Question

2p^2-6p-20.
mid term splitting method solve is plzz​

Answer 1

$\mathcal{\green{\underline{\blue{GIVEN:}}}}$

We are given this equation:

2p²-6p-20.

$\mathcal{\green{\underline{\blue{TO \:\: FIND:}}}}$

We need to split the middle term and factorise.

$\mathcal{\green{\underline{\blue{SOLUTION:}}}}$

Now, how can we split the middle term?

STEP 1 - Convert the equation into it's standard form. We dont have to do that because it is already in the standard form.

STEP 2 - Multiply the coefficient of the first term , i.e., 2 [Include the sign] and the constant, i.e., -20  [Include the sign].

⇒2× -20 = -40.

STEP 3 - We need to split the middle term -6p in such way that the product of its terms are -40 and the sum of its terms are -6.

-10×4 = -40   [Product is -40 ✓✓]

And -10+4 = -6.  [Sum is -6 ✓✓]

Thus, we need to split the middle term as -10 and 4.

STEP 4 - SPLIT THE MIDDLE TERM:

⇒2p²-6p-20.

⇒2p²-10p+4p-20.

⇒2p(p-5)+4(p-5).

⇒(2p+4)(p-5)

Here, we can further factorise the underlined term by taking 2 common:

⇒2(p+2)(p-5)

yay! We factorised it!!!

$\huge\underline\mathfrak\purple{HOPE \:\: THIS \:\: HELPS \:\: :D}$