/3*m**2 + n*m.
-2*(m - 2)*(m - 1)/3
Let u(h) be the second derivative of h**4/36 + 5*h**3/6 - 17*h**2/3 + 3*h + 4. Suppose u(l) = 0. Calculate l.
-17, 2
Let r = -15 + 17. Let -63*z**3 + 62*z**3 - z**r + 3 - 3 = 0. What is z?
-1, 0
Let p(w) be the second derivative of 1/30*w**5 + 13*w + 0*w**2 + 1/18*w**4 + 1/27*w**3 + 1/135*w**6 + 0. Solve p(z) = 0.
-1, 0
Let q(d) = -d + 2. Let w be q(-3). Find h, given that -h - h**3 - w*h**2 - 3 - 4*h - 2*h = 0.
-3, -1
Let d(f) be the second derivative of f**4/16 + f**3/4 - 361*f. Find j, given that d(j) = 0.
-2, 0
Let l(x) = x**2 + 2*x - 5. Let k be l(-4). Factor m**k + 37*m - 2*m**2 - 76*m + 40*m.
m*(m - 1)**2
Let p(b) be the third derivative of 0*b**4 + 1/160*b**6 + 1/240*b**5 + 0*b**3 + 0 + 1/280*b**7 + 5*b**2 + 0*b + 1/1344*b**8. Factor p(i).
i**2*(i + 1)**3/4
Let q(s) = -5*s**2 + 105*s + 173. Let o(u) = -10*u**2 + 200*u + 345. Let z(b) = -3*o(b) + 5*q(b). Find l such that z(l) = 0.
-2, 17
Let i = 929 - 927. What is f in 4*f**3 + i*f + 0*f**4 - 2/3*f**5 - 16/3*f**2 + 0 = 0?
-3, 0, 1
Determine a, given that 12*a**3 + 33*a - 3/2*a**4 - 63/2*a**2 - 12 = 0.
1, 2, 4
Let h(z) be the second derivative of 11*z - 1/90*z**6 - 1/9*z**3 + 0 + 1/36*z**4 + 0*z**2 + 1/30*z**5. Find d such that h(d) = 0.
-1, 0, 1, 2
Suppose 7*c = -40*c. Solve -12/7*w**2 + c + 2/7*w**3 + 10/7*w = 0 for w.
0, 1, 5
Factor 33*r**3 - 13*r**3 - 49*r**2 - 14*r**3 - 9*r**3 + 34*r.
-r*(r + 17)*(3*r - 2)
Let f(m) be the third derivative of m**8/3528 + 13*m**7/735 + 2*m**6/7 - 40*m**5/63 + m**2 - 6*m. Factor f(k).
2*k**2*(k - 1)*(k + 20)**2/21
Let g(u) be the second derivative of u**8/1176 - u**6/210 + u**4/84 + 8*u**2 + u. Let b(w) be the first derivative of g(w). Solve b(d) = 0.
-1, 0, 1
Let k(d) = -d**2 + 4*d + 1. Let w(g) = g**2 + 51*g + 16. Let z(c) = -6*k(c) + 3*w(c). Suppose z(l) = 0. Calculate l.
-14, -1/3
Factor -22*o**4 + 79*o**4 - 20*o**3 - 23*o**4 - 30*o**4.
4*o**3*(o - 5)
Let f(u) = -2 - 16*u + 10*u - 3*u + u**2 - 1. Let c(l) = -1. Let z(p) = -28*c(p) - 4*f(p). Factor z(v).
-4*(v - 10)*(v + 1)
Let y = 33 - 31. Let c(k) be the third derivative of 0*k**3 + 1/48*k**4 + 3*k**y + 0 + 0*k - 1/60*k**5 + 1/240*k**6. Factor c(w).
w*(w - 1)**2/2
Solve 159*v**2 - 40*v - 2*v**4 - 44*v**3 - 292*v**2 + 51*v**2 = 0 for v.
-20, -1, 0
Let v(p) be the third derivative of -p**8/40320 + p**7/2520 - p**6/360 + 11*p**5/60 - 17*p**2. Let x(f) be the third derivative of v(f). Factor x(o).
-(o - 2)**2/2
Let b(d) be the first derivative of -4*d**5/15 - 22*d**4/3 + 208*d**3/3 - 656*d**2/3 + 896*d/3 + 57. Solve b(n) = 0 for n.
-28, 2
Find k, given that -16*k**2 - 5*k**3 + 38 - 60*k + 2 + 22*k**2 + 24*k**2 = 0.
2
Let w(z) be the second derivative of -z**7/210 + z**6/50 - 3*z**5/100 + z**4/60 + 66*z. What is l in w(l) = 0?
