2*s**4/3 - 30*s**3 - 44*s**2 + 735*s. Factor d(a).
4*(a - 1)*(a + 1)**3*(a + 22)
Let o(m) be the second derivative of m**6/150 + 3*m**5/100 - m**4/60 - m**3/10 + m - 191. Let o(z) = 0. What is z?
-3, -1, 0, 1
Factor 58/3*k**3 + 57 + 1/3*k**4 - 94*k + 52/3*k**2.
(k - 1)**2*(k + 3)*(k + 57)/3
Suppose 3*i - 1098 + 102 = 0. Let o = i - 992/3. Factor o*p**2 + 0 - 4/3*p.
4*p*(p - 1)/3
Let s(k) be the first derivative of -95/3*k**3 + 0*k - 65/4*k**4 - 89 - 15*k**2. Factor s(o).
-5*o*(o + 1)*(13*o + 6)
Let f(s) be the third derivative of 105*s**2 - 16*s**4 - 1/30*s**6 + 192*s**3 + 0*s - 22/15*s**5 + 0. Factor f(l).
-4*(l - 2)*(l + 12)**2
Let i(m) be the first derivative of -m**6 + 21*m**5/10 + 117*m**4/4 - 253*m**3/2 + 129*m**2 + 90*m + 10312. Solve i(t) = 0 for t.
-5, -1/4, 2, 3
Factor 0*w - 2/7*w**3 + 0 - 4010/7*w**2.
-2*w**2*(w + 2005)/7
Let y = 13204/207 - 1462/23. Factor -2/3*v**2 + 0 + 8/9*v - y*v**3.
-2*v*(v - 1)*(v + 4)/9
Let x = -180 - -195. Suppose -33 = -6*y - x. Suppose -2/11*p**2 + 0*p - 2/11*p**4 + 0 + 4/11*p**y = 0. Calculate p.
0, 1
Suppose -198*h + 179*h = -4731. Let v = h - 247. Find u such that -2/15*u**v - 2/3*u + 4/5 = 0.
-6, 1
Let g be ((-25)/9 - -3) + (-203021)/117. Let f = -8673/5 - g. Factor 1/5*r**4 + 3/5 - 4/5*r**2 + 2/5*r**3 - f*r.
(r - 1)**2*(r + 1)*(r + 3)/5
Factor 268/5*i - 4*i**2 + 168/5.
-4*(i - 14)*(5*i + 3)/5
Let s = -916678/3 - -305560. Factor -40/3*c + 6*c**2 + 0 - s*c**3.
-2*c*(c - 5)*(c - 4)/3
Let m(x) be the second derivative of -16/17*x**2 - 4*x - 16/51*x**3 + 0*x**4 + 2/85*x**5 - 5 + 1/255*x**6. Factor m(r).
2*(r - 2)*(r + 2)**3/17
Determine b so that 644/3*b**2 - 428/3*b**4 + 220/3*b - 72 + 8/3*b**5 - 76*b**3 = 0.
-1, 1/2, 1, 54
Factor -40/7 - 22/3*i - 32/21*i**2 + 2/21*i**3.
2*(i - 20)*(i + 1)*(i + 3)/21
Let i be (2/14)/(2/10). Let r(k) be the second derivative of 7/3*k**3 + 0 - 4*k**5 + 2*k - 2*k**2 + k**4 - i*k**7 + 44/15*k**6. Solve r(q) = 0.
-2/5, 1/3, 1
Let x(d) be the second derivative of -d**5/70 - 2*d**4/21 - 5*d**3/21 + 13*d**2/2 - 33*d + 2. Let u(p) be the first derivative of x(p). Factor u(v).
-2*(v + 1)*(3*v + 5)/7
Let s(z) be the third derivative of z**8/1344 + 3*z**7/280 + z**6/60 - 8*z**5/15 - 4*z**4 - 32*z**3/3 + 133*z**2 - 8*z. Factor s(j).
(j - 4)*(j + 1)*(j + 4)**3/4
Let d = 269 + -329. Let o be ((-24)/54)/(8/d). Solve 0 - 5/3*g**3 + 0*g - o*g**2 = 0 for g.
-2, 0
Let w(c) be the third derivative of c**10/50400 - c**9/5040 + c**8/2240 + 3*c**5/10 + c**4/12 + 7*c**2. Let i(j) be the third derivative of w(j). Factor i(m).
3*m**2*(m - 3)*(m - 1)
Let j be (-44)/16 - (-2)/(-8) - (1171 + -1179). Determine n so that -4/11*n**3 + 0 + 0*n**2 + 0*n - 2/11*n**j - 6/11*n**4 = 0.
