0. Let q(p) be the first derivative of -16/3*p - 8/3*p**2 - 4/9*p**t + 4. Determine a, given that q(a) = 0.
-2
Let g(r) be the first derivative of r**5/10 - r**4/6 - r**3/3 + r**2 + 38*r - 22. Let a(k) be the first derivative of g(k). Factor a(f).
2*(f - 1)**2*(f + 1)
Let w be (7 + 468/(-65))*(-20)/6. Let n(d) be the first derivative of -w*d + 2/3*d**2 - 2/9*d**3 - 5. Determine h, given that n(h) = 0.
1
Suppose 14*k - 10*k = k. Find y such that 4/7*y + k + 2/7*y**3 + 6/7*y**2 = 0.
-2, -1, 0
Determine g, given that -6/5*g**5 + 21*g**4 - 348/5*g**2 - 426/5*g**3 + 432/5*g + 243/5 = 0.
-1, -1/2, 1, 9
What is c in -8/5*c - 4/5*c**4 - 4*c**2 - 16/5*c**3 + 0 = 0?
-2, -1, 0
Let r(g) be the first derivative of -2*g**3/11 + 228*g**2/11 - 8664*g/11 - 230. Factor r(n).
-6*(n - 38)**2/11
Let f(j) be the first derivative of j**7/14 - 3*j**6/10 + 9*j**5/20 - j**4/4 - 2*j - 11. Let p(q) be the first derivative of f(q). What is g in p(g) = 0?
0, 1
What is q in -16*q**2 + 172912*q**3 + 8*q - 172914*q**3 + 60 + 38*q = 0?
-10, -1, 3
Let a(m) = 4*m**3 + 32*m**2 - 40*m - 44. Let q(t) = 3*t**3 + 30*t**2 - 39*t - 46. Let j(g) = -5*a(g) + 6*q(g). Factor j(z).
-2*(z - 7)*(z - 4)*(z + 1)
Factor -15360*u**2 - u**4 + 15360*u**2 + 5*u**3.
-u**3*(u - 5)
Factor -2/5*c**2 - 4/5*c + 2/5*c**3 + 0.
2*c*(c - 2)*(c + 1)/5
Let w be (6/(-9)*1)/(-5). Suppose 552*q - 568*q = 0. Factor 2/15*z**5 - 2/15*z**2 + 2/15*z**4 - w*z**3 + q + 0*z.
2*z**2*(z - 1)*(z + 1)**2/15
Let s be 4/8*(0 - 0). Suppose 6*r + 118*r = 27*r. Factor 2/3*d**4 + 0*d**2 + r*d + s - 2/3*d**3.
2*d**3*(d - 1)/3
Suppose -6*l - 30 = -21*l. Solve -2/9*b**l + 0*b + 0 = 0 for b.
0
Let t(g) be the first derivative of 5*g**3 - 33*g**2 + 72*g + 364. Determine l so that t(l) = 0.
2, 12/5
Let g = -83 - -93. Factor -g - 6*t + 3*t**2 + 0*t**2 - 14.
3*(t - 4)*(t + 2)
Suppose o + 5*m - 22 = -0*m, -o + 5*m = 18. Let x be 8 + -4 - 0/o. Determine d so that -6*d**2 + 9*d**2 + 8 - 4*d**x + 9*d**2 - 20*d + 4*d**3 = 0.
-2, 1
Let x(u) = u**3 - 6*u**2 - 4*u + 14. Let z be x(7). Suppose -z*l - 70 = -40*l. What is f in -4*f - l*f**2 - 2/7 = 0?
-1/7
Let c(y) be the third derivative of 31*y**7/105 - 11*y**6/10 + 4*y**5/15 - 16*y**2. Factor c(o).
2*o**2*(o - 2)*(31*o - 4)
Determine i so that 12 + 30 - 30*i + 3*i**2 + 6 = 0.
2, 8
Let -804/7*r + 13467/7*r**2 + 12/7 = 0. What is r?
2/67
Let g(c) be the second derivative of -9*c**5/40 + 11*c**4/8 + c**3 - 866*c. Factor g(o).
-3*o*(o - 4)*(3*o + 1)/2
Let o(j) be the third derivative of -11/40*j**6 + 0*j + 2*j**2 - 3/35*j**7 + 3/2*j**4 + 0 - 1/10*j**5 + 4*j**3 - 1/112*j**8. Suppose o(z) = 0. What is z?
-2, -1, 1
Let z(s) be the first derivative of 7*s**2 - 12*s - 30 - 2/3*s**3. Suppose z(t) = 0. What is t?
