 k(z) be the third derivative of m(z). Find x, given that k(x) = 0.
0, 4
Let x = 58 - 55. Suppose 12 = x*j, -4*j + 11 = -3*q + 4. Factor 2/7 + 2/7*l - 2/7*l**2 - 2/7*l**q.
-2*(l - 1)*(l + 1)**2/7
Let c(r) be the third derivative of -r**8/12 + 269*r**7/630 - 7*r**6/12 + r**5/36 + r**4/3 - 2*r**3/9 + 23*r**2. Find k, given that c(k) = 0.
-1/3, 1/4, 2/7, 1, 2
Let g = 8989/12 - 749. Let l(v) be the second derivative of 4*v - 1/6*v**3 + 0 + g*v**4 - v**2. Let l(a) = 0. What is a?
-1, 2
Let r be 2/(-12) + 551/174. Let k be (((-48)/18)/8)/((-4)/9). Factor 3/2 + k*z**2 - 3/2*z**r + 15/4*z.
-3*(z - 2)*(z + 1)*(2*z + 1)/4
Let t(k) be the third derivative of -k**6/60 - 52*k**5/45 - 205*k**4/108 - 34*k**3/27 - k**2 + 138. Factor t(i).
-2*(i + 34)*(3*i + 1)**2/9
Let j = 4446 + -4444. Determine u, given that 0*u + 6/11*u**3 - 14/11*u**j + 8/11 = 0.
-2/3, 1, 2
Suppose -4 = -5*m + 4*c, 2*m - 2*c = -11 + 13. Factor -s + 1/5*s**2 + m.
s*(s - 5)/5
Let d(t) be the second derivative of 1/3*t**3 - 13*t - 1/24*t**4 + 1/4*t**2 + 0 - 1/10*t**5. Factor d(h).
-(h - 1)*(h + 1)*(4*h + 1)/2
Let d be ((-2)/24*-2)/((-172)/(-1376)). Factor 0*z + d*z**3 - 2/3*z**2 + 0 - 2/3*z**4.
-2*z**2*(z - 1)**2/3
Let f(n) = 6*n**2 - 4*n + 2. Let w be f(1). Let r(a) be the second derivative of 1/24*a**4 + 0 + 1/3*a**3 + 3/4*a**2 + w*a. Factor r(g).
(g + 1)*(g + 3)/2
Let i(t) be the third derivative of -t**7/10080 + t**6/720 - t**5/120 + t**4/8 + 12*t**2. Let m(x) be the second derivative of i(x). Let m(d) = 0. What is d?
2
Let m be 6 + -3 + -2 + 0 + 3. Factor 2*p**m + 112*p**3 + p**2 + 4*p - 118*p**3 - 3*p**2 + 2*p**5.
2*p*(p - 1)**2*(p + 1)*(p + 2)
Factor 45*m + 216 - 3/4*m**3 - 3*m**2.
-3*(m - 8)*(m + 6)**2/4
Let p(o) be the second derivative of -o**7/35 - o**6/75 + o**5/30 - o**4/90 - o - 15. Suppose p(w) = 0. What is w?
-1, 0, 1/3
Suppose 8 = -31*v + 23*v. Let d be (-2)/((-2)/(-1))*(1 + v). Solve 2/11*r**3 + 2/11*r**2 - 2/11*r**4 + d - 2/11*r = 0.
-1, 0, 1
Let x be 2 + 2592/624 + 0 + -6. Let x*k**4 + 0*k - 4/13*k**2 + 0 - 2/13*k**3 = 0. What is k?
-1, 0, 2
Let m = 41342 - 41342. Factor m*q**2 - 2/3*q + 1/6*q**3 + 0.
q*(q - 2)*(q + 2)/6
Let g(y) = -4*y**2 + 71*y - 400. Let w(c) = -c**2 + 18*c - 100. Let k(p) = -2*g(p) + 9*w(p). Suppose k(v) = 0. Calculate v.
10
Let d(r) be the third derivative of -r**6/160 + 47*r**5/80 - 2*r**2 + 5*r. Suppose d(f) = 0. What is f?
0, 47
Suppose 4*k + 3*j = 13, 4*j + 5 = -5*k + 21. Factor -3*q**2 + k*q - 3*q**2 + 0*q - 6*q**2.
-4*q*(3*q - 1)
Let d be 5*(-1 + (-28)/(-20)). Find l such that 3*l - 6*l + 4*l**2 + 3*l**3 - 9*l**4 + 5*l**d = 0.
-1, 0, 1/3, 1
Let m = -30390 + 212733/7. Factor 0*y - m*y**2 + 3/7.
-3*(y - 1)*(y + 1)/7
Let d(r) = -20*r**4 - 16*r**3 + 16*r - 4. Let l(o) = -o**4 - o**3 + o. Let z(n) = -n**2 - 3*n + 19. Let g be z(-6). Let q(y) = g*d(y) - 24*l(y). Factor q(u).