-2, -1, 0
Let c be 2/(-14) + (-31)/(-63) + (-2)/(-9). Solve 44/7*t**3 - 22/7 - 6*t + c*t**2 - 2/7*t**5 + 18/7*t**4 = 0 for t.
-1, 1, 11
Let r be (6/(-5))/(-3) - (9 + (-731)/85). Let x(o) be the third derivative of 0*o + 0*o**3 - 6*o**2 - 1/20*o**4 + r + 1/100*o**5. Suppose x(b) = 0. What is b?
0, 2
Let m(t) be the first derivative of 9*t**4/8 + 109*t**3/2 - 651*t**2/2 + 360*t - 751. What is v in m(v) = 0?
-40, 2/3, 3
Factor -339*t**2 + 20*t**4 + 5*t**5 + 430*t**2 - 125*t**3 - 231*t**2.
5*t**2*(t - 4)*(t + 1)*(t + 7)
Let l(a) be the first derivative of a**6/40 - 3*a**5/20 + a**4/4 - 41*a**2/2 + 7. Let n(t) be the second derivative of l(t). Factor n(s).
3*s*(s - 2)*(s - 1)
Let a(f) be the first derivative of 90 - 2/5*f**2 + 1/25*f**5 + 3/5*f**3 - 3/10*f**4 + 0*f. What is m in a(m) = 0?
0, 1, 4
Let a(h) = -h**3 + 1881*h**2 + 219020*h - 220905. Let g(u) = -8*u**3 + 16928*u**2 + 1971180*u - 1988144. Let r(j) = 44*a(j) - 5*g(j). Let r(t) = 0. Calculate t.
-235, 1
Suppose 214*g - 562*g = -696. Factor -11/9 + 4/3*o - 1/9*o**g.
-(o - 11)*(o - 1)/9
Suppose 5*j = 0, 12*c + 5*j - 5640 = 17*c. Let h = 1128 + c. Find r, given that 9*r**2 + h - 9/4*r**4 - 7/4*r**5 + 2*r + 13/2*r**3 = 0.
-2, -1, -2/7, 0, 2
Let l be (-42)/(1 - 4/(-8)). Let f be (16/l)/((-4)/98). Find h such that -f*h**3 + 6*h**2 - 16*h**3 + 42*h**4 + 9*h**3 - 33*h**4 = 0.
0, 1/3, 2
Let z = -1891 + 1894. Suppose 13*h = -z*h + 3*h. Factor h + 4/3*v - 2/3*v**2 - 2/3*v**3.
-2*v*(v - 1)*(v + 2)/3
Let -52*s**3 - 17*s**2 - 36*s**3 + 60*s**3 + 28*s + 26 - 2*s**4 - 7*s**2 = 0. Calculate s.
-13, -1, 1
Let q(g) be the second derivative of 21*g**5/20 + 47*g**4/4 - 70*g**3 + 54*g**2 - 944*g. Factor q(b).
3*(b - 2)*(b + 9)*(7*b - 2)
Let x(o) be the third derivative of o**6/30 - 2*o**5/5 - 56*o**4/3 - 2*o**2 + 853*o. Determine k so that x(k) = 0.
-8, 0, 14
Let q(d) = d**2 - 17*d + 37. Let c be q(2). Factor 8 - 3874*m**2 + 3887*m**2 - c*m - 14*m.
(m - 1)*(13*m - 8)
Let v(s) be the first derivative of -2*s**3/39 + 7*s**2/13 + 60*s/13 - 2557. Find z such that v(z) = 0.
-3, 10
Let l(q) be the second derivative of 0 + 0*q**2 - 8/9*q**3 - 13/9*q**4 - 177*q - 14/15*q**5 - 1/42*q**7 - 23/90*q**6. Determine g, given that l(g) = 0.
-4, -2, -1, -2/3, 0
Let y(s) be the first derivative of -1925*s**3/3 - 1930*s**2 - 20*s + 4270. Suppose y(c) = 0. Calculate c.
-2, -2/385
Let l be 14/(308/65263)*4/(-10). Let y = l + 1193. Solve 4/5*c**4 - 16/5*c + y*c**2 + 0 - 4*c**3 = 0 for c.
0, 1, 2
Let h(v) be the first derivative of v**6/18 - v**5/15 - 3*v**4/4 + v**3/9 + 10*v**2/3 + 4*v + 1328. Let h(a) = 0. Calculate a.
-2, -1, 2, 3
Let f(p) be the second derivative of -5*p**4/12 - 485*p**3/6 + 2675*p**2 + 10688*p. Determine c so that f(c) = 0.
-107, 10
Let w(x) be the third derivative of -x**5/15 - 11*x**4 + 134*x**3/3 + 21*x**2 - 14*x. Factor w(t).
