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f(a) (aa)˜h(a) 0 ? f(a) 0. Hence, any polynomial f(x) will be divisible by (xa), if and only if f(a) 0. This formula is known ...

0DWK,;;)RUPD = x^2 (xy)xy(xy) 2 y^2 (xy) = (xy)(x^2 xy 2 y^2 ) = (xy)(x^2  2 xyxy 2 y^2 ) = (xy){x(x 2 y)y( ...

3 ⋅6 Forming and applying algebraic formulae in solving real life problems In our daily business we face the realistic problems ...

where, v = speed per hour t = total time. (4) Related to pipe and water tank : Amount of water in a tank at a definite time, Q(t ...

r = profit of unit principal at unit time A = principal with profit after time n. Example 1. For a function of Annual Sports, me ...

Solution : Let, Rafiq and Shafiq together can finish the wok in d days. Let us make the following table : Name Number of days fo ...

or, ̧ ̧ ¹ · ̈ ̈ © §  1 2 1 1 2 t t x u Subtracting equation (ii) from equation (i) we get, ̧ ̧ ¹ · ̈ ̈ © §  2 1 2 1 1 t t v x ...

Activity : For a picnic, a bus was hired at Tk. 2400 and it was decided that every passenger would have to give equal fare. But ...

Again, if cost price is Tk. 100, selling price at the profit of s% is Tk. ( 100 s) ? ,, ,, ,, ,, Tk. 1 ,, ,, ,, ,, ,, ,, ,, ,, ...

0DWK,;;)RUPD = 25 3 148877 (^12525) 53 53 53 3 15 u u u u = 1786524 25 446631 ˜ ? compound principal is Tk. 17865 ˜ 24 ? c ...

Which one of the following is the value of {( ) ( )} 2 (^122) ab ab? (a) 2 (a^2 b^2 ) (b) a^2 b^2 (c) 2 ab (d) 4 ab If 3 ...

Which one of the following is the total area of the table above? (a)x^2  5 x 30 (b) x^2 x 30 (c)x^2  6 x 30 (d) x^2 x 30 ...

(3)^33 1 x x  = what? (a) 3 (b) 2 (c) 1 (d) 0 A can do a work in p days and B can do it in 2 p days. They started to do the wo ...

If the simple profit of Tk. 300 in 4 years and the simple profit of Tk. 400 in 5 years together are Tk. 148, what is the percen ...

Chapter Four Exponents and Logarithms Very large or very small numbers or expressions can easily be expressed in writing them by ...

If ais any real number, successive multiplication of ntimes a; that is, auauau..... uais written in the form an, where nis a pos ...

anbn a a a a b b b b ( u u u.......u )u( u u u........u ) Formula 4. ̧ ,( z 0 ) ¹ · ̈ © § b b a b a n n n We observe, 3 (^33) 2 ...

0DWK,;;)RUPD = anum amn ? (am)n amn Example 1. Find the values (a) 3 2 5 5 (b) 5 5 3 2 3 2  ̧ ¹ · ̈ © § ̧u ¹ · ̈ © § Sol ...

4.3nth root We notice, 2 2 1 2 1 2 1 5 5 5 ̧ ¹ · ̈ © § u Again, 5 2 5 21 2 1 2 1 2 1 2 1 5 5 5  u u 5 5. 2 2 1 ? ̧ ¹ · ̈ © § Sq ...

i.e.nth power of an 1 a a n n ̧ ̧ ¹ · ̈ ̈ © § 1 and nth root of a=an an 1 1 () =na.nth root of ais written as na. Example 4. Sim ...