Question

write the expression of the polynomial
$3x ^{2} - 4x + 15$
​

Answer 1

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 2

Answer:

This polynomial has only one variable x.

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