t k(x) be the first derivative of 2*x**3 - 21 + 9/4*x**4 + 1/2*x**2 + 0*x + 4/5*x**5. What is w in k(w) = 0?
-1, -1/4, 0
Let t(n) be the third derivative of n**6/30 + 2*n**5/15 - 4*n**4 + 2*n**2 + 131*n. Factor t(v).
4*v*(v - 4)*(v + 6)
Let h(o) be the first derivative of -o**5/15 - 7*o**4/12 - 14*o**3/9 - 4*o**2/3 + 60. Factor h(n).
-n*(n + 1)*(n + 2)*(n + 4)/3
Suppose 0 = 3*s + y, -y = 4*s - 5*y. Suppose s = -15*c + 7*c + 24. Factor a + 0*a**2 - 4*a**2 + 5*a**3 - c*a + a.
a*(a - 1)*(5*a + 1)
Let p = 38 + -52. Let l be ((-3)/(-24))/((-7)/p). Factor -1/2 + l*s + 3/4*s**2.
(s + 1)*(3*s - 2)/4
Suppose 22*g = -6 + 6. Let n(w) be the first derivative of -2/25*w**5 + 1/15*w**3 + 0*w + 1/20*w**4 + g*w**2 + 8. Let n(a) = 0. Calculate a.
-1/2, 0, 1
Let j(q) be the third derivative of q**5/120 + 7*q**4/24 - 5*q**3/4 + 14*q**2 - 4. Factor j(p).
(p - 1)*(p + 15)/2
Let x(h) = h**2 + 16*h - 10. Let i be x(-12). Let y = -58 - i. Factor k + y - 3/2*k**2.
-k*(3*k - 2)/2
Let v(k) be the third derivative of -19/20*k**5 + 16*k**2 - 7/6*k**3 + 3/40*k**6 - 41/24*k**4 + 0 + 0*k. Suppose v(z) = 0. Calculate z.
-1/3, 7
Let l(m) = 5*m**2 - 2. Let g(v) = 1. Let j be (0 - 1)/(-6 + (1 - -4)). Let q(d) = j*l(d) - 3*g(d). Factor q(x).
5*(x - 1)*(x + 1)
Suppose 0 - 3/8*u**3 + 1/4*u + 1/8*u**4 - 1/8*u**2 + 1/8*u**5 = 0. What is u?
-2, -1, 0, 1
Let t(x) = -2*x**2 + 91*x + 244. Let v be t(48). Determine n so that 24/7*n + 0 + 12*n**2 + 15/7*n**v + 66/7*n**3 = 0.
-2, -2/5, 0
Let r(c) be the second derivative of -c**6/120 - c**5/40 + c**4/16 + c**3/3 + c**2/2 - 56*c. Factor r(y).
-(y - 2)*(y + 1)**2*(y + 2)/4
Let p(h) = 2*h + 25. Let t = -7 - 4. Let x be p(t). Let -448*v**x - 1408*v**2 - 1361*v + 547*v**5 - 68*v**4 - 687*v - 1024 - 551*v**5 = 0. Calculate v.
-4, -1
Let v(j) = -5*j**2 - 31*j - 62. Let r(g) = -g + 3. Let z(a) = 4*r(a) + v(a). Factor z(l).
-5*(l + 2)*(l + 5)
Let d(g) be the first derivative of 1/8*g**6 - 11 - 3/10*g**5 + g**3 - 3/2*g + 3/8*g**2 - 3/8*g**4. Let d(j) = 0. Calculate j.
-1, 1, 2
Let i = 6644 - 59792/9. Factor 0 + 64/9*d**5 + 0*d + i*d**3 + 32/9*d**4 + 0*d**2.
4*d**3*(4*d + 1)**2/9
Find n such that 0 + 2/11*n**2 + 4/11*n = 0.
-2, 0
Let h(z) be the third derivative of -z**5/660 + 47*z**4/264 + 8*z**3/11 - 2*z**2 - 119. Suppose h(r) = 0. What is r?
-1, 48
Let m(i) be the second derivative of i**6/120 - i**5/20 + i**4/12 + 11*i**2/2 + 11*i. Let q(o) be the first derivative of m(o). Factor q(w).
w*(w - 2)*(w - 1)
Let x = -1 + 14. Let l(j) = -j**2 + 10*j + 13. Let n be l(11). What is o in o + 3*o**4 + x*o**n + 9*o**3 + 0*o + 2*o - 4*o**2 = 0?
-1, 0
Factor 0 + 0*r + 2/3*r**4 + 8/3*r**3 - 10/3*r**2.
2*r**2*(r - 1)*(r + 5)/3
Let m(y) be the second derivative of y**5/20 - y**4/4 + y**3/3 - y - 6. Let m(q) = 0. Calculate q.
