Write any five quadratic and cubic equations own your own, and factorise them by splitting the middle term.
Answers
Factorize each of the following expressions:
(i) x2 + 6x + 8 (ii) x2 + 4x –21
Solution:
(i) In order to factorize x2 + 6x + 8, we find two numbers p and q such that p + q = 6 and pq = 8.
Clearly, 2 + 4 = 6 and 2 × 4 = 8.
We know split the middle term 6x in the given quadratic as 2x + 4x, so that
x2 + 6x + 8 = x2 + 2x + 4x + 8
= (x2 + 2x) + (4x + 8)
= x (x + 2) + 4 (x+ 2)
= (x + 2) (x + 4)
(ii) In order to factorize x2 + 4x – 21, we have to find two numbers p and q such that
p + q = 4 and pq = – 21
Clearly, 7 + (– 3) = 4 and 7 × – 3 = – 21
We now split the middle term 4x of
x2 + 4x – 21 as 7x – 3x, so that
x2 + 4x – 21 = x2 + 7x – 3 x – 21
= (x2 + 7x) – (3x + 21)
= x (x + 7) – 3 (x + 7) = (x + 7) (x – 3)
Answer:
Atomic mass is also known as atomic weight. Atomic mass is the weighted average mass of an atom of an element based on the relative natural abundance of that element's isotopes. The mass number is a count of the total number of protons and neutrons in an atom's nucleus.