Question

Factorize The Following By Spiliting The Middle Term
$3 {x}^{2} + 19x + 30$
Factorize The Following By Split ing Middle Term ​

Answer 1

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3*x^2+19*x-(-30)=0

Step by step solution :

STEP

1

:

Equation at the end of step 1

(3x2 + 19x) - -30 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 3x2+19x+30

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

The middle term is, +19x its coefficient is 19 .

The last term, "the constant", is +30

Step-1 : Multiply the coefficient of the first term by the constant 3 • 30 = 90

Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is 19 .

-90 + -1 = -91

-45 + -2 = -47

-30 + -3 = -33

-18 + -5 = -23

-15 + -6 = -21

-10 + -9 = -19

-9 + -10 = -19

-6 + -15 = -21

-5 + -18 = -23

-3 + -30 = -33

-2 + -45 = -47

-1 + -90 = -91

1 + 90 = 91

2 + 45 = 47

3 + 30 = 33

5 + 18 = 23

6 + 15 = 21

9 + 10 = 19 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 9 and 10

3x2 + 9x + 10x + 30

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 :

10 • (x+3)

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

(3x+10) • (x+3)

Answer 2

Answer:

your answer is in the attachment