1, 1
Let d(h) be the second derivative of 1/5*h**5 + 0 + 5/12*h**4 + 1/3*h**3 + 1/30*h**6 - 6*h + 0*h**2. Determine g, given that d(g) = 0.
-2, -1, 0
Let h = -99 + 102. Solve 0 + y - 1/2*y**h + 1/2*y**2 = 0.
-1, 0, 2
Let l(c) be the third derivative of c**7/1400 - c**6/300 + c**5/200 - c**3/6 - 2*c**2. Let b(p) be the first derivative of l(p). Find u such that b(u) = 0.
0, 1
Let d(k) be the second derivative of -k**5/50 - 3*k**4/10 - 9*k**3/5 - 27*k**2/5 - 3*k. Solve d(z) = 0 for z.
-3
Let x = 22 + -19. Determine m, given that 2*m**5 + m**4 - 2*m**3 - m**5 - 3*m**4 + x*m**4 = 0.
-2, 0, 1
Suppose 4*l = 5*p, 0 = -5*p + 8*p - 4*l. Suppose -11/4*x**4 + 0 - 3/4*x**5 - 3*x**3 + p*x - x**2 = 0. What is x?
-2, -1, -2/3, 0
Suppose 2*b - 5 = -1. Let t(l) = l**2 - 4*l - 2. Let c(o) = 6*o**2 - 20*o - 9. Let h(f) = b*c(f) - 11*t(f). What is y in h(y) = 0?
-2
Let j(l) be the third derivative of 0 + 1/90*l**5 + 0*l + 0*l**3 + 3*l**2 + 1/36*l**4. Factor j(i).
2*i*(i + 1)/3
Let v(t) be the first derivative of -t**5/5 + 3*t**4/4 - t**3/3 - 3*t**2/2 + 2*t - 11. Factor v(l).
-(l - 2)*(l - 1)**2*(l + 1)
Let c(x) be the third derivative of x**7/210 + x**6/60 + x**5/60 + 3*x**2. Factor c(o).
o**2*(o + 1)**2
Let j be (-58 - -62)*(-6)/(-8). Suppose 9/5 - h**2 + 3/5*h + 1/5*h**j = 0. What is h?
-1, 3
Let p be ((-2)/30)/(-1 + 4/5). Factor -p*h + 0 + 1/3*h**2.
h*(h - 1)/3
Let z = -2/109 + 331/218. Let t(c) be the first derivative of 75/8*c**4 + 1 + 33/4*c**2 - z*c - 35/2*c**3. Suppose t(b) = 0. What is b?
1/5, 1
Let r(i) be the third derivative of 1/30*i**5 - 1/180*i**6 + 0*i - 2*i**2 - 1/12*i**4 - 1/2*i**3 + 0. Let x(n) be the first derivative of r(n). Factor x(k).
-2*(k - 1)**2
Let u(d) be the third derivative of d**7/3780 + d**6/1620 - d**3/2 - 2*d**2. Let s(z) be the first derivative of u(z). Determine y, given that s(y) = 0.
-1, 0
Suppose 1 = -4*t - 0*n + 3*n, 0 = 3*n - 9. Let u(b) be the second derivative of 1/15*b**6 + 3*b + 0 + b**t + 0*b**5 + 0*b**3 - 1/3*b**4. Solve u(a) = 0.
-1, 1
Let a be (8/6 - 2)*18. Let w be 2/6 - (-1)/a. Factor -1/4 + 0*j + w*j**2.
(j - 1)*(j + 1)/4
Let m(n) = -7*n**3 + 3*n**2 - 8*n - 6. Let f = 14 + -8. Let l(y) = -8*y**3 + 3*y**2 - 9*y - 7. Let r(k) = f*l(k) - 7*m(k). Factor r(w).
w*(w - 2)*(w - 1)
Solve 0*f**2 - 11*f**3 + 9*f**5 + 5*f**2 + 10*f - 5*f**4 - 4*f**3 - 4*f**5 = 0.
-1, 0, 1, 2
Let u(h) be the second derivative of 0 + 0*h**2 - 1/42*h**4 + 3*h + 0*h**3 + 1/147*h**7 + 1/105*h**6 - 1/70*h**5. Factor u(x).
2*x**2*(x - 1)*(x + 1)**2/7
Determine c so that 0*c - 1/2*c**2 + 1/2 = 0.
-1, 1
Let h(d) = d**3 - 10*d**2 - 8*d - 15. Let w be h(11). Let v be (-2)/(-7) + w/35. Determine j so that 6/5*j - 2/5*j**2 - v = 0.
1, 2
Find z such that -4/9*z**2 - 2/9*z - 2/9*z**5 + 2/9*z**4 + 4/9*z**3 + 2/9 = 0.