0, 1, 2
Suppose -39/4*v**3 + 0 - 3/4*v**5 + 0*v - 6*v**4 - 9/2*v**2 = 0. What is v?
-6, -1, 0
Let k = -28 - -31. Suppose 5*n = k*u - 4 - 2, -4*u + 8 = -4*n. Solve -m**3 - m**2 + 2*m**3 + 4 + 3*m**2 - 5*m**u = 0.
-1, 2
Let i = 21281 + -21279. Factor -2*m - 2/3*m**4 + 0 + 2/3*m**i + 2*m**3.
-2*m*(m - 3)*(m - 1)*(m + 1)/3
Let z = 38 - 32. Determine p, given that z*p**2 + 2*p**2 - 5*p - 6 - 3*p**2 + 1 + 5*p**3 = 0.
-1, 1
Let p(d) be the third derivative of -d**7/840 + 37*d**6/480 - 39*d**5/20 + 45*d**4/2 - 72*d**3 + 4*d**2 - 7. Suppose p(t) = 0. Calculate t.
1, 12
Let u(k) = 14*k + 28. Let g be u(-8). Let a be 72/g*2/(-4). Find l, given that -a*l**5 - 3/7*l**3 + 0*l**2 + 6/7*l**4 + 0 + 0*l = 0.
0, 1
Let g(n) be the third derivative of -n**5/120 - 5*n**4/48 + 2*n**3 + 48*n**2. Determine s so that g(s) = 0.
-8, 3
Let s(k) be the third derivative of k**6/30 + 118*k**5/15 + 1798*k**4/3 + 13456*k**3/3 + 470*k**2. Let s(g) = 0. What is g?
-58, -2
Let t be (-413)/(-118) - 3/(-2). Let k(n) be the first derivative of 4/5*n**t - 7 - 2*n**3 + 3/2*n**4 + 0*n - 2*n**2. Factor k(d).
2*d*(d - 1)*(d + 2)*(2*d + 1)
Factor 0 - 3/5*f**3 + 5*f**2 + 1/5*f**5 - 9/5*f**4 + 18/5*f.
f*(f - 9)*(f - 2)*(f + 1)**2/5
Let x(l) be the first derivative of 2*l**3/39 - 2*l/13 - 365. Factor x(g).
2*(g - 1)*(g + 1)/13
Suppose 33/2*h + 15 + 3/2*h**2 = 0. Calculate h.
-10, -1
Let r be -4 - (-7 + 1/(-1)). Determine p, given that -2*p**r + 2*p**2 - 9*p**3 + 10*p**4 - p**4 = 0.
0, 2/7, 1
Factor a**5 - 10*a**4 + 40*a**4 - 26*a**4 + 0*a**5 - 16*a - 16*a**2.
a*(a - 2)*(a + 2)**3
Let n(y) = -2*y**3 - 115*y**2 - 646*y - 248. Let f(d) = -d**3 + d**2 - d + 2. Let i(l) = 6*f(l) + 2*n(l). Factor i(w).
-2*(w + 11)**2*(5*w + 2)
Let x be (34/255)/(1/5). Let h(d) be the first derivative of 5 + 0*d**2 + 0*d + x*d**3. What is r in h(r) = 0?
0
Suppose -60 = -f - 4*f. Let h(d) = -d + 14. Let t be h(f). Let -3*r + 2*r + 2*r**3 + 2*r**3 - r + t*r**2 = 0. Calculate r.
-1, 0, 1/2
Let s(d) be the first derivative of 3*d**4/4 - 8*d**3 + 24*d**2 + 429. Determine v, given that s(v) = 0.
0, 4
Let z = 27808 + -83420/3. What is p in -2/3*p**2 - z*p - 2/3 = 0?
-1
Let d(r) be the third derivative of r**8/840 - r**7/525 - 11*r**6/300 + 29*r**5/150 - 13*r**4/30 + 8*r**3/15 - 829*r**2. Solve d(f) = 0 for f.
-4, 1, 2
Let c(u) = -u - 10 + 14 + 15. Let w be c(15). Solve 30 + 0*b**4 + 5*b**4 - 38 - 12*b + 4*b**2 + 12*b**3 - b**w = 0.
-2, -1, 1
Suppose -4*y + 34 = -5*y. Let p = 12 - y. Factor -9*n + 29*n + 15*n**3 - 40 + p*n**2 + 4*n**2.
5*(n + 2)**2*(3*n - 2)
Let z(g) be the second derivative of -g**4/6 + 23*g**3/3 - 60*g**2 + 251*g - 1. Determine j, given that z(j) = 0.
