
Let w(c) be the third derivative of -c**7/630 - c**6/60 + c**5/180 + c**4/12 - 5*c**2 + 46. Determine y, given that w(y) = 0.
-6, -1, 0, 1
Let t = 7 - 19. Let l(d) = 12*d**5 + 16*d**4 + 10*d**3 - 2*d**2. Let m(r) = r**5 - r**4 - r**3 + r**2. Let c(j) = t*m(j) + 2*l(j). What is f in c(f) = 0?
-2, 0, 1/3
Suppose -11*t + 17*t + 1854 = 0. Let j = t - -1551/5. Factor -3/5 - 3/5*m**2 + j*m.
-3*(m - 1)**2/5
Let g(l) = -7*l + 28. Let o be g(4). Let p(i) be the first derivative of 1/18*i**3 + o*i - 6 + 1/6*i**2. Factor p(r).
r*(r + 2)/6
Let g(z) be the first derivative of 5/2*z**6 + 36*z**2 + 81/5*z**5 + 165/4*z**4 + 53*z**3 - 16 + 12*z. Factor g(m).
3*(m + 1)**3*(m + 2)*(5*m + 2)
Suppose 10*b - 16*b - b = -28. What is g in -2/21*g**b + 0*g + 4/21*g**2 + 0 + 2/21*g**3 = 0?
-1, 0, 2
Let t(r) be the third derivative of 0*r + 3/40*r**5 + 0 - 2*r**3 - 1/8*r**4 + 5*r**2. Factor t(f).
3*(f - 2)*(3*f + 4)/2
Let m(z) be the second derivative of -11*z**5/15 + z**4/3 - 7*z**2/2 - 6*z. Let n(u) be the first derivative of m(u). Suppose n(w) = 0. What is w?
0, 2/11
Let g(q) be the second derivative of q**4/4 - 99*q**3 + 29403*q**2/2 - 3*q + 202. Factor g(d).
3*(d - 99)**2
Let u(r) = -r**3 - 2*r**2 - 1. Let p(l) = 5*l**3 - 4*l**2 + 21*l - 6. Let y(k) = -p(k) - 4*u(k). Factor y(a).
-(a - 10)*(a - 1)**2
Let o(p) be the first derivative of -p**4/2 + 50*p**3/3 + 54*p**2 - 559. Factor o(j).
-2*j*(j - 27)*(j + 2)
Let x be ((-3)/10)/((-63)/84). Factor 8/5*p - 16/5 - x*p**3 + 4/5*p**2.
-2*(p - 2)**2*(p + 2)/5
Let n(o) be the first derivative of -o**3/3 + 3*o**2/2 - 2*o - 288. Find j such that n(j) = 0.
1, 2
Factor 2/9*p**4 + 8/9*p**3 - 8/9 - 8/9*p + 2/3*p**2.
2*(p - 1)*(p + 1)*(p + 2)**2/9
Let c(n) = 2*n**3 - 3*n**2 + 2*n. Let y be c(2). Determine o so that 204 - 12*o**3 - 2*o**5 - 2*o + y*o**4 - 204 + 8*o**2 = 0.
0, 1
Let k(i) = i**4 - 2*i**2 - 2*i. Let w(m) = 20*m**4 + 204*m**3 - 152*m**2 - 48*m. Let d(o) = -8*k(o) - w(o). Find n such that d(n) = 0.
-8, -2/7, 0, 1
Let u(x) = 12*x**2 - 64*x + 48. Let c(z) = -4*z**2 + 21*z - 16. Let a(v) = -16*c(v) - 5*u(v). Factor a(j).
4*(j - 2)**2
Factor 211*k - 1 - 190*k + 7 - k**3 + 12 - 2*k**3.
-3*(k - 3)*(k + 1)*(k + 2)
Let s(w) be the second derivative of -1/2*w**2 + 0*w**3 + 1/105*w**6 + 0 + 1/210*w**5 + 8*w + 0*w**4. Let j(a) be the first derivative of s(a). Factor j(c).
2*c**2*(4*c + 1)/7
Let n(m) be the third derivative of 0*m**3 + 0*m**4 + 11/540*m**6 + 0*m + 0 + 1/216*m**8 - 1/135*m**5 - 16/945*m**7 - 7*m**2. What is u in n(u) = 0?
0, 2/7, 1
Let k(g) be the second derivative of 0 - 14*g + 1/30*g**6 + 0*g**3 + 0*g**2 + 1/20*g**5 + 0*g**4. Let k(h) = 0. What is h?
-1, 0
Let v(w) be the second derivative of -w**5/5 - 99*w**4 - 19602*w**3 - 1940598*w**2 - 5*w - 4. Let v(i) = 0. What is i?
