 and −2 negative 2 since 15⋅(−2)=−30 15 times negative 2 equals negative 30 and $15 15 dollars + (-2) = 13$.

  4. Rewrite the middle term 13⁢x 13 x using the two numbers found: 10⁢x2+15⁢x−2⁢x−3 10 x squared plus 15 x minus 2 x minus 3

  5. Factor by grouping the first two terms and the last two terms: 5⁢x⁢(2⁢x+3)−1⁢(2⁢x+3) 5 x times open paren 2 x plus 3 close paren minus 1 times open paren 2 x plus 3 close paren

  6. Factor out the common binomial (2⁢x+3) open paren 2 x plus 3 close paren to obtain the final factored form.

Final Answer

10⁢x2+13⁢x−3=(5⁢x−1)⁢(2⁢x+3) 10 x squared plus 13 x minus 3 equals open paren 5 x minus 1 close paren times open paren 2 x plus 3 close paren

Want more problems? Check here!