0, 1
Let g(p) = -3*p**3 - p**2 - p - 1. Let f be g(-1). Let h = -27 + 27. Factor h*l**2 - 4*l**2 - f*l + l**3 - 3*l**3.
-2*l*(l + 1)**2
Let q(r) be the second derivative of -r**6/225 - r**5/30 + r**4/10 + 9*r**3/5 + 36*r**2/5 + 227*r. Factor q(g).
-2*(g - 4)*(g + 3)**3/15
Suppose -4*j + 3*j + 36 = 0. Let h be j/8*(-8)/(-18). Factor 5*d + h - d**4 + 3*d**2 - d**3 + 0*d**4 + 0*d**4.
-(d - 2)*(d + 1)**3
Let g = -2129/24 - -731/8. Determine y, given that 44/3*y**2 + 0 - g*y = 0.
0, 2/11
Let b(g) be the third derivative of -g**7/840 + 5*g**6/96 - 63*g**5/80 + 81*g**4/32 + 243*g**3/4 + 25*g**2. Solve b(p) = 0.
-2, 9
Let p(y) be the first derivative of 13 + y**2 + 0*y**4 + 0*y - 4/3*y**3 - 1/3*y**6 + 4/5*y**5. Factor p(l).
-2*l*(l - 1)**3*(l + 1)
Let u = 41 + -28. Suppose -15*g + 10*g**4 - u*g + 8*g - 5*g**4 + 15*g**3 = 0. Calculate g.
-2, 0, 1
Let j(o) be the first derivative of -2/3*o**2 + 12 + 1/9*o**3 + o. What is c in j(c) = 0?
1, 3
Let y(j) = j**2. Let g(f) = 15*f**2 + 630*f + 19845. Let a(k) = -g(k) + 10*y(k). Factor a(r).
-5*(r + 63)**2
Let o = 10415 + -10413. Solve -2/13*h**o + 2/13*h + 12/13 = 0.
-2, 3
Suppose 0 + 5*q - 4/3*q**4 + 28/3*q**2 + 10/3*q**3 - 1/3*q**5 = 0. Calculate q.
-5, -1, 0, 3
Factor 384 + 432*o + 99/2*o**2 + 3/2*o**3.
3*(o + 1)*(o + 16)**2/2
Let z be -3*(-2)/30*(6 - (-9)/6). Factor -3*s**2 + 6*s + 12 - z*s**3.
-3*(s - 2)*(s + 2)**2/2
Let r be (-3)/10 + 1312/2240. Let u = 2 + -2. Determine l so that u*l**2 + 0*l + 0 + 2/7*l**4 - r*l**3 = 0.
0, 1
Let f(m) be the second derivative of -5*m**4/12 - 220*m**3/3 - 4840*m**2 - 451*m. Factor f(r).
-5*(r + 44)**2
Suppose 22 = 5*q - 4*o, 2*q = -0*q + 5*o + 2. Suppose q = l + l. Factor 0 + 1 - 1 + 2 + l*m + m**2.
(m + 1)*(m + 2)
Let s(n) = -n - 8. Let b be s(-15). Suppose h + 3*h - b = m, -4*m + 4 = 0. Factor 1/3 + 2*o + 3*o**h.
(3*o + 1)**2/3
Let x be 264/2508 + 4/(-38). Factor 3/4*f**4 + x*f**2 + 1/2*f**3 + 1/4*f**5 + 0*f + 0.
f**3*(f + 1)*(f + 2)/4
Let r(n) be the first derivative of n**5 - 5*n**4/4 - 20*n**3/3 + 10*n**2 - 231. Determine j, given that r(j) = 0.
-2, 0, 1, 2
Suppose 34*n - 27*n = -m - 5, -n = 4*m + 20. Suppose -1/10*i**4 - 1/5*i**2 + 0 + n*i + 3/10*i**3 = 0. What is i?
0, 1, 2
Let d be -3 + 21/6*2. Let k be 8/12*(-18)/(-4). Determine c so that -2*c**3 + c**2 + c - 1 - 4*c**2 + c**k - d*c = 0.
-1
Let m = -7979 + 55859/7. Let -12/7*f**3 + 8/7*f**2 + 0 + m*f**4 + 0*f - 1/7*f**5 = 0. Calculate f.
0, 2
Let k(a) be the second derivative of 3*a - 49/12*a**5 - 5/6*a**3 - 35/12*a**4 + 5*a**2 + 0. Let t(n) be the first derivative of k(n). Factor t(h).
-5*(7*h + 1)**2
Let g(w) be the third derivative of -w**8/1008 - w**7/126 - 7*w**6/360 - w**5/60 - 2*w**2 + 49. Let g(n) = 0. Calculate n.
