, 6
Let p(z) be the second derivative of 0*z**2 + 21*z - 3/2*z**3 + 0 - 1/4*z**4. Determine s, given that p(s) = 0.
-3, 0
Determine b so that 4*b**4 + 2*b**3 - 12 + 0*b**4 - 5*b**4 - 15*b - 27*b**2 - 11*b**3 - 16*b = 0.
-4, -3, -1
Let c(v) be the third derivative of -v**5/60 + 5*v**4/12 - 3*v**3/2 + 805*v**2. What is h in c(h) = 0?
1, 9
Suppose -16*b + 3*b = -26. Let u(z) be the first derivative of z**4 - 8*z - 2*z**2 + 8/3*z**3 - b. Factor u(i).
4*(i - 1)*(i + 1)*(i + 2)
Suppose -81*q**3 + 225 + 335*q**3 - 255*q - 31*q**4 - 194*q**2 - 4*q**5 + 3*q**5 + 2*q**5 + 0*q**5 = 0. Calculate q.
-1, 1, 15
Let h(f) be the first derivative of f**3/9 + 5*f**2/6 + 4*f/3 + 11. Factor h(k).
(k + 1)*(k + 4)/3
Let d = 8326/1561 - 2/4683. Let -100/3*b**4 + 64/3*b**2 + d*b + 0 + 20/3*b**3 = 0. What is b?
-2/5, 0, 1
Let x(n) be the third derivative of -11*n**5/120 + 21*n**4/32 + 3*n**3/8 + 280*n**2. Factor x(g).
-(g - 3)*(22*g + 3)/4
Let o = 15406 - 15404. Suppose -1 + f**o + 1/2*f**3 - 1/2*f = 0. Calculate f.
-2, -1, 1
Let p = 242/507 + 32/169. Factor p*y**3 + 8/3*y**2 + 0*y + 0.
2*y**2*(y + 4)/3
Let o(z) be the first derivative of 2*z**3/33 - 36*z**2/11 + 648*z/11 - 181. Let o(q) = 0. What is q?
18
Let a(o) = 7*o - 68. Let b be a(10). Let t = 1 + 0. Find j such that -9/2*j - 7/2*j**b - t = 0.
-1, -2/7
Let u(x) be the second derivative of -x**4/30 + x**3 - 36*x**2/5 - 407*x. Suppose u(m) = 0. What is m?
3, 12
Let x(i) be the second derivative of i**5/5 + 11*i**4/3 + 56*i**3/3 + i + 78. Factor x(y).
4*y*(y + 4)*(y + 7)
Let n = 2449 - 2447. Solve -2/3*p**5 + 10/3*p**4 + 14/3*p**n - 6*p**3 + 0 - 4/3*p = 0.
0, 1, 2
Let m(o) be the first derivative of -3*o**4/16 + 15*o**3/4 + 36*o**2 + 60*o + 66. Factor m(w).
-3*(w - 20)*(w + 1)*(w + 4)/4
Let z(p) be the second derivative of p**4/4 + 34*p**3 - 110*p. Solve z(y) = 0.
-68, 0
Let p be (-1)/(-2)*138*(-220)/42. Let m = p - -362. Find f such that -2/7*f**2 - 2/7 + m*f = 0.
1
Let x be (-16)/(-7) + -13 + 13 + -2. Factor 2/7*q**3 - 2/7*q**2 + 2/7 - x*q.
2*(q - 1)**2*(q + 1)/7
Let d(o) be the first derivative of 4/3*o**3 - 2*o**2 - 32 + 0*o. Let d(v) = 0. Calculate v.
0, 1
Find o such that -12/7 - 2/7*o**3 + 2*o + 0*o**2 = 0.
-3, 1, 2
Suppose -j = 5*p + 15, -p = -j - 7 + 10. Factor j*s - 2/7*s**3 - 2/7*s**2 + 0.
-2*s**2*(s + 1)/7
Let a(k) = 9*k**4 - 63*k**3 + 69*k**2 + 15*k - 5. Let s(b) = b**4 + b**3 + b**2 + 3*b - 1. Let l(y) = a(y) - 5*s(y). Factor l(f).
4*f**2*(f - 16)*(f - 1)
Let y be (-45 + 23 - -22)/11. Find o such that y + 8/7*o - 2/7*o**2 = 0.
0, 4
Let m(f) be the second derivative of -f**5/4 - 25*f**4/24 - 5*f**3/3 + 7*f**2/2 - 11*f. Let c(r) be the first derivative of m(r). Find i such that c(i) = 0.
-1, -2/3
Let a be 30/56 - (-12 + 860/70). Let w(c) be the first derivative of -9 + 0*c + 4/3*c**3 + 0*c**2 - a*c**4. Factor w(v).
