 be the first derivative of 2*t**6/3 - t**4 + 11. Factor c(q).
4*q**3*(q - 1)*(q + 1)
Suppose -3*f = 5*k, 4*f = -f - k. Suppose -8 = -2*j - f*j. Find o, given that -2*o**5 + 0*o**5 - 6*o**2 + 0*o**3 + 6*o**4 - 2*o**3 + j*o = 0.
-1, 0, 1, 2
Let l be ((-8)/(-4) - 1)/((-3)/(-2)). Let m(s) = -s**3 - s**2. Let p be m(-1). Factor p*q**4 + 0 + l*q**3 - 1/3*q - 1/3*q**5 + 0*q**2.
-q*(q - 1)**2*(q + 1)**2/3
Factor -3/4*f**3 + 0 - 3/4*f**2 + 0*f.
-3*f**2*(f + 1)/4
Let t(y) = -y**3 - y + 8. Let f be t(0). Determine s, given that -4*s**2 - 5*s**2 + f*s**2 + 2*s - 3*s = 0.
-1, 0
Let y(r) be the second derivative of 7*r**5/10 - r**4/3 + 22*r. Factor y(v).
2*v**2*(7*v - 2)
Let d(h) be the second derivative of 3*h**5/100 - h**4/6 + h**3/10 + 11*h. Factor d(v).
v*(v - 3)*(3*v - 1)/5
Let q(u) be the third derivative of u**11/332640 - u**5/30 + 2*u**2. Let z(s) be the third derivative of q(s). Determine l, given that z(l) = 0.
0
Let c(t) be the second derivative of -3*t**5/5 - t**4/3 + 7*t. Let c(x) = 0. What is x?
-1/3, 0
Solve -3/2*n**3 + 3/2*n**5 + 0*n**2 + 0*n**4 + 0*n + 0 = 0.
-1, 0, 1
Suppose -6*r = -2*r - 2*j - 4, -5*j = 5*r + 10. Suppose -3*n + n + 4*k - 8 = r, n - 5*k = -13. Solve -3*p**n - 2*p + 3*p + 2*p**2 = 0 for p.
0, 1
Let l(m) be the first derivative of -m**4/4 - 2*m**3/3 + 3*m**2/8 + 9*m/4 + 7. Find j such that l(j) = 0.
-3/2, 1
Factor 4/9*s**2 + 16/9 - 20/9*s.
4*(s - 4)*(s - 1)/9
Let m = -8/35 + 142/315. Let k(v) be the first derivative of 0*v + 0*v**2 - m*v**3 + 8/15*v**5 + 1/2*v**4 + 3. Solve k(c) = 0 for c.
-1, 0, 1/4
Let g(c) be the first derivative of -c**6/360 - c**5/60 - c**4/24 - 4*c**3/3 + 7. Let s(j) be the third derivative of g(j). What is x in s(x) = 0?
-1
Let s be ((-18)/(-15))/((-4)/(-10)). Let g = 3 - s. Factor 5/3*l**3 + 1/3*l**2 + g*l + 4/3*l**4 + 0.
l**2*(l + 1)*(4*l + 1)/3
Let z(w) be the third derivative of w**8/672 - w**6/120 + w**4/48 + 4*w**2. Factor z(q).
q*(q - 1)**2*(q + 1)**2/2
Let d = 76 - 73. Let f = 2 + -2. Factor -3/2*v**2 + 2*v**4 - 1/2*v + 0 + f*v**d.
v*(v - 1)*(2*v + 1)**2/2
Factor 2/9*h - 2/9*h**3 + 4/9*h**2 - 4/9.
-2*(h - 2)*(h - 1)*(h + 1)/9
Let q(m) = -3*m**3 + 19*m**2 + m. Let j(i) = -2*i**3 + 10*i**2. Let u(p) = 7*j(p) - 4*q(p). Suppose u(f) = 0. Calculate f.
-2, -1, 0
Suppose -14*a + 40 = -4*a. What is x in 18*x**3 - 8/3*x**2 + 36*x**a + 0 + 18*x**5 - 8/3*x = 0?
-1, -2/3, 0, 1/3
Let c(d) be the second derivative of -3*d - 29/50*d**6 + 1/5*d**3 + 99/100*d**5 + 9/70*d**7 + 0*d**2 - 3/4*d**4 + 0. Factor c(g).
3*g*(g - 1)**3*(9*g - 2)/5
Let l(y) = 3*y**4 - 15*y**3 + 6*y**2 - 9*y. Let z(u) = -u**3 + u**2 - u. Suppose 4*t - 33 = 27. Let b(n) = t*z(n) - l(n). Let b(f) = 0. Calculate f.
-2, 0, 1
Let j(i) = -i + 6. Let z be j(5). Let f be (0/(-3) - -4)*z. Suppose -7 + s**f + s**3 + 7 = 0. Calculate s.