-99
Let w(b) be the second derivative of b**7/126 - b**6/45 - b**5/60 + b**4/18 - 6*b - 2. Factor w(f).
f**2*(f - 2)*(f - 1)*(f + 1)/3
Let s be ((-57)/(-6) + 4)*(-6)/(-36). Let x(o) be the first derivative of -s*o**4 + o**3 - 3 + 0*o + 0*o**2. Factor x(p).
-3*p**2*(3*p - 1)
Let h(k) be the third derivative of -k**7/1470 - k**6/420 + k**5/21 - k**4/7 - 7*k**2 - 3. Factor h(a).
-a*(a - 2)**2*(a + 6)/7
Let 0*b**4 + 360/11*b**3 + 12/11 + 340/11*b**2 - 54/11*b**5 + 10*b = 0. Calculate b.
-2, -1/3, 3
Let z(i) be the third derivative of 0 + 11*i**2 - 1/6*i**4 + 0*i - 1/3*i**3 - 1/30*i**5. Factor z(u).
-2*(u + 1)**2
Suppose 3*a - 2 = z - 8, z + 2*a - 1 = 0. Let g(d) be the second derivative of 0*d**z + 0 + 2*d - 1/66*d**4 + 0*d**2. Solve g(h) = 0 for h.
0
Suppose 0 = -5*w - m + 15, 6*m + 9 = 3*w + 4*m. Let p be (0 + (-4)/w)*-12. Suppose -p + 4*v**2 - 60*v**3 + 17*v + 31*v + 0*v**2 = 0. What is v?
-1, 2/5, 2/3
Let y(w) be the second derivative of -w**6/24 - w**5/12 - 13*w**2/2 - 4*w. Let g(k) be the first derivative of y(k). Factor g(a).
-5*a**2*(a + 1)
Factor 2/9*d**4 + 0 + 0*d - 52/9*d**2 + 50/9*d**3.
2*d**2*(d - 1)*(d + 26)/9
Suppose -14 = -r + 11. Let h = 76/3 - r. Determine m so that 0*m - h*m**2 + 1/3 = 0.
-1, 1
Let d = 7 - 5. Factor 15*m**d + m**3 + 4*m**3 - 235*m + 245*m.
5*m*(m + 1)*(m + 2)
Suppose -f = 4*f - 10. Suppose 4*u - 38 = -2*g, 0*u + 3*u = f*g + 18. Factor -3*i**2 - 1 + u*i + i**2 - i**3 - i**3 + 9.
-2*(i - 2)*(i + 1)*(i + 2)
Let w(h) be the third derivative of h**6/480 + 3*h**5/80 - h**4/2 + 13*h**3/6 - 9*h**2. Suppose w(i) = 0. Calculate i.
-13, 2
Let b(v) = 4*v**4 + 2*v**3 - v**2 + 4*v. Let q(d) = 5*d**4 + 3*d**3 - d**2 + 5*d. Suppose -2*s - 4 + 10 = 0. Let u(f) = s*q(f) - 4*b(f). Factor u(i).
-i*(i - 1)**2*(i + 1)
Let j(c) = c**2 + 8*c - 4. Let p be j(-9). Find q, given that -10*q**2 + 16*q**p + 0*q**3 - 5*q**3 - 11*q**5 + 10*q**4 = 0.
-2, -1, 0, 1
Let d(n) be the second derivative of -13*n - 1/7*n**3 - 1/4*n**4 + 2/35*n**6 + 3/28*n**5 + 0 + 0*n**2. Determine m, given that d(m) = 0.
-2, -1/4, 0, 1
Let y(l) be the third derivative of 1/504*l**8 + 2/315*l**7 - 1/45*l**5 + 0 + 0*l**6 - 1/36*l**4 + 10*l**2 + 0*l + 0*l**3. Suppose y(p) = 0. Calculate p.
-1, 0, 1
Let t(x) = -434*x - 6072. Let s be t(-14). Solve 3/2*o - 3/2*o**3 + 1/2*o**2 + 1/2*o**s - 1 = 0.
-1, 1, 2
Suppose -6*v = -9*v + 6. Let r = -3 + 6. Determine l, given that -5*l**2 - 2 - 7*l**v - 8*l + 2*l**4 - 4*l**4 - 8*l**r = 0.
-1
Let h be (6/110)/(4/(-10) + (-14)/(-28)). Factor -4/11*s**5 - 2/11*s**2 + 10/11*s**4 + 2/11*s - h*s**3 + 0.
-2*s*(s - 1)**3*(2*s + 1)/11
Let i(c) be the second derivative of c**5/110 + 2*c**4/11 + 16*c**3/11 + 64*c**2/11 + 2*c - 28. Factor i(o).