-v**2*(v - 4)
Solve -6 + 19 + 141*d - 285*d + 320*d**2 + 36*d**3 + 3 - 81*d**4 = 0.
-2, 2/9, 2
Let s(l) be the second derivative of 0*l**2 + 1/14*l**4 + 21*l + 0 + 1/70*l**5 + 2/21*l**3. Suppose s(t) = 0. What is t?
-2, -1, 0
Let a(f) be the second derivative of f**4/12 - 106*f**3/3 + 5618*f**2 - 94*f. Determine y, given that a(y) = 0.
106
Let d(v) = v**3 - 5*v**2 - v + 7. Let r be d(5). Suppose 52 - 8*h - 26 - 32 - 2*h**r = 0. Calculate h.
-3, -1
Let s(h) be the third derivative of h**6/420 + h**5/30 + h**4/6 + 8*h**3/21 + 106*h**2. Determine t, given that s(t) = 0.
-4, -2, -1
Determine y so that -306*y**2 + 488 + 956*y - 10901*y**3 + 10911*y**3 - 56 = 0.
-2/5, 4, 27
Let g(q) = 5*q**4 + 131*q**3 - 186*q**2 - 45*q + 91. Let c(f) = f**4 - f**3 + 3*f + 1. Let w(y) = 2*c(y) + 2*g(y). Solve w(n) = 0 for n.
-23, -2/3, 1
Suppose -3*f = -5*x - 14, f - 2*x - 17 = -4*f. Let l = f + -1. Solve 3*t**3 - 3*t**5 - 5*t**4 - 3*t**l + 4*t**4 + 4*t**4 = 0.
-1, 0, 1
Let m(x) be the second derivative of 28561*x**6/285 + 8788*x**5/95 + 676*x**4/19 + 416*x**3/57 + 16*x**2/19 - 2*x - 2. Factor m(z).
2*(13*z + 2)**4/19
Let c(y) be the first derivative of 0*y**3 + 1/39*y**6 + 0*y**2 + 2/65*y**5 + 4 + 0*y + 0*y**4. What is o in c(o) = 0?
-1, 0
Let a = 18916 - 18913. Suppose 24/7 - 40/7*k + 22/7*k**2 - 4/7*k**a = 0. What is k?
3/2, 2
Let y be (-51)/((-8211)/184)*(-7)/(-4). Factor -4/3 + 2*z - 2/3*z**y.
-2*(z - 2)*(z - 1)/3
Let n(c) = 5*c - 1. Let v be n(1). Suppose -3*i + 3*l - 6 = 0, l - v*l = i - 14. Suppose 8*g**2 - g + g - i*g - 8*g**3 = 0. Calculate g.
0, 1/2
Let c = -32 - -34. Factor -10 - 5*s - 3*s**2 + 10*s**c + 3*s**2 + 5*s**3.
5*(s - 1)*(s + 1)*(s + 2)
Factor 128/5 + 288/5*q + 162/5*q**2.
2*(9*q + 8)**2/5
Let y be 8*(6/12 + 2 - 2). Let d(p) be the first derivative of -y*p + 2*p**2 + 1/5*p**5 + p**3 - p**4 + 1. Factor d(r).
(r - 2)**2*(r - 1)*(r + 1)
Let a(i) be the third derivative of -1/16*i**3 + 25*i**2 + 0*i + 0 + 3/64*i**4 + 1/320*i**6 - 3/160*i**5. Suppose a(n) = 0. Calculate n.
1
Suppose 20*p = -700 - 980. Let c be p/22 - ((-3 - -4) + -5). Factor 0*a**2 - c*a**3 + 0 + 2/11*a.
-2*a*(a - 1)*(a + 1)/11
What is a in 14*a + 71965*a**2 - 17 + 2 - 71964*a**2 = 0?
-15, 1
Determine r so that 1/3*r**2 + 5/3 - 2*r = 0.
1, 5
Let t(y) be the third derivative of 4*y**8/21 + 16*y**7/105 - 21*y**6/10 - 32*y**5/15 - 2*y**4/3 + y**2 + 42. Solve t(n) = 0 for n.
-2, -1/4, 0, 2
Let v(c) be the first derivative of 4*c**2 - 6*c**2 + 40 + c**4 - 6. Factor v(u).
4*u*(u - 1)*(u + 1)
Let w(i) = 2*i + 3*i - 14 + 10*i - i**3 - 7*i**2 - 8*i**2. Let p be w(-16). Factor -75/4*g**4 - p*g - 55/2*g**3 - 13*g**2 + 0.
-g*(3*g + 2)*(5*g + 2)**2/4
Let w = 72 - 56. Suppose 0 = -b + 18 - w. Factor -1/3 - g - 2/3*g**b.
