*4 - 8*s - 2*s**2 - 3*s**4 + 6*s**3. Let i(b) = -8*h(b) + t(b). Factor i(d).
2*d**2*(d - 1)*(d + 1)
Let h be -1 + -4 + -7*3/(-3). Suppose -1/6*g**4 + 0 + 0*g + 1/6*g**h + 1/6*g**3 - 1/6*g**5 = 0. What is g?
-1, 0, 1
Let b(r) be the first derivative of -11/3*r**3 + 11/2*r**2 - 2/3*r**6 + 2 - 7/4*r**4 + 13/5*r**5 - 2*r. Let b(x) = 0. Calculate x.
-1, 1/4, 1, 2
Let l(q) be the third derivative of q**7/1260 - q**6/240 + q**5/120 - q**4/144 - 10*q**2. Suppose l(b) = 0. Calculate b.
0, 1
Let m(j) = -j - 6*j + 6*j + 2*j + 4. Let s be m(4). Let o(i) = 11*i**2 - 6*i - 17. Let u(a) = 17*a**2 - 9*a - 26. Let p(n) = s*o(n) - 5*u(n). Factor p(g).
3*(g - 2)*(g + 1)
Let k(d) = -5*d**3 - 20*d + 25. Let g(h) = h**3 + h**2 + h - 1. Let y(v) = -25*g(v) - k(v). Let y(f) = 0. Calculate f.
-1, -1/4, 0
Suppose -2*s = -3*s + 3. Suppose -2 - 3 + s + q**2 - q = 0. Calculate q.
-1, 2
Let l(j) be the second derivative of -j**8/112 - j**7/35 - j**6/40 + 3*j**2/2 + 2*j. Let p(x) be the first derivative of l(x). Factor p(a).
-3*a**3*(a + 1)**2
Let 1/3*i + 2/9 - 5/9*i**2 = 0. What is i?
-2/5, 1
Let y(d) = d - 1. Suppose 3*k = 4*k - 4. Let n be y(k). Factor 0 + 0*w**n + 1/4*w - 1/2*w**4 + 1/2*w**2 - 1/4*w**5.
-w*(w - 1)*(w + 1)**3/4
Let x = -161/3 + 54. Factor -2/3 + 0*k**2 + x*k**3 - k.
(k - 2)*(k + 1)**2/3
Determine l, given that -4*l**4 - 96*l**5 + 8*l**3 - 94*l**5 + 186*l**5 = 0.
-2, 0, 1
What is c in -220/7*c**2 + 104/7*c - 88/7*c**4 - 16/7 + 206/7*c**3 + 2*c**5 = 0?
2/7, 1, 2
Let v(r) = r**2 + 2*r + 1. Let b(y) = -3*y**2 - 7*y - 4. Let w(k) = -6*b(k) - 21*v(k). Factor w(n).
-3*(n - 1)*(n + 1)
Let f = 10 - 4. Suppose 4*y**3 - f*y**3 - 4*y**4 - y**4 - 3*y**4 = 0. What is y?
-1/4, 0
Let l(o) be the third derivative of 1/16*o**4 + 0*o**5 - 3*o**2 + 0 - 1/240*o**6 + 1/6*o**3 + 0*o. Solve l(w) = 0 for w.
-1, 2
Let m(t) be the third derivative of -t**7/525 + t**6/50 - 13*t**5/150 + t**4/5 - 4*t**3/15 + 5*t**2. Solve m(c) = 0.
1, 2
Factor 6 - 8*d + 13*d**2 + 13*d**2 - 24*d**2.
2*(d - 3)*(d - 1)
Let l be -4 - 428/(-3 + -1). Solve -6*h**2 + 2*h**2 - 83*h - 16 + l*h = 0 for h.
1, 4
Let t(i) be the first derivative of 4*i**3/15 + 16*i**2/5 + 64*i/5 + 8. Factor t(c).
4*(c + 4)**2/5
Let q be (-5 + 6)*(1 - 1). Factor 1/4*v**3 + 0 + 1/4*v**4 + 0*v**2 + q*v.
v**3*(v + 1)/4
Suppose 0 = -3*r - 0*r. Factor r*t + 3*t**2 + 3*t**2 + 2*t.
2*t*(3*t + 1)
Let m(t) be the second derivative of -t**7/840 + t**6/160 - t**5/80 + t**4/96 - t**2 + 4*t. Let g(d) be the first derivative of m(d). Let g(a) = 0. Calculate a.
0, 1
Suppose -y = -1 - 2. Suppose 2*l = 3*l - y. Suppose -18*s**2 - 22*s**l - 13*s**4 - 7*s - 1 + 1 - 1 - 3*s**5 = 0. What is s?
