r**2. Let p(c) = -1. Let h(z) = 6*p(z) - 3*w(z). Find o, given that h(o) = 0.
1, 2
Factor 75/2 - 27/2*m**2 + 3/2*m**3 + 45/2*m.
3*(m - 5)**2*(m + 1)/2
Let u(c) be the second derivative of -5*c + 1/3*c**2 + 1/30*c**5 + 0 - 1/9*c**3 - 1/18*c**4. Factor u(h).
2*(h - 1)**2*(h + 1)/3
Let q(f) be the first derivative of 0*f + 14/45*f**5 + 1/6*f**4 - 5/27*f**6 + 2/9*f**2 - 7 - 14/27*f**3. What is y in q(y) = 0?
-1, 0, 2/5, 1
Let g = -34 - -34. Let o(u) be the second derivative of 1/126*u**7 + 0 + 0*u**4 - 1/45*u**6 + g*u**3 + 0*u**2 + 3*u + 1/60*u**5. Factor o(y).
y**3*(y - 1)**2/3
Let i = 197/2 + -967/10. Let a = i - 13/10. Determine o, given that -a + 0*o + 0*o**3 + o**2 - 1/2*o**4 = 0.
-1, 1
Let d(c) be the third derivative of c**8/112 + c**7/70 - 3*c**6/40 - c**5/4 - c**4/4 - 22*c**2. Factor d(x).
3*x*(x - 2)*(x + 1)**3
Let f(p) be the second derivative of -p**6/1440 - p**5/480 + p**3/6 + 2*p. Let s(k) be the second derivative of f(k). Determine b, given that s(b) = 0.
-1, 0
Let v(s) = -6 - 2*s + s**3 + 4 + 4 - 10*s**2. Let y(m) be the first derivative of -m**4/4 + 5*m**3/3 + m**2/2 - m - 1. Let h(j) = -4*v(j) - 7*y(j). Factor h(o).
(o + 1)**2*(3*o - 1)
Let j(t) be the third derivative of -t**5/40 - 3*t**4/8 + 7*t**3/4 - 16*t**2. Factor j(l).
-3*(l - 1)*(l + 7)/2
Let w = -2 - -2. Let q(g) be the third derivative of 0 - 1/735*g**7 + 0*g**6 - 2*g**2 + 0*g**3 + 0*g**5 + 0*g + w*g**4. Solve q(d) = 0.
0
Let o(k) be the first derivative of k**8/1680 - k**7/420 + k**5/60 - k**4/24 - k**3/3 - 1. Let i(a) be the third derivative of o(a). Factor i(y).
(y - 1)**3*(y + 1)
Let t(s) be the third derivative of -s**7/210 - s**6/60 + s**5/20 + s**4/3 + 2*s**3/3 + 12*s**2. Suppose t(d) = 0. Calculate d.
-2, -1, 2
Factor 2/13*u**4 - 8/13*u**3 + 0 + 8/13*u**2 + 0*u.
2*u**2*(u - 2)**2/13
Let a(k) be the third derivative of -k**6/180 - k**5/60 - k**4/72 - 13*k**2. Solve a(w) = 0.
-1, -1/2, 0
Suppose -81/4*s**5 - 3 - 18*s + 135/4*s**4 + 117/4*s**3 - 87/4*s**2 = 0. Calculate s.
-2/3, -1/3, 1, 2
Suppose -17*x - 4*c = -15*x - 12, -4*c = 3*x - 12. Factor 0 + x*q + 1/3*q**4 + 0*q**2 + 0*q**3.
q**4/3
Suppose 4*x - 32 = 3*x. Let i = x - 32. Let -1/2*w**3 + i + 0*w + 1/2*w**2 = 0. What is w?
0, 1
Let i(p) be the second derivative of 1/20*p**4 + 1/10*p**2 + 1/20*p**5 + 6*p + 0 - 1/6*p**3 - 2/75*p**6. Solve i(q) = 0 for q.
-1, 1/4, 1
Factor 0*l + 0*l**3 + 0*l**2 - 2/9*l**4 + 0.
-2*l**4/9
Find u such that -16/11*u + 2/11*u**5 + 2/11*u**2 + 14/11*u**3 - 10/11*u**4 + 8/11 = 0.
-1, 1, 2
Let w(c) be the first derivative of -2 - 2/9*c - 2/27*c**3 - 2/9*c**2. Suppose w(s) = 0. What is s?
-1
Let z(r) be the second derivative of -r**5/30 + r**4/9 - r**3/9 + 2*r. Suppose z(o) = 0. What is o?
0, 1
Let j(m) = -3*m**2 + 3*m - 11. Let n = -3 - 8. Let p(x) be the second derivative of -x**4/12 + x**3/6 - 2*x**2 + 5*x. Let h(k) = n*p(k) + 4*j(k). Factor h(g).