3, 20
Suppose -34*t + 28*t - 48 = 0. Let x(f) = 4*f**4 - 8*f**3 + 9*f**2 + 5. Let o(p) = -6*p**4 + 12*p**3 - 14*p**2 - 8. Let d(s) = t*x(s) - 5*o(s). Factor d(i).
-2*i**2*(i - 1)**2
Let a(v) be the third derivative of v**7/70 - 9*v**6/20 + 24*v**5/5 - 16*v**4 - 96*v**2. Factor a(d).
3*d*(d - 8)**2*(d - 2)
Let t(g) be the first derivative of -3/2*g**3 - 21/16*g**4 + 9/20*g**5 + 0*g + 9 + 0*g**2. Determine r, given that t(r) = 0.
-2/3, 0, 3
Let t(b) = b - 9. Let s be t(11). Suppose 2*r + 2 = 5*c - 3, 0 = r - 5. Suppose -2*i + 5*i**c - 2*i + 3*i**s - 2*i**3 - 2*i = 0. What is i?
-2, 0, 1
Suppose -s + 0*s - 29 = -g, 0 = -s - 5*g - 47. Let d be (-11)/22*s/26. Solve -6/13*c**2 + d*c - 2/13 = 0 for c.
1/3, 1
Let v(x) be the second derivative of x**6/1440 - x**5/80 + 5*x**4/96 - 14*x**3/3 + 3*x. Let r(c) be the second derivative of v(c). Factor r(j).
(j - 5)*(j - 1)/4
Let o(b) be the third derivative of b**7/1680 - b**6/192 - b**5/48 + 5*b**4/48 + b**3/2 + 4*b**2 - 2. Find z such that o(z) = 0.
-2, -1, 2, 6
Let v(r) = 15*r**2 - 58*r - 3. Let g be v(4). Let n(q) be the second derivative of -1/5*q**g - 5*q - 1/3*q**3 + 1/2*q**4 + 0 + 0*q**2. Factor n(o).
-2*o*(o - 1)*(2*o - 1)
Let w(x) be the third derivative of x**5/30 + 47*x**4/108 + 10*x**3/27 + 15*x**2 + 2. Factor w(d).
2*(d + 5)*(9*d + 2)/9
Let y(k) be the first derivative of k**4/7 - 19*k**3/21 - 29*k**2/14 - 6*k/7 - 17. Let y(u) = 0. What is u?
-1, -1/4, 6
Let b = -2/24289 + 485794/170023. Factor 0 + b*v**4 + 24/7*v**3 + 0*v + 4/7*v**2.
4*v**2*(v + 1)*(5*v + 1)/7
Let p = 28998121/8104818 - 14606/3077. Let r = -1/439 - p. Determine i, given that 1/2 + 1/3*i**2 - r*i = 0.
1/2, 3
Suppose -c + t = 2*t, 3*t + 15 = 0. Suppose -3*j + 71 = 4*q, -39 = q - 3*q - c*j. Factor 5*x**3 - q*x - 8*x**2 + 13*x**3 - 27*x**5 + 18*x.
-x*(x + 1)*(3*x - 1)**3
Let w be ((-5)/3)/((-6)/108*6). Let r(x) be the third derivative of 0 + x**2 + 0*x + 0*x**3 + 0*x**4 - 1/735*x**7 + 1/105*x**6 - 1/70*x**w. Factor r(d).
-2*d**2*(d - 3)*(d - 1)/7
Let x(q) = -3*q**3 - 2*q**2 + 9*q - 6. Let u(k) = 10*k**3 + 7*k**2 - 28*k + 18. Let v(p) = 4*u(p) + 14*x(p). Determine j so that v(j) = 0.
-3, 1, 2
Let g be (-22)/(-22)*(-2)/((-9 + 2)*2). Let -1/7*x**4 - g + 2/7*x**2 + 2/7*x**3 - 1/7*x**5 - 1/7*x = 0. Calculate x.
-1, 1
Let s(f) be the second derivative of f**5/80 + f**4/48 - 17*f**3/24 + 15*f**2/8 - 4*f - 24. Factor s(i).
(i - 3)*(i - 1)*(i + 5)/4
Suppose -3*b = -5*f - 29, -3*b + 15 = -4*f - 10. Factor 4/7*n + 0 + 2/7*n**4 - 6/7*n**2 + 0*n**b.
2*n*(n - 1)**2*(n + 2)/7
Let g(q) = 3*q - 26. Let l be g(10). Let c(d) be the second derivative of -1/20*d**5 - 3*d + 0 + 0*d**3 - 1/12*d**l + 0*d**2. Factor c(t).
-t**2*(t + 1)
Let b be 38/48 - (-94)/(-752). Let 10/9*f**5 - 8/3*f**3 - b*f**4 + 0 + 0*f - 8/9*f**2 = 0. Calculate f.
-1, -2/5, 0, 2
Factor 32/1