
Let m(h) = -9*h**2 - 3*h + 12. Let q(c) = 19*c**2 + 6*c - 25. Let t(o) = 13*m(o) + 6*q(o). Factor t(k).
-3*(k - 1)*(k + 2)
Suppose 0 = s + 3*s. Suppose 2*d - 7*d = s. Solve d*f + 2*f**2 - 2*f - 3 - 1 = 0 for f.
-1, 2
Let r(v) be the third derivative of 0*v + 1/96*v**4 - 2*v**2 + 0*v**3 + 1/480*v**6 + 0 - 1/120*v**5. Let r(u) = 0. What is u?
0, 1
Let z(d) = 5*d**3 + 27*d**2 + 40*d + 20. Let u(s) = 10*s**3 + 55*s**2 + 80*s + 40. Let k(r) = -2*u(r) + 5*z(r). Factor k(o).
5*(o + 1)*(o + 2)**2
Let i = 19/6 - 5/2. Let b(t) be the first derivative of 0*t + 0*t**2 + 1/4*t**4 - 1/5*t**5 + i*t**3 - 2. Solve b(y) = 0 for y.
-1, 0, 2
Suppose 4*t = 4*y - 4, -2*t - 3*t + 19 = 3*y. Let a = 1461/5 + -291. Factor -2/5 - 2/5*x**y - a*x**2 - 6/5*x.
-2*(x + 1)**3/5
Determine s so that 72*s - 96 + 3/2*s**3 - 18*s**2 = 0.
4
Let v be (-2 - -1)*1/(-2). Let y(q) = 10*q + 75. Let h be y(-7). Let -1/2 + g**3 - 1/2*g + g**2 - 1/2*g**h - v*g**4 = 0. What is g?
-1, 1
Let f(y) be the first derivative of -2*y**5/45 - y**4/18 + 4*y**3/27 + 4. Find g, given that f(g) = 0.
-2, 0, 1
Let b(h) be the first derivative of h**3/15 - 3*h**2/10 + 2*h/5 - 1. What is n in b(n) = 0?
1, 2
Determine n, given that 12/5*n**3 - 3*n**2 + 0 + 3/5*n = 0.
0, 1/4, 1
Let v(u) be the second derivative of -1/80*u**5 + 0*u**4 + 0*u**2 + 0*u**6 + 2*u + 0*u**3 + 1/168*u**7 + 0. Determine d so that v(d) = 0.
-1, 0, 1
Determine z so that -3*z**3 - 10*z + 36 - 5*z**4 + 13*z**3 + 5*z**2 - 36 = 0.
-1, 0, 1, 2
Let q(h) be the first derivative of 4*h**3/15 + 4*h**2/5 - 12*h/5 + 6. Factor q(v).
4*(v - 1)*(v + 3)/5
Suppose 2*y + 4 = f, -4*f + 5*y + 10 = -6. Let b(g) be the second derivative of -1/6*g**5 + 0 - 1/15*g**6 + 1/9*g**3 - 1/18*g**f + g + 0*g**2. Factor b(w).
-2*w*(w + 1)**2*(3*w - 1)/3
Let u(v) be the second derivative of v**9/12600 + v**8/2400 + v**7/3150 + v**4/2 - 6*v. Let h(k) be the third derivative of u(k). Factor h(i).
2*i**2*(i + 2)*(3*i + 1)/5
Let p(k) = -k**5 - 2*k**4 - 2*k**3 - k. Let v(j) = -2*j**5 - 2*j**4 - 3*j**3 - j**2 - j. Let s(g) = 3*p(g) - 2*v(g). Find u such that s(u) = 0.
-1, 0, 1
Let x(a) = -2*a + 64. Let n be x(30). Determine j so that -4/9*j**2 + 4/9*j**3 + 2/9 + 2/9*j**n - 2/9*j - 2/9*j**5 = 0.
-1, 1
Let r(p) be the third derivative of -p**8/30240 + p**7/7560 + p**5/60 + 2*p**2. Let b(y) be the third derivative of r(y). Factor b(m).
-2*m*(m - 1)/3
Let q be 20/190 - (-180)/95. Factor 2/7*y**3 + 18/7 + 6/7*y - 10/7*y**q.
2*(y - 3)**2*(y + 1)/7
Let m(o) = 2*o**2 + 2*o - 10. Let a(v) = -3*v**2 - 3*v + 10. Let s(n) = -3*a(n) - 2*m(n). Suppose s(b) = 0. Calculate b.
-2, 1
Let g = 36 - 33. Let s(p) be the second derivative of 1/3*p**g - 2/3*p**4 - 3/20*p**6 + 0*p**2 + 21/40*p**5 + 0 + p. Factor s(v).
