 the first derivative of 2*t**3/27 + 4*t**2 + 72*t - 4. Let k(x) = 0. What is x?
-18
Let b(v) = 2*v**2 + 14*v + 4. Let y be b(0). Suppose 5 + 3 = 4*p. Factor -18*r**4 + 20*r**y + p*r**5 + 0*r**5.
2*r**4*(r + 1)
Solve 5*v**3 + 19*v**3 - 32*v**3 + 7*v**3 - 2*v**3 - 3*v**2 + 90*v = 0 for v.
-6, 0, 5
Let m(t) be the second derivative of -t**6/60 + t**4/12 - 7*t**2 - 5*t. Let f(l) be the first derivative of m(l). Factor f(n).
-2*n*(n - 1)*(n + 1)
Let u(h) be the second derivative of 0*h**6 + 10*h + 2/189*h**7 + 0*h**2 + 0*h**3 + 0 + 0*h**4 - 1/45*h**5. Find v such that u(v) = 0.
-1, 0, 1
Let h be 11/((-22)/(-8)) - (-4 + (-108)/(-15)). Factor h*p**3 + 0 + 12/5*p + 16/5*p**2.
4*p*(p + 1)*(p + 3)/5
Let u(a) be the first derivative of -a**5 + 285*a**4/4 - 1400*a**3 + 1960*a**2 - 647. Determine j, given that u(j) = 0.
0, 1, 28
Let p(t) be the third derivative of -t**7/210 + t**6/120 + t**5/10 - t**4/6 - 4*t**3/3 + 4*t**2. Factor p(q).
-(q - 2)**2*(q + 1)*(q + 2)
Suppose 0 = 30*w - 48 + 48. Let z(o) be the first derivative of -1 + 0*o**2 + w*o**4 + 0*o**3 + 0*o + 1/20*o**5 + 1/24*o**6. Find s such that z(s) = 0.
-1, 0
Let i(n) = 8*n**3 - 101*n**2 + 1456*n + 1571. Let f(o) = -70*o**3 + 912*o**2 - 13104*o - 14138. Let k(s) = 6*f(s) + 52*i(s). Solve k(q) = 0.
-1, 28
Let a(t) = 3*t - 17*t + 8*t + 7*t. Let l(j) be the second derivative of -j**4/6 - j**3/2 + 2*j**2 + j. Let i(p) = -5*a(p) - l(p). What is q in i(q) = 0?
-1, 2
Factor -6/7*v**3 + 0 + 12/7*v - 6/7*v**2.
-6*v*(v - 1)*(v + 2)/7
Let s(c) be the second derivative of c**7/14 - c**6/2 - 3*c**5/20 + 41*c**4/4 - 36*c**3 + 54*c**2 + 2*c - 266. What is k in s(k) = 0?
-3, 1, 2, 3
Let q be 4232/3190 - 8/10. Let z = -10/29 + q. Factor z*n**3 + 0 - 2/11*n**4 + 2/11*n**2 - 2/11*n**5 + 0*n.
-2*n**2*(n - 1)*(n + 1)**2/11
Suppose 3*c = -5*c + 16. Factor y**4 - y**4 - 3*y**c + y**4 + 2*y**3.
y**2*(y - 1)*(y + 3)
Let j = 10 + -7. Suppose -16 = r - 19. Factor -7*u**2 + 2 - 2*u**3 + 2*u**5 - 1 + r*u**2 + j*u**4.
(u - 1)*(u + 1)**3*(2*u - 1)
Let w = 1460/5083 - -8/391. Factor -w + 4/13*t**4 + 2/13*t**5 - 16/13*t**2 - 4/13*t**3 - 14/13*t.
2*(t - 2)*(t + 1)**4/13
Factor 5*x**3 - 328*x**2 - 153*x**2 + 6615*x - 46305 + 166*x**2.
5*(x - 21)**3
Let n(j) = -j**3 + 5*j**2 + j. Let o be n(5). Factor 3 - 7*p**2 - 4*p + 0*p + o*p**2 + 3*p**2.
(p - 3)*(p - 1)
Let h(m) be the first derivative of m**3/12 - 75*m**2/2 + 5625*m - 289. Factor h(p).
(p - 150)**2/4
Let h be 10*(1/4 - (-176)/320). Let g = 3 + -1. Let 12*t**3 + 2*t - 15*t + t - h + 8*t**g = 0. Calculate t.
-1, -2/3, 1
Let m be 2/(22/1) + (-765)/(-297). Let v = -14 - -18. Suppose 14/3*z**2 - 4/3*z - 14/3*z**v + 0 + 4*z**3 - m*z**5 = 0. What is z?
-2, -1, 0, 1/4, 1
Let y be -1*4/3*-3. Suppose 59*n + 6 = 124. Factor -8*j**3 - n*j - 1/5 - 33/5*j**2 - 16/5*j**y.