-1, 1
Let t(j) = -j**4 + j**3 - j - 1. Suppose -5*f = -2*f + 9. Let q(o) = 6*o**4 - 8*o**3 + 7*o + 7. Let m(b) = f*q(b) - 21*t(b). Find g such that m(g) = 0.
-1, 0
Let o be (-9)/6*56/(-21). Let n be ((-6)/16)/((-9)/o). Factor -n*h**2 + 1/6*h + 0.
-h*(h - 1)/6
Let f(p) be the first derivative of 1/21*p**6 + 3/14*p**4 - 2/21*p**3 + 0*p + 1 + 0*p**2 - 6/35*p**5. Solve f(c) = 0.
0, 1
Suppose 4 + 2 = 3*t. Factor -16*h**3 + 26*h**4 - 16*h - 72*h**t + 24*h**4 - 44*h**3.
2*h*(h - 2)*(5*h + 2)**2
Let m(y) = -y**2 - 4*y - 1. Let u(n) = n**2 - n. Let d be u(-1). Let x = d + -4. Let v(q) = 3*q**2 + 9*q + 3. Let z(p) = x*v(p) - 5*m(p). Solve z(i) = 0 for i.
1
Let c(b) = b**2 - 20*b + 25. Let o(x) = x**2 - 41*x + 49. Let v(l) = -5*c(l) + 2*o(l). Find d, given that v(d) = 0.
3
Let i(w) = -w**3 - 2*w**2 + w - 2. Let m(c) = c**3 + 3*c**2 - c + 3. Let k(g) = -3*i(g) - 2*m(g). Factor k(r).
r*(r - 1)*(r + 1)
Suppose -1 = -t + j, -5*t + 13 = -2*j + 5*j. Find z such that 247/4*z**4 + 17*z**2 - t*z - 105/4*z**5 - 101/2*z**3 + 0 = 0.
0, 2/7, 2/5, 2/3, 1
Let f(o) be the first derivative of 2/5*o + 4 - 2/5*o**2 + 2/15*o**3. Let f(u) = 0. What is u?
1
Suppose 3*y - 8 = 4, 3*s + 11 = 2*y. Let i be (-4 - -1)/(s - 0). Suppose 0 - 3/2*j**2 - 3/4*j - 3/4*j**i = 0. Calculate j.
-1, 0
Find t such that -1/5*t**5 + 3/5*t**4 - 3/5*t**3 + 0 + 0*t + 1/5*t**2 = 0.
0, 1
Factor -v - 12*v + 6*v**2 - 2*v + 4*v - 2.
(v - 2)*(6*v + 1)
Suppose 3*t - 6 = 4*t. Let p(k) = -23*k**4 + 6*k**3 + 35*k**2 - 47*k - 5. Let n(w) = 4*w**4 - w**3 - 6*w**2 + 8*w + 1. Let r(g) = t*p(g) - 34*n(g). Factor r(d).
2*(d - 1)**3*(d + 2)
Let r(c) be the third derivative of 0 + 1/90*c**6 - 4*c**2 + 2/9*c**3 + 0*c + 7/36*c**4 + 7/90*c**5. Factor r(x).
2*(x + 1)*(x + 2)*(2*x + 1)/3
Let x be 42/90 + (-1)/3. Let n(l) be the first derivative of 0*l**2 - 8/27*l**3 + x*l**5 + 2 + 0*l + 1/3*l**6 - 4/9*l**4. Find i, given that n(i) = 0.
-2/3, 0, 1
Let s(a) = -a**3 - 1. Let g(q) = 3*q**4 + 10*q**3 + 12*q**2 - 2. Let i(b) = -g(b) + 2*s(b). Solve i(l) = 0.
-2, 0
Let f(d) be the third derivative of d**5/360 + d**4/72 + d**3/36 + 6*d**2. Factor f(p).
(p + 1)**2/6
Let g be 0/((-4 - -3)*3). Let d(p) be the second derivative of 0*p**3 + 1/10*p**5 + 0*p**4 + g*p**2 + 0 + 2*p. Determine r, given that d(r) = 0.
0
Let c be (-3 + 5)*2/4. Suppose 4*q + c = 9. Find y, given that -3*y + 3*y - 2*y**q + 2*y**4 = 0.
-1, 0, 1
Let -12/5*l**3 - 8/5*l**2 + 0 - 2/5*l - 2/5*l**5 - 8/5*l**4 = 0. Calculate l.
-1, 0
Let j(v) be the third derivative of v**6/160 + 11*v**5/240 + v**4/8 + v**3/6 + 8*v**2. Factor j(z).
(z + 1)*(z + 2)*(3*z + 2)/4
Let g be (-5 - (-16)/3) + 1. Factor g*v - 2/3*v**2 + 0.