-v*(v - 1)*(3*v - 2)**2/2
Let d(x) be the third derivative of -16*x**7/105 + 2*x**6/15 + x**5/2 - 3*x**4/4 + 11*x**2. Suppose d(v) = 0. What is v?
-1, 0, 3/4
Let w be (6/15)/((-1)/(-5)). Determine b so that 4*b**4 + 2*b**2 + 4*b**4 + 8*b**3 + 10*b**w + 8*b - 6*b**4 + 2 = 0.
-1
Let f(w) be the first derivative of 0*w**3 + 1/6*w - 1/12*w**4 - 1/30*w**5 + 1/6*w**2 - 10. Factor f(y).
-(y - 1)*(y + 1)**3/6
Let v(r) be the third derivative of 0*r**4 + 1/60*r**6 + 0 + 0*r**3 + 0*r + 0*r**5 - r**2. Solve v(j) = 0.
0
Let d = -605/3 + 203. Factor 0*s + d*s**5 + 0*s**2 + 1/3*s**3 + 0 - 4/3*s**4.
s**3*(2*s - 1)**2/3
Let w = 76 - 74. Let z(q) be the second derivative of 0 + 2*q - 1/50*q**5 + 0*q**w + 0*q**3 + 1/30*q**4. Solve z(k) = 0 for k.
0, 1
Suppose x = -5*h + 10, -5*h + 0 = -x - 10. Let b(c) be the first derivative of 0*c**3 + 2/5*c**5 + 1/4*c**4 + 0*c + 1/6*c**6 + 2 + x*c**2. Solve b(y) = 0.
-1, 0
Suppose 0 = 5*u - 0*u - 10. Factor -2*r**2 - 2*r**2 - 2 + 6*r**u.
2*(r - 1)*(r + 1)
Let -v + 3 + 0*v**3 + 2*v**2 + v**3 - 4*v**2 - 1 = 0. What is v?
-1, 1, 2
Suppose 0*v - 3*v = 0. Let x(s) be the second derivative of -2*s + 1/9*s**4 + 0*s**3 + 0*s**2 + 1/30*s**5 + v. Factor x(g).
2*g**2*(g + 2)/3
Let r(w) be the first derivative of w**6/150 - 9*w**5/200 + w**4/20 + w**3/3 + 6. Let f(h) be the third derivative of r(h). Factor f(m).
3*(m - 2)*(4*m - 1)/5
Let q(d) = -d + 14. Let b be q(6). Let m = b - 5. Factor o**2 + 6*o**3 - o - m*o**3 + o**2.
o*(o + 1)*(3*o - 1)
Let q(z) be the second derivative of 4*z**6/75 + 13*z**5/30 + 11*z**4/18 - 10*z**3/9 + 8*z**2/15 - 18*z. Determine g so that q(g) = 0.
-4, -2, 1/4, 1/3
Let m(a) be the second derivative of a**7/273 + a**6/65 + a**5/65 - 4*a. Factor m(d).
2*d**3*(d + 1)*(d + 2)/13
Factor 0*o**2 + 2/5*o**5 + 0*o + 4/5*o**4 + 0 + 2/5*o**3.
2*o**3*(o + 1)**2/5
Let t = -8 + 18. Suppose -4*q = -g - t, 0 = -0*g + 4*g + 2*q - 14. Factor -1/2*p**3 + 0 + 0*p + p**g.
-p**2*(p - 2)/2
Suppose 4*w - 4 = 8. Let q(i) be the second derivative of -2*i - 11/30*i**5 - 16/189*i**7 + 0 - 1/27*i**w + 0*i**2 - 8/27*i**6 - 5/27*i**4. Factor q(x).
-2*x*(x + 1)**2*(4*x + 1)**2/9
Factor 2/9*n**2 - 8/9*n + 2/3.
2*(n - 3)*(n - 1)/9
Factor 3/7*l**2 - 3/7*l + 2/7*l**3 - 2/7.
(l - 1)*(l + 2)*(2*l + 1)/7
Let l = -77 + 77. Let a(p) be the third derivative of -3*p**2 - 1/3*p**3 + 0*p**4 + l + 1/30*p**5 + 0*p. Factor a(m).
2*(m - 1)*(m + 1)
Let l be (-6)/144*-68 + 6/(-3). Let k(u) be the second derivative of 0*u**2 + 0 - 1/15*u**6 + 2/5*u**5 + 2/3*u**3 - l*u**4 + 2*u. Factor k(i).
-2*i*(i - 2)*(i - 1)**2
Suppose 1 = 2*n - 3. Factor n*z**2 + 0*z**2 + 15*z - 19*z.
2*z*(z - 2)
Let a(x) be the third derivative of x**5/60 - 7*x**4/24 + x**3/3 + 2*x**2. Let c be a(7). Factor 8/5 + c*w**2 - 16/5*w - 2/5*w**3.
