Check whether f(x) = x³– x + 1 is a multiple of g(x) = 2 – 3x.

Find the remainder when f(x) = x³–ax² + 6x – a is divided by (x – a)

Write the following polynomials in standard form.

S.No	Polynomial	Standard form
1	5m4 -3m + 7m2 + 8
2	\(\frac { 2 }{ 3 } y+{ 8y }^{ 3 }-12+\sqrt { 5 } { y }^{ 2 }\)
3	12p2 -8p5 -10p4 -7

If \(\left( y-\frac { 1 }{ y } \right) ^{ 3 }\) =729, then find the value of \(y-\frac { 1 }{ y } \) and \({ y }^{ 3 }-\frac { 1 }{ { y }^{ 3 } } \) .

(i) Prove that (x - 1) is a factor of x³- 7x² + 13x - 7
(ii) Prove that (x + 1) is a factor of x³ + 7x² + 13x + 7

Find the slopes of all the lines from the adjacent figure,

Check whether (5, −1) is a solution of the simultaneous equations x – 2y = 7 and 2x + 3y = 7.

Given 4a + 3b = 65 and a + 2b = 35 solve by elimination method.

Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) \(\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0\)

Find the value of k, for the following system of equation has infinitely many solutions. 2x − 3y = 7;(k + 2)x − (2k +1)y = 3(2k −1)