Q.1 Factorize the following by splitting the middle term: (a) 3x² + 11x+30 (b) 2 √2 x² +9x+5√2 (c) 4x² - 13x + 10
Q.2 Factorize the following by Factor theorem: (a)x³+9 x² +23x+15 (b) x²³+6 x² +11x+6
Q.3 Factorize the following by using a suitable identity: (a) 4x² + 12xy +9y² (b) 2a5-54 a² (c) 2√2+3 3y² (d) x²-x (c) x-y" (1)
(a-b)- (b-c)+(c-a)' (f) x'-y (g) 27x'-135x² +225x-125 Q.4 Evaluate the following using a suitable identity:
(a) 998³ (b) 10.2³ (c) 9.8³ (d) 998²-4 (e) 999²-1 (f) (-25)³ + 10³ +15³ (g) 10.2 9.8 Q.5 If 5 is a zero of x³ + kx² + 2x +8 find k.
Q.6 If (x-2) is a zero of of x³-4x²+ kx -8 find k. Q.7 If (x-2) and (x+3) are factors ax² +bx -30, find a and b. of x³ +
Q.8 If x+y+z= 8 and xy +yz+zx = 20 find the value of x+y+z³-3xyz.
Q.9 If a+b+c= 9 and a² +b+c²-35 find the value of a+b+c³-3abc.
Q.10 Find the value of 2.7³ -1.6-1.1³ using a suitable identity.
Q.11 Factorize the following by using a suitable identity: (a) a³ + b³ - 8c³ + 6abc (b) (a/b)³ + (b/c) + (c/a) -3 (c) 8x-27y³ + 125 z³ + 90xyz
Q.12 Find the value of a³ + 8b³ if a + 2b = 10 and ab = 15. Q.13 Find the value of a³-27b³ if a-3b =(-6) and ab = (-10)
Q.14 Find the values of m and n if y²-1 is a factor of y' + my³ +2y²-3y +n. Q.15 (x+2) is a factor of mx³ +nx²+x-6. It leaves the remainder 4 when divided by
(x-2). Find m and n.
Q.16 The polynomials kx + 3x² -3 and 2x³-5x +k leave the same remainder when
divided by (x-4). Find k.
Q.17 Factorize: x³ + 1/x³ - 2
Q.18 If ab + bc+ ca = 10 and a² +b² +c²= 44 find a³ + b³ + c³ -3abc. Q.19 Show that x-2 is a factor p(x)=x²-12x²+44x-48
Q.20 Factorize x³-2x²-5x+6
Q.21 If x+p is a factor of p(x) = x-p²x²+2x+p+1 find the value of p Q.22 Factorize: (a) a² + 1/a²+2 (b) 3(x+2)² + 17 (x+2) + 10 (c)4x² - 9 y² + 20x + 25
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Since mass doesn't change, when the kinetic energy of an object changes, its speed must be changing. deals with faster-moving objects. The faster an object moves, the more necessary it is to use this theory in order to be accurate. As an object moves faster, its mass increases.
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