Write the expression of the polynomial

1.	Write the expression of the polynomial
Answer» Answer: (x−3)⋅(3x+5) Step by Step Solution: 1 : Equation at the end of step 1 (3x2 - 4x) - 15 STEP 2 : Trying to factor by splitting the middle term 2.1 Factoring 3x2-4x-15 The first term is, 3x2 its COEFFICIENT is 3 . The middle term is, -4x its coefficient is -4 . The last term, "the constant", is -15 Step-1 : Multiply the coefficient of the first term by the constant 3 • -15 = -45 Step-2 : Find two factors of -45 whose sum equals the coefficient of the middle term, which is -4 . -45 + 1 = -44 -15 + 3 = -12 -9 + 5 = -4 That's it Step-3 : REWRITE the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 5 3x2 - 9x + 5x - 15 Step-4 : Add up the first 2 terms, pulling out LIKE factors : 3x • (x-3) Add up the last 2 terms, pulling out COMMON factors : 5 • (x-3) Step-5 : Add up the four terms of step 4 : (3x+5) • (x-3) Which is the desired factorization Final result : (x - 3) • (3x + 5)

Answer»

Answer:

(x−3)⋅(3x+5)

Step by Step Solution:

Equation at the end of step 1

(3x2 - 4x) - 15

STEP

Trying to factor by splitting the middle term

2.1 Factoring 3x2-4x-15

The first term is, 3x2 its COEFFICIENT is 3 .

The middle term is, -4x its coefficient is -4 .

The last term, "the constant", is -15

Step-1 : Multiply the coefficient of the first term by the constant 3 • -15 = -45

Step-2 : Find two factors of -45 whose sum equals the coefficient of the middle term, which is -4 .

-45 + 1 = -44

-15 + 3 = -12

-9 + 5 = -4 That's it

Step-3 : REWRITE the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 5

3x2 - 9x + 5x - 15

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

3x • (x-3)

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

5 • (x-3)

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

(3x+5) • (x-3)

Which is the desired factorization

Final result :

(x - 3) • (3x + 5)

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