Question

Factorise the following by splitting the middle term
A)- 3x^2+19x+30
B)- 2under root 2x^2-9x+5under root 2
C)- 4x^2-13x+10

Answer 1

Given,

a) 3x² + 19x + 30

b) 2√2x² -9x + 5√2

c) 4x² - 13x + 10

To find,

Factors of the given questions by splitting the middle term.

Solution,

We can easily solve this problem by following the given steps.

Now,

a) 3x² + 19x + 30

By splitting 19x into two terms so that their sum will be 19x and their multiply will be 3x² × 30, we get

3x² + 9x + 10x + 30

3x (x+3) +10 (x+3) [ Taking 3x common from 3x² and 9x and 10 from 10x and 30]

(x+3) (3x+10)

b) 2√2x² -9x + 5√2

By splitting 9x into two terms so that their sum will be -9x and their multiply will be 2√2x² × 5√2 (20x²), we get

2√2x² - 4x - 5x + 5√2

2√2x ( x - √2) - 5 (x - √2)

(x-√2) (2√2x - 5)

c) 4x²-13x+10

By splitting 13x into two terms so that their sum be -13x and their multiply will be 4x²×10 ( 40x²), we get

4x² - 8x - 5x + 10

4x (x-2) -5( x-2)

(x-2) (4x-5)

Hence, the factors of the given parts A, B and C are (x+3) (3x+10), (x-√2) (2√2x-5) and (x-2) (4x-5) respectively.

Answer 2

Factorization

(A) $3x^2+19x+30$,

For factorizing it by middle term split , it will be

$3x^2+19x+30=3x^2+10x+9x+30\\\\\implies x(3x+10)+3(3x+10)\\\\=(x+3)(3x+10)$

Hence, the factorization is $(x+3)(x+10)$.

(B) $2\sqrt{2}x^2-9x+5\sqrt{2}$

This expression can be factorized into ,

$2\sqrt{2}x^2-4x-5x+5\sqrt{2} \\\\=2\sqrt{2}x(x-\sqrt{2})-5(x-\sqrt{2})\\\\=(2\sqrt{2}x-5)(x-\sqrt{2})$

Hence the factorization for given expression is $(2\sqrt{2}x-5)(x-\sqrt{2})$.

(C) $4x^2-13x+10$

This expression can be factorized into,

$4x^2-13x+10\\\\=4x^2-8x-5x+10\\\\=4x(x-2)-5(x-2)\\\\=(4x-5)(x-2)$

Hence the factorization for given expression is $(4x-5)(x-2)$.