1, 6
Let u(c) be the first derivative of c**7/168 + c**6/36 - c**5/8 - 7*c**3/3 + 6. Let y(v) be the third derivative of u(v). Solve y(p) = 0.
-3, 0, 1
Let r(a) = a**3 + a. Let b be (-3)/(-4)*(5 + 3). Let l(x) = -b*x**2 - 1 + 4*x + 8*x**3 + 1 - 2*x**3. Let j(q) = -l(q) + 8*r(q). Factor j(z).
2*z*(z + 1)*(z + 2)
Let g = -495 + 499. Let a(r) be the second derivative of r - 1/6*r**4 + 0 - g*r**2 - 4/3*r**3. Factor a(n).
-2*(n + 2)**2
Let n(a) be the third derivative of a**7/252 + a**6/360 - a**4/24 - 6*a**2. Let c(h) be the second derivative of n(h). Suppose c(i) = 0. What is i?
-1/5, 0
Let l(c) be the third derivative of -c**7/42 + c**6/24 + 5*c**5/12 + 5*c**4/8 + 38*c**2. Let l(g) = 0. Calculate g.
-1, 0, 3
Let n(a) be the third derivative of a**6/40 + 7*a**5/20 + a**4 - 8*a**3 - 549*a**2. Determine j, given that n(j) = 0.
-4, 1
Let c(i) = -1039*i + 9354. Let s be c(9). Determine f so that 0 - 1/5*f**s - 1/5*f**5 + 0*f**2 + 2/5*f**4 + 0*f = 0.
0, 1
Suppose 0 = 97*n - 86*n. Factor 4/7*c**2 + n*c + 32/7*c**4 + 2*c**5 + 22/7*c**3 + 0.
2*c**2*(c + 1)**2*(7*c + 2)/7
Let k(x) be the third derivative of x**8/80640 + x**7/3360 + x**6/360 - 3*x**5/5 - 16*x**2. Let v(m) be the third derivative of k(m). Solve v(b) = 0 for b.
-4, -2
Suppose o = -3*o - 5*v, 4*v = -o. Let m(p) be the second derivative of 0 - 1/48*p**4 + 3*p + o*p**2 - 1/12*p**3. Determine i, given that m(i) = 0.
-2, 0
Suppose -s - 5 = 67. Let g = s + 28. Let a(t) = -2*t**2 - 22*t - 20. Let y(b) = b + 1. Let o(h) = g*y(h) - 2*a(h). Factor o(v).
4*(v - 1)*(v + 1)
Let j(s) = s**3 - 24*s**2 - s + 32. Let l be j(24). Factor -43*z + l*z**2 + 83*z - 44*z - 12.
4*(z + 1)*(2*z - 3)
Let q(l) = -17*l**3 + 307*l**2 - 2243*l. Let d(p) = 8*p**3 - 153*p**2 + 1122*p. Let h(c) = -7*d(c) - 3*q(c). Let h(t) = 0. Calculate t.
0, 15
Let a(r) be the third derivative of r**8/1008 - 2*r**7/315 - r**6/180 + r**5/15 + r**4/8 + 91*r**2. Factor a(w).
w*(w - 3)**2*(w + 1)**2/3
Let j(s) be the second derivative of 2*s**5/15 - 7*s**4/6 + 2*s**3 - 4*s**2 - 20*s. Let f(z) be the first derivative of j(z). Factor f(t).
4*(t - 3)*(2*t - 1)
Let p(o) = o**2 + 23*o - 58. Let i(q) = -q**2 - 47*q + 118. Let r(s) = -2*i(s) - 5*p(s). Factor r(l).
-3*(l - 2)*(l + 9)
Let x(z) = -z + 8. Let s = -17 + 22. Let d be x(s). Solve -3*h**5 - d*h**2 + h - h**3 - 9*h**4 - 8*h**3 - h = 0.
-1, 0
Let i = 76/7 + -670/63. Let f = -48308/9 - -5368. Find x such that 0 - f*x - i*x**2 = 0.
-2, 0
Let r(c) be the first derivative of 5/12*c**4 - 11 + 1/15*c**5 + 7/6*c**2 + c**3 + 2/3*c. Factor r(d).
(d + 1)**3*(d + 2)/3
Factor -64 + 28*n - 14*n**2 - 21*n**2 - 23*n**2 + 60*n**2.
2*(n - 2)*(n + 16)
Let z(t) = 2*t**4 - t**3 - 9*t**2 + 3*t + 5. Let i(u) = u + 6*u**4 + 2 + 12*u**4 - u**2 - 1 - 19*u**4. Let y(l) = 2*i(l) - z(l). Find g, given that y(g) = 0.