2*(o + 4)**3/11
Suppose -4*l + 7*p = 2*p - 27, 2*l = 3*p + 15. Factor -3*h + 6*h**l + 0*h + 2*h + 3*h**5 + 8*h**4 + 0*h**5.
h*(h + 1)**3*(3*h - 1)
Let s = 7 + -5. Let u = 50 - 44. Factor 3*g**4 - g**2 - u*g**s - 2*g**2 - 6*g.
3*g*(g - 2)*(g + 1)**2
Factor 10*k**3 - 13*k**3 + 160*k**2 + 48*k - 11*k**3 - 8*k**3 - 6*k**3.
-4*k*(k - 6)*(7*k + 2)
Let -363/4 - 75/4*w**2 - 165/2*w = 0. What is w?
-11/5
Let v(f) = -12*f**4 - 28*f**3 + 20*f**2 + 100*f + 40. Let i(w) = -4*w. Let u(z) = 6*i(z) + v(z). Solve u(a) = 0.
-2, -1, 5/3
Let g be -6*((-4)/(-8))/((-3)/2). Factor -1 + 45*f**2 - 10 - 24*f - 49*f**g.
-(2*f + 1)*(2*f + 11)
Suppose -v + 14 = 5*h - 9, -3*v - 6 = 0. Suppose z**3 - 13*z**3 + 2*z**4 - 761*z**5 + 763*z**h = 0. What is z?
-3, 0, 2
Let z(s) be the first derivative of -s**9/1008 - s**8/560 + s**7/280 + s**6/120 + 7*s**3/3 - 17. Let j(p) be the third derivative of z(p). Factor j(a).
-3*a**2*(a - 1)*(a + 1)**2
Suppose 5*t + 1434 = 2*j + 1441, -j - 11 = -5*t. What is u in 3/2*u**j - 8*u - 16/3*u**3 - 1/6*u**5 + 28/3*u**2 + 8/3 = 0?
1, 2
Let i(r) be the second derivative of r**7/2940 - r**6/315 + r**5/84 - r**4/42 - r**3/3 + 9*r. Let b(k) be the second derivative of i(k). What is d in b(d) = 0?
1, 2
Factor 0 + 8/5*j**4 + 0*j - 1/5*j**5 + 19/5*j**3 + 2*j**2.
-j**2*(j - 10)*(j + 1)**2/5
Find l, given that 12/7*l**2 - 16/7*l + 4/7*l**3 - 48/7 = 0.
-3, -2, 2
Let k(b) be the second derivative of 12*b + 0*b**2 - 1/48*b**4 + 0 + 0*b**3. Factor k(z).
-z**2/4
Let g(x) be the second derivative of 0 + 1/2*x**3 + x**2 + 1/12*x**4 + 10*x. Find s such that g(s) = 0.
-2, -1
Let z = -486 + 332. Let c = z - -470/3. Factor -2/3*v**2 - c*v - 8/3.
-2*(v + 2)**2/3
Suppose -v + 58 = 3*l + 42, -2*l = 5*v - 28. Let b(h) be the second derivative of 1/6*h**3 + 5*h + 0*h**2 - 1/12*h**v + 0. Solve b(y) = 0 for y.
0, 1
Let x(v) be the first derivative of 2*v**3/21 + 9*v**2/7 + 119. Determine m so that x(m) = 0.
-9, 0
Let n = -107 + 110. Let m(p) be the first derivative of -n*p + 1 - 1/2*p**6 - 3/5*p**5 + 3/2*p**4 - 3/2*p**2 + 2*p**3. Suppose m(f) = 0. What is f?
-1, 1
Let x(t) be the third derivative of -5*t**8/336 + t**7/14 + 7*t**6/24 - 9*t**5/4 + 15*t**4/4 - 65*t**2. Determine h so that x(h) = 0.
-3, 0, 1, 2, 3
Let h(y) = -1. Let k(j) = -3*j - 10. Let v(d) = -6*h(d) + k(d). Let b be v(-2). Factor 2*w + 8*w**3 + 12*w**2 + 2*w + b + 2*w**4 + 0*w + 4*w.
2*(w + 1)**4
Let f = -18418 - -18421. What is x in 3/4*x**4 - 9/4*x - 3/4*x**2 + 0 + 9/4*x**f = 0?
-3, -1, 0, 1
Suppose 0 = 4*q + 39*i - 43*i - 44, 0 = -3*q - 5*i - 31. Factor 6/5*f**2 - 3/5*f**3 + q*f - 18/5.
-3*(f - 3)*(f - 1)*(f + 2)/5
Let r(w) = 2*w**3 - 93*w**2 + 155*w - 900. Let j be r(45). Solve 3/4*q**4 + 0*q**3 + j*q - 3/2*q**2 + 3/4 = 0 for q.
-1, 1
Suppose -c - 270 = -6*c. Let