4*(u - 1)*(u + 1)**3
Let j(o) = -2*o. Let i(w) = 2*w**3 + 4*w**2 - 10*w. Let f(g) = -2*i(g) + 4*j(g). Factor f(d).
-4*d*(d - 1)*(d + 3)
Let x be -5 + (15 - (-12)/(-15)*10). Factor -6/7*t + 3/7*t**x - 24/7.
3*(t - 4)*(t + 2)/7
Let g = 76/477 - -10/159. Factor 20/9*t + g*t**2 + 50/9.
2*(t + 5)**2/9
Let c(w) be the third derivative of 2*w**7/105 - 41*w**6/30 + 88*w**5/3 - 200*w**4/3 - 588*w**2. Find k, given that c(k) = 0.
0, 1, 20
Determine p, given that 0*p**3 - 12/7 + 20/7*p**2 - 8/7*p**4 + 2/7*p - 2/7*p**5 = 0.
-3, -2, -1, 1
Let n = -1/341 + -878/49445. Let f = 2477/580 + n. Let -b**2 - 5/4*b**5 - f*b**4 + 0*b - 4*b**3 + 0 = 0. Calculate b.
-2, -1, -2/5, 0
Let d be ((-12)/(-21))/(390/42 - 5). Let z(n) be the third derivative of n**2 + 0*n - 1/30*n**4 + d*n**3 + 1/300*n**5 + 0. Suppose z(j) = 0. Calculate j.
2
Let h(a) be the first derivative of a**3/15 - 23*a**2/5 + 529*a/5 - 35. Factor h(j).
(j - 23)**2/5
Let y(m) be the first derivative of -m**6/30 + 68*m**5/25 - 543*m**4/10 - 476*m**3/3 - 245*m**2/2 - 402. Find x such that y(x) = 0.
-1, 0, 35
Let o(b) be the second derivative of -b**6/24 + b**5/10 - b**4/48 - b**3/12 + 2*b - 5. Factor o(h).
-h*(h - 1)**2*(5*h + 2)/4
Determine j, given that -70*j + 165 - j**2 - 240 + j**2 + 5*j**2 = 0.
-1, 15
Let g(k) = -5*k**3 + 61*k**2 - 11*k - 12. Let y be g(12). What is j in 2/3*j**2 - 4/3*j + y + 2/3*j**3 = 0?
-2, 0, 1
Suppose 4/13*v + 0 - 10/13*v**2 + 4/13*v**3 = 0. What is v?
0, 1/2, 2
What is h in 1/2*h**2 + 5*h + 9/2 = 0?
-9, -1
Let j(s) be the second derivative of -s**8/10080 - s**7/945 - s**6/216 - s**5/90 + 3*s**4/4 + 11*s. Let q(g) be the third derivative of j(g). Factor q(r).
-2*(r + 1)**2*(r + 2)/3
Factor 1/2*d**2 - 13 + 25/2*d.
(d - 1)*(d + 26)/2
Let g(q) = -3*q**4 - 6*q**3 + 6*q - 5. Suppose -u + 2*u = -3. Let w(t) = -t**4 - 2*t**3 + 2*t - 2. Let p(m) = u*g(m) + 8*w(m). Solve p(l) = 0.
-1, 1
Let y = -11476 + 80334/7. Factor 0 + 4/7*n - y*n**3 - 2/7*n**2.
-2*n*(n - 1)*(n + 2)/7
Suppose -6 = 5*l - 3*y, 5*l = -2*y - 9 - 12. Let u = 5 + l. Let -6/7*g**u - 2/7*g**4 - 6/7*g**3 + 0 - 2/7*g = 0. Calculate g.
-1, 0
Factor 53*r + 11*r**4 + 0*r**5 - 2*r**5 - 55*r - 12*r**3 + 0*r**5 - 19*r**4 - 8*r**2.
-2*r*(r + 1)**4
Determine n, given that 0*n**2 - n**3 + 1/2*n**4 + 0*n + 1/2*n**5 + 0 = 0.
-2, 0, 1
Suppose 10*v = 23*v - 5*v - 4*v. Determine h, given that 2/5*h**3 + 0 - 1/5*h**2 + v*h - 1/5*h**4 = 0.
0, 1
Let f(s) be the first derivative of -s**6/135 + s**5/45 + 9*s - 14. Let b(v) be the first derivative of f(v). Factor b(q).
-2*q**3*(q - 2)/9
Suppose -3*d - 5*a = -d + 10, 5*d - 45 = 5*a. Factor 11*h**3 - d*h**4 - 6*h**3 - 2*h + 2*h.
