
Determine i, given that 0 + 0*i + 6/11*i**3 + 18/11*i**2 = 0.
-3, 0
Let l(q) be the first derivative of 3*q**5/20 - 15*q**4/8 + 3*q**3 + 87*q**2/4 + 105*q/4 + 819. Find r such that l(r) = 0.
-1, 5, 7
Let y(n) = -n - 8. Let s be y(6). Let o be 6/24 - s/8. Find t, given that -4*t**4 + 8*t**2 + 12*t**2 - 27*t**o + 11*t**2 = 0.
-1, 0, 1
Let o(x) be the first derivative of x**6/105 - 2*x**5/35 + 5*x**4/42 - 2*x**3/21 - 3*x + 3. Let j(w) be the first derivative of o(w). Let j(c) = 0. Calculate c.
0, 1, 2
Let f(d) be the second derivative of -17*d - 3/2*d**3 + 0*d**4 + 0 + 3*d**2 + 3/20*d**5. Factor f(i).
3*(i - 1)**2*(i + 2)
Let q(j) = 15*j**3 - 8*j**2 - 16*j - 27. Let t(s) = -4*s**3 + 2*s**2 + 4*s + 6. Let m(u) = -4*q(u) - 18*t(u). Factor m(v).
4*v*(v - 1)*(3*v + 2)
Determine h, given that -4/5 - 12/5*h - h**2 = 0.
-2, -2/5
Let l be 10/25 - (-6)/(-15). Let h(j) be the third derivative of 0*j**4 + 0*j + l*j**5 + 5*j**2 + 0 - 1/840*j**7 + 0*j**3 - 1/240*j**6. Solve h(x) = 0 for x.
-2, 0
Factor 2/9*q**2 + 2/9*q**3 + 0 - 2/9*q**4 - 2/9*q.
-2*q*(q - 1)**2*(q + 1)/9
Let r be (-317)/(-7) + 2 + 16/(-7). Suppose -39*w**4 - 28*w**2 - 10*w**4 - 8*w - r*w**3 + 157*w**3 + w**4 = 0. What is w?
-1/6, 0, 1/2, 2
Suppose 0 = -275*r + 283*r - 40. Let q(s) be the first derivative of 0*s**2 + 4/25*s**r + 0*s + 8/15*s**3 - 3/5*s**4 - 2. Suppose q(m) = 0. What is m?
0, 1, 2
Let d(f) be the first derivative of -f**6/160 + f**4/32 + 27*f**2/2 + 36. Let v(b) be the second derivative of d(b). Factor v(j).
-3*j*(j - 1)*(j + 1)/4
Let q = 11 - 21. Let v = -8 - q. Factor 9*b**4 - v*b**5 + 6*b**3 - b**2 - 9*b**4 - 3*b**2.
-2*b**2*(b - 1)**2*(b + 2)
Solve -7/4*o + 147/4 - 11/4*o**2 - 1/4*o**3 = 0 for o.
-7, 3
Let n(o) = -5*o**3 + 41*o**2 - 162*o + 237. Let u(j) = 4*j**3 - 40*j**2 + 166*j - 236. Let h(p) = -4*n(p) - 6*u(p). Factor h(x).
-4*(x - 13)*(x - 3)**2
Let y(q) be the first derivative of q**6/160 + q**5/80 - q**4/32 - q**3/8 + 16*q**2 - 33. Let d(i) be the second derivative of y(i). Find p such that d(p) = 0.
-1, 1
Let f = 12 + -10. Let 4*c - 4*c**f - 4*c**4 - 2*c**3 + 2*c + 0*c + 12*c**2 = 0. Calculate c.
-1, 0, 3/2
Let h be (-3)/((-12)/48*102). Factor 0*o**2 + 2/17 + 4/17*o**3 - h*o**4 - 4/17*o.
-2*(o - 1)**3*(o + 1)/17
Let v be (36/84)/((-2)/(-28)) + 1. Let y(m) be the third derivative of -1/90*m**6 + 0 + 0*m**4 + 0*m**3 + 0*m - 1/45*m**5 + v*m**2. Factor y(n).
-4*n**2*(n + 1)/3
Suppose 916*g = 921*g. Factor -5/2*x**2 + g + 0*x.
-5*x**2/2
Let w = 6552 + -26207/4. What is h in -1/4 + w*h + 1/4*h**2 - 1/4*h**3 = 0?
-1, 1
Let x(s) be the second derivative of s**4/4 + s**3/6 + s**2/2 - 7*s. Let i be x(2). Find o, given that -2*o**3 + 8 - i*o**2 - 45*o + 3 - 21 + 22*o**3 = 0.
