Question

$\huge{\underline {\underline{\sf{\orange {Q᭄uesTion}}}}}$
✿Explain "Middle Term Splitting".
✿Provide some good examples.
✿Provide an example for 'Polynomials' for the same topic. ​

Answer 1

Step-by-step explanation:

▪︎Middle Term Splitting..

=Quadratic factorization using splitting of middle term : In this method splitting of middle term in to two factors. In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

▪︎Good Examples::

=Example 1: Factorize the quadratic expression: x2 -8x -9

Let's rewrite this expression as: x2 -8x -9

The middle term needs to be split into two terms whose product is -9x2 while the sum remains -8x

 x2 - 9x  + 1x  -9

= x(x - 9) + 1 (x - 9)

= (x - 9) (x + 1)

=Example 2: Factorize the quadratic expression: x2 +13x -168

Let's rewrite this expression as: x2 +13x -168

The middle term needs to be split into two terms whose product is -168x2 while the sum remains +13x

 x2 + 21x  - 8x  -168

= x(x + 21) - 8 (x + 21)

= (x + 21) (x - 8)

▪︎For polynomials

=

Example 3: Factorize the quadratic expression: x2 +3x -40

Let's rewrite this expression as: x2 +3x -40

The middle term needs to be split into two terms whose product is -40x2 while the sum remains +3x

 x2 + 8x  - 5x  -40

= x(x + 8) - 5 (x + 8)

= (x + 8) (x - 5)

=Example 4: Factorize the quadratic expression: x2 +5x -300

Let's rewrite this expression as: x2 +5x -300

The middle term needs to be split into two terms whose product is -300x2 while the sum remains +5x

 x2 - 15x  + 20x  -300

= x(x - 15) + 20 (x - 15)

= (x - 15) (x + 20)

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Answer 2

$\sf\large\underline\purple{Middle\: term\: splitting:-}$

Splitting middle term is the process by which you can factorise the equation or polynomial. In this process at first we have to find out the factors of the middle term and it is divided in two part such that the factors are divisible. We also add variable with constant term such as 3x and 5x her x is variable and 3, 5 are constant:

$\sf\large\underline\purple{Example\:of\: splitting\: middle\: term:-}$

$\tt{\implies x^2+27x+92}$

• Here we have to split the middle term and middle term is 27x we have to find out the factors for 27x by helping of constant term. Here constant term is 92 now we have to find the certain factors for 27x so, the factors of 92= 41 × 2, 23 × 4. Here 23 × 4 is the certain factors of the given equation.

$\tt{\implies x^2+27x+92}$

$\tt{\implies x^2+23x+4x+92}$

$\tt{\implies x(x+27)+4(x+23)}$

$\tt{\implies (x+4)(x+23)}$

$\sf\large\underline\purple{Polynomial:}$

Polynomial are many types like monomials, binomial trinomials, quardric polynomial, cubic polynomial:

Monomials=>It indicates single term for example 4x, 7x ,11x

Binomial=>It indicates two terms for example 2x+7, 9x+3, 3x+4

Trinomials=>It indicates three terms for example x²+2x+6, 3x²+7x+9, x²-x+6

$\sf\large\underline\purple{Quardric\: polynomial:-}$

In quardric polynomial the maximum power upon variable is 2 for example. x²+9x+40

$\sf\large\underline\purple{Cube\: polynomial:-}$

In cube polynomial The maximum power upon variable is 3 for example. x³+6x²+7x+9