-3, -1, 0
Let h(k) be the second derivative of k**6/360 + k**5/40 + k**4/12 - k**3 + 13*k. Let u(i) be the second derivative of h(i). Let u(v) = 0. What is v?
-2, -1
Let v(g) = 6*g**3 - 195*g**2 + 363*g - 156. Let x(y) = 3*y**3 - 97*y**2 + 181*y - 79. Let l(a) = -4*v(a) + 9*x(a). Suppose l(o) = 0. What is o?
1, 29
Let d(q) be the first derivative of 0*q**4 + 0*q + 21 + 0*q**3 - 5/6*q**6 + 0*q**5 + 0*q**2. Factor d(m).
-5*m**5
Suppose 23*n = 1203 + 1718. Let k = n - 125. Find m, given that 0*m - 8/5*m**4 - 12/5*m**3 + 0 - 4/5*m**k = 0.
-1, -1/2, 0
Let u(x) = 155*x**3 - 880*x**2 + 2200*x - 1940. Let q(b) = -7*b**3 + 40*b**2 - 100*b + 88. Let c(k) = 45*q(k) + 2*u(k). Factor c(o).
-5*(o - 4)*(o - 2)**2
Let x(d) be the third derivative of d**6/360 + 7*d**5/60 + 49*d**4/24 - 17*d**3/6 + 24*d**2. Let p(m) be the first derivative of x(m). Factor p(n).
(n + 7)**2
Let y(x) be the third derivative of -x**5/140 + 23*x**4/28 - 529*x**3/14 - 6*x**2 - 3*x. Factor y(u).
-3*(u - 23)**2/7
Suppose 0 = -8*a + 5 + 19. Let l(q) be the third derivative of -4*q**2 - 1/40*q**6 - 1/20*q**5 + 0*q + 1/2*q**a + 0 + 1/8*q**4. Factor l(z).
-3*(z - 1)*(z + 1)**2
Let d(r) be the first derivative of r**6/180 - r**5/300 - 11*r**3/3 + 14. Let k(q) be the third derivative of d(q). Suppose k(g) = 0. Calculate g.
0, 1/5
Let u(a) = 7*a**4 - 89*a**3 - 49*a**2 + 11*a + 11. Let l(s) = s**4 - 18*s**3 - 10*s**2 + 2*s + 2. Let w(y) = -33*l(y) + 6*u(y). Suppose w(d) = 0. Calculate d.
-6, -2/3, 0
Let k be (6/28)/(4 - (-52)/14). Let f(h) be the second derivative of -2*h + 0 + 0*h**3 + 1/90*h**6 - k*h**4 + 0*h**2 + 0*h**5. Factor f(s).
s**2*(s - 1)*(s + 1)/3
Let x(l) be the third derivative of -l**5/600 - l**4/8 - 15*l**3/4 + 12*l**2 + 2*l. Determine s, given that x(s) = 0.
-15
Let k(b) be the first derivative of 0*b - 3/5*b**5 - 4 + 4/3*b**2 - 44/9*b**3 + 19/6*b**4. Determine c so that k(c) = 0.
0, 2/9, 2
Let j(r) = -26*r - 14 - 2 + 167*r**3 - 15*r**2 - 183*r**3. Let q(f) = 3*f**3 + 3*f**2 + 5*f + 3. Let o(h) = -4*j(h) - 22*q(h). Factor o(y).
-2*(y + 1)**3
Let f(a) be the second derivative of 5*a**4/12 - 35*a**3/6 - 75*a**2 - 67*a. Let f(g) = 0. What is g?
-3, 10
Suppose -n = -6*n + 25, 4*q + n - 137 = 0. Factor -22*r**4 - 12*r**4 + r**2 + q*r**4.
-r**2*(r - 1)*(r + 1)
Let s(z) be the second derivative of -z**5/25 + z**4/3 - 8*z**3/15 + z - 31. Determine w so that s(w) = 0.
0, 1, 4
Let v(n) be the second derivative of -1/4*n**5 + 0 + 37*n - 40*n**3 - 90*n**2 - 65/12*n**4. Factor v(l).
-5*(l + 1)*(l + 6)**2
Let i be 4*(132/(-8) + 1). Let f = 64 + i. Suppose -2/7*h**f - 12/7*h - 18/7 = 0. What is h?
-3
Let z be 12*(4 - 33/9). Let -5*t - 5*t - z*t**3 - 5*t + 7*t**3 + 12*t**2 = 0. Calculate t.
-5, 0, 1
Let y(m) be the third derivative of 25*m