-4*(t - 1)*(t + 67)
Let l(c) = 96*c + 47. Let b be l(-13). Let y = -1199 - b. Find u, given that -2/13*u + 0*u**y + 2/13*u**3 + 0 = 0.
-1, 0, 1
Let v(f) = -5*f**2 + 576*f - 562. Let q(r) = -36*r**2 + 4038*r - 3936. Let t(k) = 6*q(k) - 44*v(k). Find p such that t(p) = 0.
1, 278
Let m(b) be the second derivative of -b**5/120 - 7*b**4/72 + 145*b**3/36 - 425*b**2/12 - 192*b - 3. Find k, given that m(k) = 0.
-17, 5
Solve 47/5*y**3 - 1/5*y**4 - 2646/5 + 2457/5*y - 657/5*y**2 = 0 for y.
2, 3, 21
Let j(g) be the first derivative of 35*g**3/18 + 10*g**2 + 50*g/3 + 832. Factor j(c).
5*(c + 2)*(7*c + 10)/6
Let q be (-10)/14 - (-79920)/24864. Find v, given that 5/4*v**4 + q*v**2 + 5*v**3 - 5*v - 15/4 = 0.
-3, -1, 1
Solve 3136/5 + 1536/5*f + 42*f**3 - 1388/5*f**2 - 2/5*f**4 = 0.
-1, 4, 98
Let g(w) be the second derivative of -w**7/462 - w**6/15 - 57*w**5/220 + 1234*w. Let g(x) = 0. What is x?
-19, -3, 0
Let h(g) be the third derivative of 0*g**5 - 10 + 0*g - 1/280*g**7 - 2*g**2 - 1/16*g**4 + 1/8*g**3 + 1/80*g**6. Factor h(c).
-3*(c - 1)**3*(c + 1)/4
Let a be (-6)/16*-10 - (-7)/28. Factor -2*o**2 + 0*o**4 + 7841*o**3 + 2*o**a - 4*o - 7837*o**3.
2*o*(o - 1)*(o + 1)*(o + 2)
Suppose 0 = -3128*x + 3124*x. Let m(b) be the third derivative of -10*b**2 + x*b**3 - 1/24*b**4 + 0*b - 1/60*b**5 + 0. Factor m(f).
-f*(f + 1)
Let r(o) be the first derivative of -33/2*o**2 + 46/3*o**3 - 1/6*o**6 + 77 + 9/5*o**5 + 9*o - 15/2*o**4. Suppose r(n) = 0. Calculate n.
1, 3
Let m(j) = -5*j**2 + 227*j - 298. Let a(t) = -t**2 + 2*t - 20. Let f(g) = 12*a(g) - 3*m(g). Find y such that f(y) = 0.
1, 218
Factor 2600/7*f + 144/7*f**3 + 1140/7*f**2 + 4/7*f**4 + 0.
4*f*(f + 5)**2*(f + 26)/7
Let j(u) = -4*u**3 - 55*u**2 + 21*u + 101. Let b be j(-14). What is n in -3*n + 3/2 + 1/3*n**b + 4/3*n**2 - 1/6*n**4 = 0?
-3, 1, 3
Suppose p = 5*f, -2*p + 4*p + 6 = 3*p + f. Let -3/2*w**p + 837/2*w + 84*w**2 - 27*w**4 - 117*w**3 + 243 = 0. Calculate w.
-9, -1, 2
Let s(b) = -2*b**2 + 96*b + 708. Let q(f) = f**2 - 5*f - 1. Let x(u) = 4*q(u) + s(u). Factor x(p).
2*(p + 16)*(p + 22)
Let u = -137589 - -275183/2. Solve -1/2*b**2 - 2*b + u = 0.
-5, 1
Let x be 58/21*-1 - (-7 + 4). Let w(d) be the third derivative of -x*d**3 + 13*d**2 + 1/42*d**5 + 0*d + 0 + 1/420*d**6 - 1/84*d**4. Factor w(h).
2*(h - 1)*(h + 1)*(h + 5)/7
Let z(d) be the second derivative of 1/90*d**6 + 0*d**2 + 0*d**3 - 2 + 1/30*d**5 + 1/36*d**4 + 46*d. Determine i so that z(i) = 0.
-1, 0
Let v = 37 - 32. Suppose -52*l = -47*l. Factor l*o + 1/2*o**4 + 1/2*o**v - 1/2*o**3 - 1/2*o**2 + 0.
o**2*(o - 1)*(o + 1)**2/2
Let w be (256/(-54))/1*-5*5579145216/283770. Let 8192/3*s**2 + 4/9*s**4 - 524288/9*s - 512/9*s**3 + w = 0. What is s?
32
Suppose 11*g + 588 + 6067 = 0. Let p 