-1, -1/3
Let y(g) = -g - 2. Let a be y(-4). Suppose 2*c**4 + 7*c - 4*c**3 + 2*c**5 - c**a - 5*c + 2 - c**2 - 2*c**2 = 0. What is c?
-1, 1
Let t(x) be the second derivative of -1/12*x**4 + 1/20*x**5 - 1/3*x**3 + 0 + 0*x**2 - 7*x. Factor t(j).
j*(j - 2)*(j + 1)
Suppose -3*j + 19 = d, -11 - 2 = 3*d - 5*j. Suppose 5*x**4 - 10*x**3 + 10*x - 13*x**d + 9*x**2 + 2 - 3*x**2 = 0. What is x?
-1, -1/4, 1
Let c(j) be the first derivative of 5*j**4/4 - 15*j**3 + 135*j**2/2 - 135*j + 1. Factor c(d).
5*(d - 3)**3
Let g = 1014/5 + -201. Find n such that -3/5*n**2 + g*n - 6/5 = 0.
1, 2
Suppose 0 = 2*s + 4*l - 14, -2*s = 5*l - 0*l - 16. Let f(z) be the first derivative of -15*z**2 - 1 + 4*z + 56/3*z**s. Factor f(j).
2*(4*j - 1)*(7*j - 2)
Let a be (-1)/(-17)*1/3. Let c = a + 11/17. Factor 0*o + 2/3*o**4 - c*o**2 + 0 + 0*o**3.
2*o**2*(o - 1)*(o + 1)/3
Suppose 6*g - 6 - 12 = 0. Factor 0*b - 3/5*b**2 + 0 + 3/5*b**g.
3*b**2*(b - 1)/5
Let k(y) be the first derivative of 2*y**6/15 - y**5/10 - y**4/3 + y**3/3 - 2*y - 2. Let v(z) be the first derivative of k(z). Solve v(h) = 0.
-1, 0, 1/2, 1
Let z be ((-1)/16)/((-3)/(-36)*-2). Factor -3/8*f**3 + 3/8*f - z*f**2 + 0 + 3/8*f**4.
3*f*(f - 1)**2*(f + 1)/8
Let v(s) be the first derivative of s**7/756 + s**6/540 - s**5/270 - 8*s**3/3 + 2. Let z(q) be the third derivative of v(q). Find r such that z(r) = 0.
-1, 0, 2/5
Suppose 7*n**2 - 4*n**2 + 33*n - 2 + n**3 - n**4 - 34*n = 0. Calculate n.
-1, 1, 2
Let u(b) be the first derivative of -b**3 - 9*b**2/2 - 6*b + 20. Suppose u(a) = 0. Calculate a.
-2, -1
Suppose -u + 9 + 5 = 0. Suppose -5*j + 6 = -u, -3*x - 4*j = -25. Factor 2*o**2 + 6 - 2*o**x - 6.
-2*o**2*(o - 1)
Let p(i) be the third derivative of i**5/30 - i**4/9 + i**3/9 - 4*i**2. Suppose p(o) = 0. What is o?
1/3, 1
Let h(p) = p**3 - 2*p**2 - 3*p - 4. Let b be h(3). Let i = b + 7. Solve -i + 0 - z + 5 - z**2 = 0 for z.
-2, 1
Let m(w) be the first derivative of -w**6/27 - 2*w**5/45 + w**4/18 + 2*w**3/27 + 11. Factor m(x).
-2*x**2*(x - 1)*(x + 1)**2/9
Let a(n) = 5*n**2 + 5. Let s(b) = b**3 - 4*b**2 + b - 6. Let w(c) = -6*a(c) - 5*s(c). Factor w(g).
-5*g*(g + 1)**2
Factor -u**3 + u - 1/3*u**4 + 5/3*u**2 - 4/3.
-(u - 1)**2*(u + 1)*(u + 4)/3
Let q(x) be the first derivative of -3*x**4/16 + 5*x**3/12 - x**2/8 - x/4 + 2. Factor q(u).
-(u - 1)**2*(3*u + 1)/4
Let s(t) = t + 8. Let b be s(-6). Let k be (1 - 1) + 0 + b. Factor -4 - k*i**2 + 3 + 3*i**2.
(i - 1)*(i + 1)
Let s = -4 - -4. Suppose 5*v - 2*j - 35 + 11 = s, 5*v + 5*j - 10 = 0. Find g such that -1 - v*g - 1 - 3*g**2 + 6 = 0.
-2, 2/3
Let u(o) = -2*o - 6. Let y be u(-7). Let b = y + -4. Determine g, given that -3*g**3 - 2*g**2 - 2 + 2*g**2 + b*g**2 + 5*g = 0.
-1, 1/3, 2
Suppose 12 = -4*y + 28. Factor g**5 - 2*g**3 + 5*g**3 + 2*g**4 + g**2 + g**y.
g**2*(g + 1)**3
Let h(p) be the second derivative of -1/4*p**4 + 1/5*p**5 + 0 - 1/6*p**3 + 0*p**2 + 4*p. Determine c, given that h(c) = 0.