-g*(g - 1)
Let s(x) be the first derivative of -x**6/10 + x**4/4 - 4*x - 2. Let a(f) be the first derivative of s(f). Factor a(r).
-3*r**2*(r - 1)*(r + 1)
Let f(y) be the first derivative of 32/13*y - 32/13*y**2 - 2 + 2/65*y**5 + 16/13*y**3 - 4/13*y**4. Suppose f(q) = 0. What is q?
2
Solve -2/17*l - 2/17*l**2 + 0 = 0 for l.
-1, 0
Let w(q) be the second derivative of q**6/15 - 13*q**5/40 + 5*q**4/8 - 7*q**3/12 + q**2/4 + 16*q. Let w(z) = 0. Calculate z.
1/4, 1
Let u(l) be the second derivative of -l**6/660 + l**4/44 - 2*l**3/33 - 5*l**2/2 + l. Let f(v) be the first derivative of u(v). Factor f(q).
-2*(q - 1)**2*(q + 2)/11
Let j = -1240/9 - -138. Find i such that 0*i - 4/9*i**3 + j*i**4 + 0 + 2/9*i**2 = 0.
0, 1
Let r = 16 - 14. What is n in 15*n**2 + 3*n**3 + 0*n**3 - 15*n**r - 3*n**4 = 0?
0, 1
Let h(w) = -8*w**3 - 10*w**2 - 4*w - 2. Let n(v) = v**3 + v**2 + v + 1. Let m be (-48)/12 - (-1 - 2). Let x(l) = m*h(l) - 6*n(l). Suppose x(k) = 0. Calculate k.
-2, -1, 1
Suppose 3*h = -h - 3*w + 333, 2*h - 3*w = 171. Let o be (8/10)/(h/30). Factor -2/7*f**2 + 0*f + o.
-2*(f - 1)*(f + 1)/7
Let 81/7*t**2 + 12/7 - 60/7*t**3 + 72/7*t = 0. Calculate t.
-2/5, -1/4, 2
Let -6*c**2 - 18*c**2 - 32*c**2 - 48*c**3 + 4*c**5 - 20*c - 8*c**4 = 0. Calculate c.
-1, 0, 5
Let f = 14 - 10. Suppose r - f*j = -8, 2*r = -2*j - 2*j + 8. What is o in 16/9*o**4 + 2/3*o**5 + 4/9*o**2 + 14/9*o**3 + r + 0*o = 0?
-1, -2/3, 0
Let r(s) be the second derivative of -s**6/50 - s**5/20 - s**4/30 - 6*s. Factor r(n).
-n**2*(n + 1)*(3*n + 2)/5
Let s(h) be the third derivative of -h**6/960 + h**5/240 + h**4/192 - h**3/24 + 2*h**2. Factor s(l).
-(l - 2)*(l - 1)*(l + 1)/8
Let j(f) be the third derivative of -1/8*f**3 + 0 - 1/32*f**4 + 4*f**2 + 1/80*f**5 + 1/160*f**6 + 0*f. Factor j(v).
3*(v - 1)*(v + 1)**2/4
Let i(t) be the second derivative of -t**7/189 - t**6/135 + t**5/45 + t**4/27 - t**3/27 - t**2/9 + 8*t. Factor i(b).
-2*(b - 1)**2*(b + 1)**3/9
Suppose -35*y**2 - 5*y**4 - 10*y + 10*y**2 - 6*y**3 - 14*y**3 = 0. Calculate y.
-2, -1, 0
Let i = 14 - 26. Let a be (i/27)/((-2)/3). Determine c so that -1/3*c**2 - a*c**3 + 0*c + 0 - 1/3*c**4 = 0.
-1, 0
Suppose 4*i + 14 - 26 = 0. Suppose 29*u - 29*u - i*u**3 - 6*u**5 + 9*u**4 = 0. Calculate u.
0, 1/2, 1
Let w = -5 - -8. Suppose -5*p - w*i - 1 = 4, -4*p + 2*i = -18. Factor 0 + 0 + k**p + k.
k*(k + 1)
Let x(h) be the third derivative of 0*h**4 + 0*h - 1/560*h**8 + 0*h**3 + 0 - 4*h**2 + 1/350*h**7 - 1/100*h**5 + 1/200*h**6. Solve x(g) = 0 for g.
-1, 0, 1
Let r(y) be the second derivative of y**2 - 1/60*y**5 + 0 + 0*y**3 + 1/24*y**4 + 4*y. Let d(c) be the first derivative of r(c). Find l such that d(l) = 0.