-(j + 1)**2*(4*j + 1)**2/5
Let u = 45 + -38. Let c(o) = -3*o**3 - 11*o**2 - 21*o - 13. Let m(i) = -6*i**3 - 23*i**2 - 42*i - 25. Let a(h) = u*c(h) - 4*m(h). Factor a(s).
3*(s + 1)**2*(s + 3)
Let y(z) = 11*z**3 + 2*z**2 - 5*z + 2. Let t be y(1). Suppose 9*g = 4*g - t*g. Factor -2/7*a - 6/7*a**3 - 2/7*a**4 + g - 6/7*a**2.
-2*a*(a + 1)**3/7
Let w(f) be the third derivative of -f**5/100 - 17*f**4/40 + 2*f**2 - 36. Factor w(a).
-3*a*(a + 17)/5
Let s(a) = -3*a**4 + 12*a**3 - 36*a**2 + 60*a - 21. Let v(l) = 5*l**4 - 23*l**3 + 72*l**2 - 117*l + 41. Let x(q) = 11*s(q) + 6*v(q). Let x(k) = 0. Calculate k.
-5, 1
Let p(o) be the first derivative of -3*o**6/5 - 108*o**5/25 - 8*o**4 - 4*o**3 + 9*o**2/5 + 8*o/5 + 409. Solve p(f) = 0 for f.
-4, -1, -1/3, 1/3
Let x(j) = -2*j - 49. Let m be x(-22). Let u(n) = 2*n**3 + 3*n**2 + 8*n - 3. Let d(s) = 3*s**3 + 3*s**2 + 9*s - 3. Let h(r) = m*d(r) + 6*u(r). Factor h(i).
-3*(i - 1)**2*(i + 1)
Let v(t) be the first derivative of t**4/2 - 2*t**3 - 9*t**2 + 54*t + 217. Let v(s) = 0. What is s?
-3, 3
Suppose -59*m + 60*m = 3. Let f(n) be the second derivative of 5/16*n**4 + 3/4*n**m + 3/8*n**2 - 5*n + 0. Factor f(k).
3*(k + 1)*(5*k + 1)/4
Let r(y) = 5*y**2 - 36*y + 31. Suppose -3*n = -1 - 8. Suppose x = n*x - 14. Let m(u) = -2*u**2 + 12*u - 10. Let v(o) = x*m(o) + 2*r(o). Factor v(i).
-4*(i - 2)*(i - 1)
Let y(d) = -3*d - 16. Let k be y(-8). Let g be (k/6)/((-6)/(-9)). Solve 1/4*z**g + 0*z - 1/4 = 0 for z.
-1, 1
Let l(d) = -d**3 - 4*d**2 + 3*d - 2. Let v(h) = 25*h**3 + 110*h**2 - 80*h + 55. Let p(o) = -55*l(o) - 2*v(o). Solve p(y) = 0 for y.
-1, 0, 1
Let c = -18215 + 18219. Factor 0*b + 0*b**2 + 0 - 1/4*b**c - 1/4*b**3.
-b**3*(b + 1)/4
Factor 14/3*c - 5 - c**2.
-(c - 3)*(3*c - 5)/3
Let f(w) = -10*w**3 - 5*w**2 - 99*w - 183. Let h(s) = -6*s**3 - 6*s**2 - 100*s - 182. Let v(y) = -2*f(y) + 3*h(y). Solve v(b) = 0.
-3, 10
Let -24*h**4 - 101/3*h**3 + 2*h**2 + 0 + 0*h + 35/3*h**5 = 0. Calculate h.
-1, 0, 2/35, 3
Suppose 2*w - 4 = -3*q, 13*w = 11*w - 2. Let u(m) be the second derivative of 0*m**3 + 1/4*m**q - 4*m - 1/24*m**4 + 0. Find o such that u(o) = 0.
-1, 1
Let l(d) = -3*d**2 + 25*d + 9. Let w be l(8). Suppose w*x - 16*x**2 - x - 12*x = 0. Calculate x.
0, 1/4
Factor 21/2*n + 21/4*n**2 + 6 + 3/4*n**3.
3*(n + 1)*(n + 2)*(n + 4)/4
Let u = -1 + 4. Let a be 16/(-6)*u/(-4). Let 124*g**5 + 99*g**5 + 111*g**5 + 9*g**5 + 135*g - 350*g**3 - 90*g**a + 245*g**4 - 27 = 0. Calculate g.
-1, 3/7
Factor -65*n**2 + 4 + 118*n**2 - 57*n**2.
-4*(n - 1)*(n + 1)
Let t(f) be the second derivative of 0 + 8*f**3 + 2/5*f**5 - 25*f + 61/21*f**4 + 2/105*f**6 + 72/7*f**2. Let t(q) = 0. What is q?