-1, -1/4, 2
Let f(r) be the first derivative of r**7/420 - r**6/180 - r**5/30 + 8*r**3/3 - 3. Let a(q) be the third derivative of f(q). Factor a(s).
2*s*(s - 2)*(s + 1)
Let p(i) be the first derivative of -2*i**5/15 + 4*i**4/3 - 10*i**3/9 - 38*i**2/3 - 16*i + 133. Suppose p(z) = 0. Calculate z.
-1, 4, 6
Let j = 5303 - 5303. Factor 0*l**3 + 0*l**2 + j + 0*l - 2/5*l**5 - 4/5*l**4.
-2*l**4*(l + 2)/5
Let t(a) = -2*a**3 + 26*a**2 + 194*a - 2. Let y(o) = o**3 - 23*o**2 - 195*o + 3. Let l(f) = -3*t(f) - 2*y(f). Factor l(d).
4*d*(d - 12)*(d + 4)
Find d such that 0 - 2/5*d + 2/5*d**3 - 1/5*d**2 + 1/5*d**4 = 0.
-2, -1, 0, 1
Let t(z) be the first derivative of -8 + 9/4*z**2 + 7*z + 3/40*z**5 - 3/8*z**4 - 1/4*z**3. Let m(h) be the first derivative of t(h). Find c such that m(c) = 0.
-1, 1, 3
Let m(b) be the third derivative of -b**8/1176 + b**7/735 + b**6/140 - b**5/42 + b**4/42 + b**2 + 120. Determine d so that m(d) = 0.
-2, 0, 1
Factor -2/11*t**2 - 2*t + 120/11.
-2*(t - 4)*(t + 15)/11
Let s be (-5)/4 + (-4)/(-16). Let o be ((-3 + 7)/(-1))/s. Suppose -6*v**4 + 5*v**4 - 24*v**2 - 3*v - 45*v**3 + 20*v**o + 5*v**4 + 48*v**5 = 0. Calculate v.
-1, -1/4, 0, 1
Solve -56*o**3 - 11 - 4 + 4 - 10*o**5 - 56*o**4 + 92*o**2 + 66*o - 25 = 0.
-3, -1, 2/5, 1
Factor 1/2*a**2 + 0*a + 0 + 1/2*a**3.
a**2*(a + 1)/2
Let b(o) be the second derivative of o**5/105 + 5*o**4/42 + 8*o**3/21 + 2*o**2 - 10*o. Let w(c) be the first derivative of b(c). What is v in w(v) = 0?
-4, -1
Let u(v) be the second derivative of -v**4/4 + 7*v**3/2 - 15*v**2 - 149*v + 2. Factor u(m).
-3*(m - 5)*(m - 2)
Let y(r) be the second derivative of r**4/12 - 5*r**3/24 - 750*r. Factor y(b).
b*(4*b - 5)/4
Let b = -18567 + 18569. Factor 2/13*v**b - 2/13*v + 0.
2*v*(v - 1)/13
Let v(c) be the first derivative of -76*c**5/15 - 2*c**4/3 + 76*c**3/9 + 4*c**2/3 - 83. Solve v(a) = 0 for a.
-1, -2/19, 0, 1
Suppose 107 = 5*g - 4*x, -3*x + 86 = g + 4*g. Determine l, given that 23*l**2 + 4 - 7*l - g*l**2 - l + 0*l = 0.
1
Suppose -2*b + 10 + 0 = -5*k, -2*k - 4 = b. Find f, given that -2*f**2 + 5*f + b*f**2 - 9*f = 0.
-2, 0
Factor -35*y**3 + 45*y**3 - 16*y + 6*y**2 + 30*y**2.
2*y*(y + 4)*(5*y - 2)
Let n = 44343/10 - 4434. Factor -1/10*g**2 + n - 1/5*g.
-(g - 1)*(g + 3)/10
Let b(z) be the first derivative of -9*z**2 - 8*z**3 - 3/5*z**5 + 9/2*z**4 + 5 + 27*z. Let b(t) = 0. What is t?
-1, 1, 3
Factor 24*u**2 - 3*u + 8 + 3*u - 56*u**2 + 30*u**2.
-2*(u - 2)*(u + 2)
Let j(n) = 4*n**2 - 141*n + 122. Let t(k) = k**2 - 2*k - 4. Let h(q) = j(q) - 3*t(q). Factor h(f).
(f - 134)*(f - 1)
Let g(l) be the second derivative of l**6/60 + l**5/30 - l**4/12 - l**3/3 - 5*l**2 - 14*l. Let u(c) be the first derivative of g(c). Solve u(s) = 0 for s.