-1/4, 0, 1
Let p = -2 + 4. Let q(i) = -i**3 - 6*i**2 - 5*i + 4. Let w be q(-5). Factor -6*x + 0 + 2*x**p + w + 0*x**2.
2*(x - 2)*(x - 1)
Let a = 10 - 5. Let 3 + a + 3*x - 3 - 3 + x**2 = 0. What is x?
-2, -1
Let l = -21713/42 + 517. Let c(k) be the second derivative of -1/7*k**2 + 0 - k + l*k**4 + 0*k**3. Solve c(p) = 0.
-1, 1
Suppose -n = n - 4. Suppose -3*f**n - 8*f + 7*f**2 + 6*f**2 + 2 - 4*f**3 = 0. Calculate f.
1/2, 1
Let o = -21 - -30. Suppose 3*l - 3 = 3. Determine f so that f + f - 4*f + o*f**l = 0.
0, 2/9
Let n be (-3)/6*90/(-3). Let x(y) be the first derivative of -7*y**4 - 49/5*y**5 + 2 + n*y**3 + 4*y + 14*y**2. Factor x(b).
-(b - 1)*(b + 1)*(7*b + 2)**2
Let a(y) = -3*y**3 + 15*y**2 + 9*y - 9. Let c(l) = l**3 - 7*l**2 - 4*l + 4. Let s(p) = 4*a(p) + 9*c(p). Factor s(q).
-3*q**2*(q + 1)
Suppose 3*b = 8*b - 10. Let c(h) be the second derivative of 1/24*h**4 - 1/4*h**3 + 0 + 1/2*h**b + 2*h. Factor c(d).
(d - 2)*(d - 1)/2
Let s(l) be the second derivative of -1/10*l**6 + 3*l + 0 + 0*l**2 + 0*l**3 + 1/12*l**4 + 1/10*l**5. Determine c so that s(c) = 0.
-1/3, 0, 1
Let d(r) = -r**2 + r + 7. Let u be d(3). Let l(o) be the first derivative of -u + 1/2*o**2 + 1/4*o**4 + 0*o - 2/3*o**3. Factor l(k).
k*(k - 1)**2
What is b in 3/4*b - 9/4*b**2 + 1/2 = 0?
-1/3, 2/3
Let o(n) be the second derivative of n**4/54 + n**3/27 + 7*n. Factor o(r).
2*r*(r + 1)/9
Let d be (1 + -1 + 2)*93/1023. Factor -2/11*n**2 + 0 - d*n**3 + 2/11*n + 2/11*n**4.
2*n*(n - 1)**2*(n + 1)/11
Let j(y) be the second derivative of -y**6/540 + y**5/180 + y**4/18 - y**3/2 - 5*y. Let s(h) be the second derivative of j(h). Suppose s(r) = 0. What is r?
-1, 2
Let c(f) be the second derivative of -5*f**5/8 + 5*f**4/24 + 25*f**3/12 - 5*f**2/4 + 10*f. Factor c(l).
-5*(l - 1)*(l + 1)*(5*l - 1)/2
Let n(k) be the third derivative of -k**8/448 - k**7/280 + 3*k**6/160 + k**5/16 + k**4/16 + 17*k**2. Factor n(b).
-3*b*(b - 2)*(b + 1)**3/4
Find v, given that 1/4*v**2 + 1 + 2*v - 1/4*v**4 + 1/4*v**5 - 5/4*v**3 = 0.
-1, 2
Let l be 3 + (-4)/(-1 - 1). Let n = -376/55 - -84/11. Let 2/5 + n*w**2 - 6/5*w - 6/5*w**4 + 2/5*w**l + 4/5*w**3 = 0. What is w?
-1, 1
Let i(v) be the first derivative of 2*v**4/7 + 2*v**3/7 - 9*v**2/7 + 4*v/7 + 3. Factor i(z).
2*(z - 1)*(z + 2)*(4*z - 1)/7
Suppose 29 = 3*x - 5*j, -5*j + j - 10 = 2*x. Let y = 33/161 + 94503/805. Factor 16/5 - 686/5*g**x + y*g**2 - 168/5*g.
-2*(7*g - 2)**3/5
What is k in -1/3*k**3 + 4/3*k + 1/3*k**2 - 4/3 = 0?
-2, 1, 2
Suppose 3*l**2 + 2*l**3 + 7*l + l**2 - 5*l = 0. Calculate l.
-1, 0
Determine f, given that -2*f**3 - 2*f**5 + 3*f - 4*f**3 + 0*f**3 + 5*f**5 = 0.
-1, 0, 1
Let g(o) be the second derivative of -4/11*o**2 + o - 5