-2*(w - 2)**2*(w - 1)/5
Let s(i) be the second derivative of 75*i**4/22 + 20*i**3/11 + 4*i**2/11 - 35*i. Solve s(m) = 0.
-2/15
Suppose 0*j + j - 2 = i, -26 = -2*i - 4*j. Suppose 0 = -4*p + i*p. Let 0*x + 0 - 6/5*x**5 + 2/5*x**4 + 4/5*x**3 + p*x**2 = 0. What is x?
-2/3, 0, 1
Let d = -2 + 5. Suppose -2*g - 1 = -3*s, 5*s - 4 - 19 = -2*g. Find c such that -d + c**4 - c**2 + s = 0.
-1, 0, 1
Let t(s) be the first derivative of 0*s + 0*s**2 - s**3 - 1 - 21/8*s**4 - 3/2*s**5. Factor t(r).
-3*r**2*(r + 1)*(5*r + 2)/2
Let j(d) = -d**2 - d. Let x be j(0). Suppose 5*r = -2*o + 12, 4*r = -4*o + 5 + 7. Factor -2/7 + 2/7*k**r + x*k.
2*(k - 1)*(k + 1)/7
Determine l so that -l + 46*l**4 + l + 36*l**2 - 42*l**4 - 24*l**3 = 0.
0, 3
Let h(n) = -n**2 + 5*n + 20. Let f(q) = -q**2 - q - 1. Let r(s) = -2*f(s) - h(s). Factor r(b).
3*(b - 3)*(b + 2)
Let p(c) be the first derivative of -3*c**5/20 - 3*c**4/16 + c**3/4 + 3*c**2/8 - 7. Factor p(s).
-3*s*(s - 1)*(s + 1)**2/4
Solve -6*u + 3 - 3*u**2 - 12 - u**2 + 3*u**2 = 0 for u.
-3
Let k(d) be the first derivative of -d**6/420 - d**5/70 - d**4/42 - d**2 - 1. Let f(r) be the second derivative of k(r). Factor f(i).
-2*i*(i + 1)*(i + 2)/7
Let o(h) be the second derivative of -40/3*h**4 - 4*h**6 + 10*h**3 - 4*h**2 + 0 + 10*h**5 - 4*h + 2/3*h**7. Suppose o(y) = 0. What is y?
2/7, 1
Let h(k) be the third derivative of -k**9/1008 - k**8/280 + 2*k**3/3 - 2*k**2. Let d(i) be the first derivative of h(i). Suppose d(n) = 0. Calculate n.
-2, 0
Let b(m) be the second derivative of 1/6*m**4 + 0 + 0*m**2 - m - 1/3*m**3. Suppose b(r) = 0. What is r?
0, 1
Let c = 21 - 21. Let t(b) be the first derivative of 2/27*b**3 + 2 + c*b + 1/9*b**4 + 2/45*b**5 + 0*b**2. Determine s so that t(s) = 0.
-1, 0
Find q, given that -4/5*q + 0 + 6/5*q**2 = 0.
0, 2/3
Let s(v) be the third derivative of -v**6/360 - v**5/60 - v**3/3 + v**2. Let j(x) be the first derivative of s(x). Find w, given that j(w) = 0.
-2, 0
Suppose -4 = 2*u - 3*r - 13, -4*u - 3*r = -9. Let f(a) be the first derivative of -2/9*a + 2/27*a**u + 0*a**2 + 3. Factor f(k).
2*(k - 1)*(k + 1)/9
Let k(p) be the third derivative of -p**6/600 + 17*p**2. Factor k(a).
-a**3/5
Let 11/8*v**3 - 1 - 3/2*v + 3/8*v**4 + 3/4*v**2 = 0. Calculate v.
-2, -2/3, 1
Let p(w) = -w**4 + 7*w**3 + 9*w**2 + w + 2. Let l(b) = 2 + 6*b**3 - 4*b**4 + 2*b**4 + b**4 + 8*b**2 + 0*b**3. Let g(u) = -6*l(u) + 5*p(u). Factor g(n).
(n - 1)**3*(n + 2)
Factor -1 + 3 - 5*b**2 + 3*b**2.
-2*(b - 1)*(b + 1)
Let w = 187/3 - 62. Let 1/3*b**5 + 0*b + 1/3*b**2 - w*b**4 - 1/3*b**3 + 0 = 0. What is b?
-1, 0, 1
Let i(p) be the second derivative of -p**9/27216 + p**7/3780 - p**5/1080 + p**3/2 - 9*p. Let h(a) be the second derivative of i(a). Factor h(c).
-c*(c - 1)**2*(c + 1)**2/9
Let a = 10 