7. \( 6 x^{2}+26 x+8 \)

To factor the expression 6x² + 26x + 8, start by factoring out the greatest common factor. Notice that all coefficients are even, so factor out a 2:   6x² + 26x + 8 = 2(3x² + 13x + 4) Now, factor the quadratic inside the parentheses: Step 1: Multiply the coefficient of x² (which is 3) by the constant term (4):   3 × 4 = 12 Step 2: Find two numbers that multiply to 12 and add to 13 (the coefficient of x). The numbers 12 and 1 work because 12 × 1 = 12 and 12 + 1 = 13. Step 3: Rewrite the middle term (13x) using these numbers:   3x² + 12x + x + 4 Step 4: Factor by grouping:   Group 1: 3x² + 12x = 3x(x + 4)   Group 2: x + 4 = 1(x + 4) Since both groups contain a common factor (x + 4), factor that out:   3x(x + 4) + 1(x + 4) = (x + 4)(3x + 1) Step 5: Don’t forget the factored-out 2:   2(3x² + 13x + 4) = 2(3x + 1)(x + 4) Thus, the completely factored form is:   2(3x + 1)(x + 4)