Which of the following show the factor equivalent to f (x) = (2x^2+7x+3) (x-3)

Final result : (2x + 1) • (x + 3) • (x - 3)

Step by step solution : Step 1 : Equation at the end of step 1 : ((2x2 + 7x) + 3) • (x - 3) Step 2 : Trying to factor by splitting the middle term

2.1 Factoring 2x2+7x+3

The first term is, 2x2 its coefficient is 2.

The middle term is, + 7x its coefficient is 7.

The last term, "the constant", is + 3

Step-1 : Multiply the coefficient of the first term by the constant 2 • 3 = 6

Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is 7.

-6 + - 1 = - 7 - 3 + - 2 = - 5 - 2 + - 3 = - 5 - 1 + - 6 = - 7 1 + 6 = 7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 6

2x2 + 1x + 6x + 3

Step-4 : Add up the first 2 terms, pulling out like factors:

x • (2x+1)

Add up the last 2 terms, pulling out common factors:

3 • (2x+1)

Step-5 : Add up the four terms of step 4:

(x+3) • (2x+1)

Which is the desired factorization

Final result : (2x + 1) • (x + 3) • (x - 3)