-2*v*(v - 2)/3
Let o(s) be the second derivative of s**8/14280 + s**7/1428 + 2*s**6/765 + s**5/255 - 4*s**3/3 - 8*s. Let y(f) be the second derivative of o(f). Factor y(r).
2*r*(r + 1)*(r + 2)**2/17
Let t = -2/113 - -236/565. Let n(d) be the first derivative of -1/10*d**4 + 0*d + 1/5*d**2 + t*d**3 - 6/25*d**5 - 3. Solve n(m) = 0.
-1, -1/3, 0, 1
Let k be 1/20*-5 + 13/36. Factor 0 + 2/9*h**2 + 0*h + k*h**3.
h**2*(h + 2)/9
Let n(w) be the first derivative of -w**5/40 + w**3/12 + 3*w - 2. Let u(l) be the first derivative of n(l). Factor u(i).
-i*(i - 1)*(i + 1)/2
Factor -64 - 15*a**2 + 23*a**2 - 12*a**2 - 68*a.
-4*(a + 1)*(a + 16)
Let y(f) be the first derivative of -f**5 - 3*f**4/4 + 2*f**3/3 - 3. Solve y(x) = 0 for x.
-1, 0, 2/5
Let u = -4 - -24. Suppose -2*r + 10 = -f - 0*r, 0 = f - 4*r + u. Determine z, given that 2/3*z + f - 4/3*z**2 - 2*z**3 = 0.
-1, 0, 1/3
Let f = -28 - -31. Factor -u**2 + 22*u - 6*u - 19 + 3 - f*u**2.
-4*(u - 2)**2
Let h be ((-6)/(-63))/((16/(-12))/(-4)). Find f such that 4/7*f - 2/7*f**2 - h = 0.
1
Let g(b) be the third derivative of -b**6/180 + b**5/18 - 7*b**4/36 + b**3/3 - 37*b**2. Factor g(c).
-2*(c - 3)*(c - 1)**2/3
Determine h, given that 0*h + 0 + 10/3*h**3 + 2/3*h**4 + 2*h**2 - 2/3*h**5 = 0.
-1, 0, 3
Let a(m) = -m**5 + m**4 + m**3 + m**2 - m - 1. Let k(u) = -3*u**5 + 21*u**4 + 55*u**3 + 81*u**2 + 51*u + 11. Let p(y) = -5*a(y) + k(y). Factor p(g).
2*(g + 1)**2*(g + 2)**3
Let g = -1/4 - -3/4. Let r(m) be the second derivative of -1/6*m**3 - 3*m + 0 - g*m**2 - 1/48*m**4. Factor r(n).
-(n + 2)**2/4
Let 2/5*y**2 + 10 - 4*y = 0. What is y?
5
Let w(p) = 4*p**3 - 92*p**2 + 208*p - 90. Let c(d) = -d**3 - d**2 + 1. Let z(a) = 6*c(a) - w(a). Factor z(o).
-2*(o - 4)**2*(5*o - 3)
Let d(f) be the second derivative of -3*f**5/5 + f**4 - f**3/2 + f. What is k in d(k) = 0?
0, 1/2
Let a(y) be the second derivative of 8*y**7/21 - 14*y**6/15 + 2*y**5/5 + y**4/3 + 6*y. Factor a(l).
4*l**2*(l - 1)**2*(4*l + 1)
Let r(z) be the second derivative of -1/10*z**5 - 4*z + 0*z**4 + 0*z**3 + 0*z**2 + 0 + 2/15*z**6 - 1/21*z**7. Factor r(k).
-2*k**3*(k - 1)**2
Factor 0*k**4 + 1/2*k**2 - 3/4*k**3 + 1/4*k**5 + 0*k + 0.
k**2*(k - 1)**2*(k + 2)/4
Let m = 214 + -1494/7. Suppose -2/7 + 0*c**3 - 2/7*c**4 + m*c**2 + 0*c = 0. Calculate c.
-1, 1
Let d(a) be the second derivative of -a**5/14 - a**4/2 - 4*a**3/21 + a. Factor d(q).
-2*q*(q + 4)*(5*q + 1)/7
Let z(r) be the second derivative of r**7/1680 + r**6/240 - r**5/240 - r**4/16 - 5*r**3/6 + r. Let c(j) be the second derivative of z(j). Factor c(w).
(w - 1)*(w + 1)*(w + 3)/2
Solve -6*n - 3 - n**2 + 4 - 2*n**2 - 4 = 0.
-1
Let x = -146/35 + 32/7. Let w(o) be the first derivative of 0*o + 1/3*o**6 + 0*o**4 - x*o**5 + 0*o**3 + 0*o**2 - 3. Find t such that w(t) = 0.
0, 1
Factor -8/7*o - 4/7*o**2 + 0.
-4*o*(o + 2)/7
Le