-1, 0
Let h(m) be the second derivative of -m**8/840 + m**7/420 + m**6/180 - m**5/60 - m**3/2 + m. Let z(n) be the second derivative of h(n). Factor z(v).
-2*v*(v - 1)**2*(v + 1)
Suppose 2*b = 7*b - 25. Factor -1/6*z + 0 - 5/2*z**3 - 2/3*z**b - 13/6*z**4 - 7/6*z**2.
-z*(z + 1)**3*(4*z + 1)/6
Determine r, given that 41*r**2 - r - 48*r**3 - 25*r**2 + r + 36*r**4 = 0.
0, 2/3
Suppose 3*x + 3*l + 12 = 0, -x - 2*x + 2*l = -3. Let q be 1/x - 534/(-6). What is p in 78*p**4 + q*p + 8 + 210*p**4 + 338*p**2 + 452*p**3 + 76*p**3 = 0?
-2/3, -1/4
Let h(a) be the first derivative of a**6/2 - 9*a**5/10 + 3*a**4/8 + 2. Factor h(i).
3*i**3*(i - 1)*(2*i - 1)/2
Factor 8*t**5 + 2*t**4 + 4*t**4 + 3*t**3 + 0*t**4 - 5*t**5.
3*t**3*(t + 1)**2
Let d(p) be the first derivative of -1 - 2/3*p**2 - 2/3*p - 2/9*p**3. Factor d(u).
-2*(u + 1)**2/3
Factor 0 - 2/3*c**3 + 2/3*c**2 + 0*c.
-2*c**2*(c - 1)/3
Suppose 2*q + 0*q - 8 = 0. Suppose -5*z + 6 = -q. Factor 4/3*x - 2/3*x**z - 2/3.
-2*(x - 1)**2/3
Let z = 1094 - 6563/6. Suppose -z*g**2 + 2/3*g - 1/2 = 0. What is g?
1, 3
Determine u so that u - 4*u - 4372*u**2 + 4360*u**2 = 0.
-1/4, 0
Let a(j) = 7*j**2 - 3*j - 5. Let m(d) = -6*d**2 + 2*d + 4. Suppose -16 = -8*y + 4*y. Let w(b) = y*a(b) + 5*m(b). Determine u, given that w(u) = 0.
-1, 0
Suppose -c + 4*c = -27. Let a be (-15)/c - 3/(-9). Determine f so that -2*f**3 - f + 2 + 3*f - f**a - f**2 = 0.
-1, 1
Factor 2 - 1/2*f**2 + 0*f.
-(f - 2)*(f + 2)/2
Let x(n) be the second derivative of -2*n**7/63 - 4*n**6/45 + 2*n**4/9 + 2*n**3/9 - n - 15. Factor x(j).
-4*j*(j - 1)*(j + 1)**3/3
Let j(p) be the second derivative of -3*p + 0*p**2 + 0 - 1/6*p**4 - 3/10*p**5 + 2/3*p**3. Determine d, given that j(d) = 0.
-1, 0, 2/3
Let s(w) = -w**4 + w**3 + w**2 + 1. Let f(b) = 4*b**3 + 4*b**2 + b + 1. Let n(q) = -5*f(q) + 5*s(q). Factor n(u).
-5*u*(u + 1)**3
Suppose 5*g - 4*s = -4, -23*s = -2*g - 19*s - 4. Determine j, given that 8/5*j**3 - j**4 + g*j + 4/5*j**2 + 0 = 0.
-2/5, 0, 2
Let c = 323/2840 - -4/355. Factor c*t + 1/8*t**3 + 0 - 1/4*t**2.
t*(t - 1)**2/8
Let b(r) be the second derivative of -1/60*r**6 + 0*r**2 + 0*r**4 - 1/21*r**7 + 0*r**5 + 0 + 0*r**3 - 4*r. Solve b(m) = 0 for m.
-1/4, 0
Find v, given that -4*v**3 + v**2 - 1 - v**4 - v - 7*v**2 - 3*v = 0.
-1
Let b be 6*(1 + 0) + -3. Suppose b*h + 27 = 4*w, w + 4*h - 11 = -28. Suppose 2/3*v**w + 2/3*v**2 - 2/3*v - 2/3 = 0. Calculate v.
-1, 1
Let k(s) be the third derivative of s**8/1344 - s**7/840 - s**6/240 + s**5/120 + s**4/96 - s**3/24 + 9*s**2. Let k(z) = 0. Calculate z.
-1, 1
Factor 2/5*c**2 + 8/5*c - 2/5*c**3 - 8/5.
-2*(c - 2)*(c - 1)*(c + 2)/5
Let c(r) be the first derivative of -4/7*r + 22/21*r**3 + 2 - 5/7*r**2 - 2/7*r**4. Factor c(n).