-(g + 1)*(2*g + 1)/3
Let g = 9 + 40. Determine k, given that 34*k**3 - g*k**2 - 314*k**2 + 32*k**3 - 3*k**4 = 0.
0, 11
Let x = 3899107/7984730 - 4/46969. Let v = x + 1/85. Find a such that -a**4 + 0 + 0*a + v*a**3 + 0*a**2 + 1/2*a**5 = 0.
0, 1
Let z(j) be the third derivative of -13*j**2 + 1/672*j**8 - 1/30*j**5 + 5/48*j**4 + 0*j + 1/105*j**7 - 1/40*j**6 + 0 + 0*j**3. Factor z(o).
o*(o - 1)**2*(o + 1)*(o + 5)/2
Let q = 1205127/311 + -3875. Let c = q - -5588/1555. Factor -6/5*a - 2/5*a**3 - 2*a**2 + c.
-2*(a - 1)*(a + 3)**2/5
Let u be 6/21 + 10/14 + 2. Suppose -u*z = -r - 11, 3*z - 27 = 2*r - 5*r. Factor -16/3*m + 8/3 - 46/3*m**2 + 110/3*m**4 + 38/3*m**3 + 50/3*m**z.
2*(m + 1)**3*(5*m - 2)**2/3
Let w(q) be the first derivative of -q**5/100 - q**4/5 - 3*q**3/2 - 5*q**2 - 33*q + 32. Let o(k) be the first derivative of w(k). Factor o(s).
-(s + 2)*(s + 5)**2/5
Suppose 0*r - 16 = -4*r. Suppose -4 = -r*l + 2*l. What is f in 0*f**2 - 2*f**3 + 77*f + l*f**2 - 73*f = 0?
-1, 0, 2
Suppose -g = r - 8, -4*g = g - 5*r. Factor -28*b**2 + 6 + 6 + 28*b + 48*b**2 + g*b**3.
4*(b + 1)**2*(b + 3)
Let b be (-22)/165 + 204/855. Factor -4/19*z**4 - b*z**5 + 0 + 0*z**3 + 4/19*z**2 + 2/19*z.
-2*z*(z - 1)*(z + 1)**3/19
Let j(p) be the first derivative of 2*p**5/15 + p**4/6 - 2*p**3/3 - 5*p**2/3 - 4*p/3 - 134. Factor j(z).
2*(z - 2)*(z + 1)**3/3
Let j(p) = -p**4 - 21*p**3 - 8*p**2. Let w(c) = 418*c**2 + 416*c**2 + c**4 + 10*c**3 - 830*c**2. Let s(f) = 2*j(f) + 5*w(f). What is n in s(n) = 0?
-2, -2/3, 0
Let m(z) = 3*z**4 + 15*z**3 - 3*z**2 - 15*z - 2. Let v(y) = -39*y**4 - 195*y**3 + 39*y**2 + 195*y + 27. Let b(a) = 27*m(a) + 2*v(a). Factor b(l).
3*l*(l - 1)*(l + 1)*(l + 5)
Let n(x) = 5*x**4 - 80*x**3 - 125*x**2 - 65*x + 25. Let d(q) = -q**4 + 20*q**3 + 31*q**2 + 16*q - 6. Let f = -77 + 52. Let t(p) = f*d(p) - 6*n(p). Factor t(a).
-5*a*(a + 1)**2*(a + 2)
Let l be 115/10 - 2/(-4). Let p = -6 + l. Factor 0 - 9/2*x**3 + 0*x - x**2 - p*x**4 - 5/2*x**5.
-x**2*(x + 1)**2*(5*x + 2)/2
Let g(z) be the first derivative of z**6/540 - z**5/45 + z**4/12 - 19*z**3/3 - 31. Let k(n) be the third derivative of g(n). Suppose k(b) = 0. What is b?
1, 3
Let f(z) = 5*z**4 - 35*z**3 + 65*z**2 - 55*z + 20. Let g(y) = 3*y**3 + 0*y**3 + y - 4*y**3 + 0*y**3. Let b(m) = -f(m) + 5*g(m). Factor b(a).
-5*(a - 2)**2*(a - 1)**2
Let q(t) be the second derivative of t**5/30 + 23*t**4/18 + 40*t**3/3 - 48*t**2 + 2*t - 6. Determine x, given that q(x) = 0.
-12, 1
Suppose -284*b + 286*b + 4*k = 8, -4*b - 5*k + 10 = 0. Suppose 0*q**4 + 1/2*q + 0 + 1/2*q**5 - q**3 + b*q**2 = 0. Calculate q.
-1, 0, 1
Let u(b) be the third derivative of b**7/630 + b**6/180 - b**5/15 - 5*b**4/24 + 9*b**2. Let q(d) 