0, 1
Let r = -95 - -195/2. Let b(c) be the first derivative of 1/2*c + 6*c**3 + 3 + 27/10*c**5 + r*c**2 + 27/4*c**4. Factor b(z).
(z + 1)*(3*z + 1)**3/2
Let p(k) = 3*k + 1. Let i be p(1). Determine d so that 4*d + 6 - 3*d**2 - 2 + i*d**2 = 0.
-2
Let k = -7 - -10. Factor 0*j + 0 + 2/5*j**k - 2/5*j**4 + 4/5*j**2.
-2*j**2*(j - 2)*(j + 1)/5
Let i(p) be the second derivative of -p**6/50 - 3*p**5/50 + p**3/5 + 3*p**2/10 + 4*p. Factor i(t).
-3*(t - 1)*(t + 1)**3/5
Let g be 7*((-110)/35)/(-11). Let p be (1 + 0)*6/21. Factor 0 + 4/7*d**3 - p*d + 2/7*d**g.
2*d*(d + 1)*(2*d - 1)/7
Let a be (-68)/(-22) - 86/946. Factor 2/3*b**a + 1/3 + 13/6*b**2 + 11/6*b.
(b + 1)*(b + 2)*(4*b + 1)/6
Suppose -8*r = 137 - 169. Find g, given that -17/3*g**3 - 5/3*g**r + 0 - 16/3*g**2 - 4/3*g = 0.
-2, -1, -2/5, 0
Let v = 1630/1227 + 2/409. Let n(p) be the first derivative of -8/3*p - 2/9*p**3 + 3 - v*p**2. Determine c so that n(c) = 0.
-2
Let m(p) be the third derivative of p**7/7560 - 7*p**4/24 - 2*p**2. Let a(j) be the second derivative of m(j). Let a(i) = 0. Calculate i.
0
Suppose 3*z - 2*z = 3*r - 6, 2*z = -r + 2. Let -2*b**2 + 0 + b + b**r + 2 = 0. Calculate b.
-1, 2
Suppose 0 = -3*u - 2*u + 35. Suppose -4*d = -5 - u, 3*d - 3 = 3*j. Factor -2*k - 18 + 2*k**3 + j*k**2 - 2*k**4 + 18.
-2*k*(k - 1)**2*(k + 1)
Suppose 5*h + 4*q = 32 + 32, -50 = -4*h - 2*q. Factor -3*f**2 + 2 + 5*f**3 - 5*f + 12*f + h*f**2 + f**4.
(f + 1)**3*(f + 2)
Suppose 4*q = -5*k + 7 + 14, -1 = q - 5*k. Factor -2*a**3 - 48*a**q + 48*a**4 + a + a**5.
a*(a - 1)**2*(a + 1)**2
Let r(g) be the third derivative of g**5/20 + g**4/4 - 3*g**3/2 - 4*g**2. Factor r(v).
3*(v - 1)*(v + 3)
Let i(o) be the third derivative of o**5/30 + o**2. Determine k, given that i(k) = 0.
0
Solve -6/5*d**3 - 1/5*d + 4/5*d**2 - 1/5*d**5 + 4/5*d**4 + 0 = 0 for d.
0, 1
Factor 1/4*g + 1/4*g**2 + 0 - 1/4*g**3 - 1/4*g**4.
-g*(g - 1)*(g + 1)**2/4
Let t be 26/6 - (-1)/(-3). Suppose 10 = -10*r + 50. Find z such that -z**r + t + z**3 + 13*z**5 - 14*z**5 + z**2 - 4 = 0.
-1, 0, 1
Suppose -4*v + 22 = -o, -18 = -2*v + o + 3*o. Suppose -v*f = -f. Let -2/3*z**4 - z**5 + 2/3*z**2 + f - 1/3*z + 4/3*z**3 = 0. What is z?
-1, 0, 1/3, 1
Let h(f) be the second derivative of f**5/50 - f**4/30 - f**3/3 - 3*f**2/5 + 21*f. Factor h(d).
2*(d - 3)*(d + 1)**2/5
What is m in -2320*m**5 + 2347*m**5 - 12*m**2 - 21*m**4 - 36*m**3 - 24*m**3 = 0?
-1, -2/9, 0, 2
Let l be (-3)/(-5 - 35/(-10)). Suppose 5/2*o**l + 2 - 1/2*o**3 - 4*o = 0. What is o?
1, 2
Let t = 13 + -5. Let r be (-2)/t - (-42)/8. Solve -j**4 + 6*j**3 - 6*j**3 + 3*j**r = 0.
0, 1/3
Let l(j) be the first derivative of j**6/240 - 3*j**5/80 + j**4/8 + 2*j**3/3 - 3. Let r(o) be the third derivative of l(o). Det