-2*(n - 2)*(n - 1)*(4*n + 1)/7
Let s = 0 + 1. Let m = s - -1. Suppose 39/2*b**3 + 21/2*b + 3/2 + 6*b**4 + 45/2*b**m = 0. What is b?
-1, -1/4
Let c = -2925/2 + 1493. Let z = 31 - c. Factor 0 + a - z*a**2.
-a*(a - 2)/2
Let y(i) = -i**3 - 20*i**2 - 15*i + 76. Let l be y(-19). Factor 3/4*o**4 - 3/2*o**3 + 3/4*o**2 + l + 0*o.
3*o**2*(o - 1)**2/4
Let y(d) = -d**2 - 8*d + 9. Let l be y(-8). Suppose l = 4*c - 11. Let -12/7*u**4 + 0 - 2/7*u**c - 26/7*u**3 - 8/7*u - 24/7*u**2 = 0. What is u?
-2, -1, 0
Suppose 23*d**2 + 4*d - d**4 + 3 - 4*d**3 - 46*d**2 + 21*d**2 = 0. What is d?
-3, -1, 1
Let g(d) be the first derivative of 2 + 2/3*d**3 + 2*d**2 + 2*d. Factor g(p).
2*(p + 1)**2
Let i(g) = -g**2 + 6*g + 4. Let s be i(6). Factor 6*w - 2 - 1 + 2 + s*w**3 - 9*w**2.
(w - 1)**2*(4*w - 1)
Determine o, given that 0 + 0*o**3 + 2/11*o**2 + 0*o - 2/11*o**4 = 0.
-1, 0, 1
Determine t so that t**4 + 74*t**2 - 2*t**3 + t**3 - t**3 - 73*t**2 = 0.
0, 1
Let i = -9 - -13. Let q(c) be the third derivative of 0*c + 0*c**3 + 0*c**6 - c**2 + 0 - 1/210*c**7 + 0*c**i + 1/60*c**5. Factor q(h).
-h**2*(h - 1)*(h + 1)
Let v(g) be the third derivative of -g**8/840 + g**7/1260 + g**6/270 + g**3 - 7*g**2. Let q(u) be the first derivative of v(u). Factor q(n).
-2*n**2*(n - 1)*(3*n + 2)/3
Suppose -3*r = w - 6, -2*w - 3*w - 6 = 3*r. Let i(m) be the first derivative of -1/3*m**2 - 2/9*m**3 - r + 0*m. What is x in i(x) = 0?
-1, 0
Let s(f) be the first derivative of -f**3/6 + f/2 - 5. Factor s(q).
-(q - 1)*(q + 1)/2
Suppose -15 + 0 = -5*a. Let w(t) be the second derivative of -49/6*t**4 + 0 - 4*t**2 + 28/3*t**a - t. Determine n, given that w(n) = 0.
2/7
Let i(o) be the third derivative of o**7/8 + 13*o**6/40 + 19*o**5/80 + o**4/16 - 7*o**2. Let i(m) = 0. Calculate m.
-1, -2/7, -1/5, 0
Let b(x) = x**2 - 4*x + 13. Let j(p) = p**2 - p + p + 7 - 3*p + p. Let f(h) = 3*b(h) - 5*j(h). Factor f(l).
-2*(l - 1)*(l + 2)
Let a(n) = -n**2 - 3*n. Let i(o) = o + 1. Let b(v) = 3*a(v) + 6*i(v). Factor b(d).
-3*(d - 1)*(d + 2)
Suppose -3*p + 13 = -5. Let d be 147/90 + p/(-45). Let -2*c - 1/2 - d*c**2 = 0. What is c?
-1, -1/3
Suppose 12 + 1/4*b**3 - 5/4*b**2 - 2*b = 0. What is b?
-3, 4
Let r(g) be the first derivative of g**4/8 - 6. Factor r(j).
j**3/2
Let b(x) be the third derivative of x**7/1260 + x**6/120 + 13*x**5/360 + x**4/12 + x**3/9 - 25*x**2. Factor b(q).
(q + 1)**2*(q + 2)**2/6
Let c = -2 - -6. Suppose -2*d - 10 = -j, -2*j + c*d + 11 = 3*d. Let 4*s**2 - 2 - 2*s**5 + s**4 - 3*s**j - 2*s + 4*s**3 + 0*s**3 = 0. What is s?
-1, 1
Let s be (39/9 + -5)*6/(-8). Let 0*h**2 - s + 1/2*h**4 + h - h**3 = 0. Calculate h.
-1, 1
Let i(d) be the first derivative of -4/3*d + 8/3*d**2 + 1/6*d**6 + 7 + 1/3*d**5 - 11/12*d**4 - d**3. Let i(g) = 0. Cal