Question

factor 10x² + 11x + 3. step - by - step solution first, notice that 10x² + 11x + 3 has no common factors and that a = 10, b = 11, and c = 3. step 1: find the value of ac. ac = 30 (simplify your answer.) step 2: find the integers m and n whose product is 30 and whose sum is 11. two integers whose product is 30 and whose sum is 11 are 5,6 (use a comma to separate answers as needed.) step 3: write ax² + bx + c = ax² + mx + nx + c. this means to replace 11x with 5x + 6x found in step 2. 10x² + 11x + 3 = 10x² + 5x + 6x + 3 (type the terms of your expression in the same order as they appear in the original expression.) step 4: factor the expression in step 3 by grouping. 10x² + 11x + 3=(10x² + 5x)+(6x + 3)=5x(2x + 1)+3(2x + 1) therefore, 10x² + 11x + 3=(2x + 1)(□)

Explanation:

Step1: Calculate \(ac\)

\(ac = 10 \times 3 = 30\)

Step2: Find \(m,n\) with \(m \cdot n=30\), \(m + n=11\)

\(m=5\), \(n=6\)

Step3: Rewrite middle term

\(10x^2 + 5x + 6x + 3\)

Step4: Factor by grouping

\((10x^2 + 5x) + (6x + 3) = 5x(2x + 1) + 3(2x + 1)\)

Step5: Factor out common binomial

\((2x + 1)(5x + 3)\)

Answer:

\((2x + 1)(5x + 3)\)