-6, -1
Let v(n) = -2*n**2 - 2*n. Let t(z) = 5 - 10 + 3*z + 5*z**2 + 3 + 3. Let q(r) = 4*t(r) + 9*v(r). Factor q(k).
2*(k - 2)*(k - 1)
Suppose -2*i = 4*r + 44, -2*i = 2*r + 17 + 17. Let s be (-2)/(-6) - 2/i. Factor s*p - 1/2*p**2 + 0.
-p*(p - 1)/2
Let g(z) be the first derivative of z**5/90 + 7*z + 9. Let k(y) be the first derivative of g(y). Factor k(w).
2*w**3/9
Let j(f) = -44*f**4 + 584*f**3 - 2012*f**2 - 2400*f + 8592. Let t(n) = 4*n**4 - 53*n**3 + 183*n**2 + 218*n - 781. Let l(s) = 3*j(s) + 32*t(s). Factor l(k).
-4*(k - 7)**2*(k - 2)*(k + 2)
Find t such that -124/5*t + 2/5*t**4 + 8*t**3 - 16 - 6/5*t**2 = 0.
-20, -1, 2
Let v be (3633/(-5190))/((-7)/2). Factor 3/5*s - v*s**2 - 2/5.
-(s - 2)*(s - 1)/5
Let b(k) = -4*k - 19. Let y be b(-6). Let w be 21/56*y/((-45)/(-6)). Factor -w*l**4 - 1/2*l**3 + 1/4 + 0*l**2 + 1/2*l.
-(l - 1)*(l + 1)**3/4
Let u = -55/2 - -331/12. Let g(r) be the first derivative of -2 + 0*r - u*r**4 + 2/9*r**3 - 1/6*r**2. Solve g(z) = 0.
0, 1
Let t(s) be the second derivative of -1/30*s**4 - 1/25*s**5 + 0*s**3 - 1/75*s**6 + 11*s + 0*s**2 + 0. Determine u so that t(u) = 0.
-1, 0
Let a(z) = 4*z**2 - 100*z - 120. Let i(t) = 24 - 6*t + 11*t - t - t**2 + 16*t. Let u(d) = 5*a(d) + 24*i(d). Factor u(j).
-4*(j + 2)*(j + 3)
Let m(c) = -39*c + 105. Let z be m(-13). Let n be (-2)/(-12) + 170/z. Let -2/9*g**2 - n*g - 2/9 = 0. What is g?
-1
Let z(s) be the second derivative of -s**7/98 + s**6/35 + 3*s**5/20 - 5*s**4/7 + 6*s**3/7 - 11*s. Let z(v) = 0. Calculate v.
-3, 0, 1, 2
Let d = 2/1709 - -1703/5127. Find t, given that 1 - d*t**2 + 2/3*t = 0.
-1, 3
Let m(b) be the second derivative of -b**6/15 + 2*b**5/5 + 5*b**4/6 - 17*b - 8. What is f in m(f) = 0?
-1, 0, 5
Let c(v) = 2*v**2 - v - 2. Let j(q) = 18*q**2 - 136*q + 2032. Let z(w) = 8*c(w) - j(w). Factor z(i).
-2*(i - 32)**2
Let l(k) be the first derivative of 9*k**4 - 17*k**3 - 39*k**2/2 - 6*k - 62. Solve l(u) = 0 for u.
-1/3, -1/4, 2
Let q(o) be the third derivative of -o**5/240 + o**4/12 - 2*o**3/3 - 121*o**2. Factor q(v).
-(v - 4)**2/4
Let j be (155/(-372))/((-15)/9). Suppose 1/4*a + 0 + j*a**2 = 0. What is a?
-1, 0
Let a(p) be the second derivative of p**5/140 - p**4/7 - 2*p**3/3 + 400*p. What is t in a(t) = 0?
-2, 0, 14
Let f(k) be the first derivative of -k**3 + 9*k**2 - 234. Factor f(m).
-3*m*(m - 6)
Let x(i) be the third derivative of -i**6/120 - i**5/60 + i**4/12 + i**2 - 9. Let x(k) = 0. What is k?
-2, 0, 1
Let r = -96 + 1064/11. Let s = -283 - -3115/11. Factor -r*y - 6/11 - s*y**2.
-2*(y + 1)*(y + 3)/11
Let i(m) be the third derivative of m**7/2520 + m**6/360 - m**5/40 - m**4/24 - 27*m**2. Let z(t) be the second derivative of i(t). Let z(u) = 0. Calculate u.
-3, 1
Let k(h) = h**2 + 7. Let b be k(0). Let n(m) be the second derivative of 1/13*m**2 + 0 - 1/78*m**4 + b*m - 