-1, 1
Suppose 5*b - 3*b - 4 = 0. Factor t**5 - 33*t**3 + 64*t**3 + t**b - t**4 - 32*t**3.
t**2*(t - 1)**2*(t + 1)
Let v(a) be the first derivative of -a**3 + 27*a**2/2 - 54*a - 269. Suppose v(m) = 0. Calculate m.
3, 6
Let g(n) be the second derivative of n**10/7560 + n**9/1890 - n**8/1680 - n**7/315 - 19*n**4/12 + 32*n. Let f(q) be the third derivative of g(q). Factor f(o).
4*o**2*(o - 1)*(o + 1)*(o + 2)
Factor 5*u**3 - 240 + 72*u**2 + 3*u**2 - 170*u + 240.
5*u*(u - 2)*(u + 17)
Factor 5/3*m**2 + 140 - 220/3*m.
5*(m - 42)*(m - 2)/3
Let h be ((3 - 11) + 4)/((-20)/58). Let j = 247/20 - h. Factor 3/4*r**2 - j*r + 0.
3*r*(r - 1)/4
Let q(p) = 5*p**4 - p**3 - 5*p**2 - 3*p + 4. Let k(t) = -9*t**4 + 2*t**3 + 9*t**2 + 5*t - 7. Let f be 4 + (1 - 3) - 6. Let h(i) = f*k(i) - 7*q(i). Factor h(l).
l*(l - 1)**2*(l + 1)
Let h(j) = j - 4. Let g be h(-5). Let r = g + 18. Suppose -7*x**5 - r*x + 8*x**2 + 3 - 2*x**5 + 18*x**3 - 6*x**4 - 9 + 4*x**2 = 0. What is x?
-1, -2/3, 1
Let s(h) be the first derivative of 7*h**3/18 - 85*h**2/12 + 2*h + 276. Let s(n) = 0. Calculate n.
1/7, 12
Suppose -4*w + 9*w = 45. Suppose 3*i - w = -3*x + 3, -3*x = 2*i - 12. Suppose -3/2*m**2 + i + 0*m + 9/2*m**3 = 0. Calculate m.
0, 1/3
Let w(u) be the second derivative of -u**4/54 + 20*u**3/27 + 23*u**2/3 - 411*u. Factor w(x).
-2*(x - 23)*(x + 3)/9
Let z(s) be the second derivative of s**6/270 - s**5/10 - s**4/108 + s**3/3 + 76*s + 1. Solve z(q) = 0 for q.
-1, 0, 1, 18
Let h(o) = -o**3 - 27*o**2 + 32*o + 114. Let n be h(-28). Factor -1/4*f**5 + 0 - 9/4*f**3 + 0*f**n + 0*f + 3/2*f**4.
-f**3*(f - 3)**2/4
Let i(a) be the second derivative of 4*a - 4/7*a**2 + 1/14*a**4 + 4/21*a**3 + 0. Factor i(s).
2*(s + 2)*(3*s - 2)/7
Let n(y) = 3*y**3 + 32*y**2 + 8*y - 163. Let x(j) = -5*j**3 - 47*j**2 - 12*j + 244. Let f(p) = -8*n(p) - 5*x(p). Solve f(m) = 0 for m.
-2, 2, 21
Let q(l) = l**3 - 13*l**2 - 12*l + 159. Let g be q(13). What is y in 2/3*y**4 - 1/3*y + 0 + 0*y**g - 2/3*y**2 + 1/3*y**5 = 0?
-1, 0, 1
Let j(d) be the second derivative of 1/48*d**4 + 0*d**3 + 0 - 11*d - 1/8*d**2. Solve j(w) = 0.
-1, 1
Let o = -167219/60 - -2787. Let b(q) be the third derivative of 1/40*q**6 + 11*q**2 + 0*q**3 + 0 - 1/12*q**4 + 0*q + o*q**5. Solve b(f) = 0.
-1, 0, 2/3
Determine y so that -2/5*y**3 - 36/5*y + 0 + 22/5*y**2 = 0.
0, 2, 9
Let m = -3657 - -10972/3. Suppose m*k**2 + k + 0 = 0. What is k?
-3, 0
Let h = 15 - 20. Let u be -4 + 3 - 1 - h. What is d in -u*d - 8*d - 3*d**2 - d - 12 = 0?
-2
Let v = 20/1839 - -14572/12873. Factor 6/7*x + v - 2/7*x**2.
-2*(x - 4)*(x + 1)/7
Suppose 8 = -n + 99. Suppose -3*z - n + 100 = 0. Determine a, given that z*a**4 - 3/4*a**5 + 0*a - 15/4*a**3 + 0 + 3/2*a**2 = 0.
0, 1, 2
Let o(b) be the second derivative of b**6/600 + 21*b**2/2 + 5*b. Let n(p) be the first derivative of o(p). Solve n(r) = 0.
0