-1, -3/4, 1
Let s(c) be the first derivative of 5*c**6/18 + c**5 + 5*c**4/12 - 5*c**3/3 - 5*c**2/3 - 177. Determine j, given that s(j) = 0.
-2, -1, 0, 1
Let u be -4*((-171)/66 + (-11)/(88/(-20))). Find d such that 0*d**2 - u*d**3 + 0*d + 0 - 10/11*d**4 = 0.
-2/5, 0
Factor 0*g**3 + 29/2*g**2 - 1/4*g**5 - 79/4*g - 2*g**4 + 15/2.
-(g - 1)**3*(g + 5)*(g + 6)/4
Let n(g) be the second derivative of 0*g**3 + 0 - 5*g - 1/160*g**6 + 1/20*g**5 + 2*g**2 - 3/32*g**4. Let p(j) be the first derivative of n(j). Factor p(i).
-3*i*(i - 3)*(i - 1)/4
Let w be (-20)/(-160) - (10/(-16))/(-5). Let p(x) be the third derivative of 0 + 0*x**6 + w*x**4 - 7*x**2 + 0*x**3 + 0*x**5 - 1/420*x**7 + 0*x. Factor p(z).
-z**4/2
Let h(d) be the first derivative of 1/5*d - 4 - 1/15*d**3 - 1/10*d**2 + 1/20*d**4. Factor h(p).
(p - 1)**2*(p + 1)/5
Let i(f) be the second derivative of f**8/4200 + f**7/2100 - f**6/900 - f**5/300 - 5*f**3/3 + 13*f. Let m(j) be the second derivative of i(j). Factor m(b).
2*b*(b - 1)*(b + 1)**2/5
Let f(h) be the first derivative of 4/5*h**5 - 8*h**2 - 44 - 4*h**4 + 8*h**3 + 4*h. Factor f(d).
4*(d - 1)**4
Factor 141*k**2 - 9*k - 18 - 36*k**3 + 51*k**2 - 156*k - 43*k + 82.
-4*(k - 4)*(3*k - 2)**2
Let y(b) be the third derivative of -b**5/450 + b**4/15 + b**3 + 4*b**2 + 17*b. Let y(h) = 0. What is h?
-3, 15
Factor -205932/7 - 1572/7*r - 3/7*r**2.
-3*(r + 262)**2/7
Let w(c) be the third derivative of c**6/720 + c**5/72 + 7*c**4/144 + c**3/12 + c**2 - 447*c. Determine y so that w(y) = 0.
-3, -1
Let z(g) be the second derivative of 5*g**4/24 - 25*g**3/3 + 45*g**2 + g - 46. Let z(j) = 0. What is j?
2, 18
Suppose 0*v**3 - 4*v**3 + 354*v**2 + 280*v**2 + 318*v**2 - 844*v**2 = 0. Calculate v.
0, 27
What is y in y**2 + 0 + 3*y + 1/3*y**4 - 5/3*y**3 = 0?
-1, 0, 3
Solve 6*p**2 + 1/2*p**3 + 41/2*p + 21 = 0 for p.
-7, -3, -2
Let y(l) = 103*l**2 + 2350*l + 12680. Let f(i) = 102*i**2 + 2352*i + 12681. Let v(o) = 5*f(o) - 6*y(o). Let v(h) = 0. Calculate h.
-65/6
Suppose 10*s - 41 = -1. Factor -7*h**2 + 4*h**2 + s*h + 6*h - 42*h**2.
-5*h*(9*h - 2)
Let b(g) = 11*g + 685. Let d be b(-62). Let u(z) be the first derivative of -2/9*z**d + 12 - 1/6*z**2 + 1/12*z**4 + 2/3*z. Find n, given that u(n) = 0.
-1, 1, 2
Factor 1/3*p**3 - 25/3 - 9*p**2 + 17*p.
(p - 25)*(p - 1)**2/3
Let f(k) = -2*k**4 + 2*k**3 + 10*k**2 + 6*k - 5. Let w(o) = o**4 - o**3 - 5*o**2 - 3*o + 3. Let b(h) = -3*f(h) - 5*w(h). Suppose b(x) = 0. Calculate x.
-1, 0, 3
Let l(b) = b - 1. Let s(n) = 5*n**2 + 788*n + 31207. Let h(d) = -2*l(d) - s(d). Factor h(x).
-5*(x + 79)**2
Let o(i) = -2 + 3 - 2*i**2 + 3*i**2. Let m(g) = 4*g**2 + 2*g + 10. Suppose -16*r + 1 = -15*r. Let k(f) = r*m(f) - 6*o(f). Factor k(x).
-2*(x - 2)*(x + 1)
Let z be 9