-5*h**3*(h - 1)
Let r(w) be the second derivative of -3/80*w**5 + 1/168*w**7 + 0 - 1/48*w**4 + 0*w**2 + 1/12*w**3 + 3*w + 1/120*w**6. Factor r(d).
d*(d - 1)**2*(d + 1)*(d + 2)/4
Let h(r) be the third derivative of r**6/360 + r**5/36 + r**4/9 + 2*r**3/9 - 144*r**2. Factor h(m).
(m + 1)*(m + 2)**2/3
Let k(y) = 2*y**3 - 13*y**2 + 31. Let x(n) = -n**3 + 7*n**2 - 16. Let l(w) = 4*k(w) + 7*x(w). Let j(p) be the first derivative of l(p). Solve j(c) = 0 for c.
0, 2
What is m in 0 - 2/7*m**2 - 26/7*m = 0?
-13, 0
Suppose 5*m - 10 = 0, 0 = -2*z - z - 4*m + 14. Factor 0*x + 5*x + 5*x**z + 3*x**2 - 3*x**2.
5*x*(x + 1)
Let q(k) be the third derivative of k**6/120 - k**5/12 + k**4/4 + 94*k**2. Let i be q(3). Factor i - 4/3*t**4 - 8/3*t**3 + 0*t - 4/3*t**2.
-4*t**2*(t + 1)**2/3
Let y(g) = g**3 - 5*g**2 - 5*g - 4. Let x be y(6). Find z such that -6*z - 4 - 8*z**2 - x*z + 4*z**2 = 0.
-1
Let p(l) be the first derivative of l**3/27 - l**2/9 - 54. Factor p(d).
d*(d - 2)/9
Let j(s) be the third derivative of -1/30*s**5 - 3/7*s**3 + 0 + 0*s - 5/28*s**4 - 17*s**2 - 1/420*s**6. Let j(h) = 0. What is h?
-3, -1
Suppose 2*j**5 - 47*j**2 - 5*j**4 - j**5 + 47*j**2 = 0. Calculate j.
0, 5
Let x(b) = b**2 + 4*b + 6. Let t be x(-4). Suppose -k + t + 4 = 2*y, 14 = 3*y + k. Factor g**2 + 0*g**3 - 14*g**3 + 5*g**2 + 4*g + y*g**2.
-2*g*(g - 1)*(7*g + 2)
Let q(r) = 3*r**2 - 32*r - 15. Let x(v) = -4*v**2 + 47*v + 23. Let p(b) = -7*q(b) - 5*x(b). Factor p(y).
-(y + 1)*(y + 10)
Let n(s) = -4*s**4 - 35*s**3 - 158*s**2 + 190*s. Let g(t) = -3*t**4 - 23*t**3 - 105*t**2 + 126*t. Let w(p) = -7*g(p) + 5*n(p). Solve w(k) = 0 for k.
-4, 0, 1, 17
Let z be -1 - (-58)/56 - 254/(-1016). Factor 0 + 1/7*s**4 - z*s + 5/7*s**2 - 4/7*s**3.
s*(s - 2)*(s - 1)**2/7
What is p in 58/15*p**3 + 1156/5 - 2482/15*p + 50/3*p**2 + 2/15*p**4 = 0?
-17, 2, 3
Let c(y) be the first derivative of y**4/120 + y**3/30 + 16*y - 13. Let n(u) be the first derivative of c(u). Factor n(k).
k*(k + 2)/10
Let c(j) be the first derivative of j**4 + 124*j**3/3 - 2*j**2 - 124*j + 512. Factor c(h).
4*(h - 1)*(h + 1)*(h + 31)
Let y(b) be the first derivative of -2 + 2/5*b**2 + 2/5*b + 2/15*b**3. Factor y(u).
2*(u + 1)**2/5
Let s(q) be the second derivative of 1/84*q**7 + 3/20*q**5 + 19*q + 1/12*q**6 - 1/6*q**4 + 0 + 0*q**2 - 2/3*q**3. Determine h so that s(h) = 0.
-2, 0, 1
Determine w, given that -1/9*w**4 - 16/9 + 2/3*w**3 - 8/3*w - 1/9*w**2 = 0.
-1, 4
Let f(h) = 12*h**2 - 15*h - 12. Let m(c) = 3*c**2 - 4*c - 3. Let i = 29 - 43. Let d = -10 - i. Let w(l) = d*f(l) - 15*m(l). Suppose w(u) = 0. Calculate u.
-1, 1
Let g(n) = n**2 - 6*n - 19. Let s be g(8). Let a be (-3)/(-24) + ((-54)/112)/s. Factor 0*j - a*j**2 + 0 + 2/7*j**4 + 2/7*j**5 - 2/7*j**3.
2*j**2*(j - 1)*(j + 1)**2/7
Let w be (((-4)/5)/2