Question

Factorise the following using middle term splitting method:
$3 {x}^{2} + 22x + 35$
​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\huge{\fbox{\fbox{\orange{\mathfrak{Answer\::-}}}}}$(3x-7) × (x-5)

Step-by-step explanation:

$3{x}^{2}+ 22x + 35$

=> 3x2-22x+35

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

The middle term is, -22x its coefficient is -22 .

The last term, "the constant", is +35

Step-1 : Multiply the coefficient of the first term by the constant 3 • 35 = 105

Step-2 : Find two factors of 105 whose sum equals the coefficient of the middle term, which is -22 .

-105 + -1 = -106

-35 + -3 = -38

-21 + -5 = -26

-15 + -7 = -22 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -7

3x² - 15x - 7x - 35

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

3x • (x-5)

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

7 • (x-5)

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

(3x-7) • (x-5)

Which is the desired factorization