. Let d(k) = 0. Calculate k.
-2, 11
Let h = 18 + -15. Factor -113 + 51 + h*z**2 + 3*z**4 - 9*z**3 + 56 + 9*z.
3*(z - 2)*(z - 1)**2*(z + 1)
Let z(n) be the third derivative of 0*n**3 + 5*n**2 + 1/168*n**4 + 0*n + 1/420*n**5 + 0. Solve z(m) = 0 for m.
-1, 0
Let d = 9 - 4. Let n = d + -1. Factor 3*a**n - 2*a**4 + a**2 - 2*a**4.
-a**2*(a - 1)*(a + 1)
Let h(o) = -22*o**3 + 36*o**2 - 18*o - 8. Let t(q) = q**3 - q**2 + 1. Let s(a) = -h(a) - 12*t(a). Factor s(m).
2*(m - 1)**2*(5*m - 2)
Let f be 7 - ((-2)/(-17) - 3569/(-731)). Determine m so that 0*m - 1/5*m**3 + 0 - 1/5*m**4 + 1/5*m**f + 1/5*m**5 = 0.
-1, 0, 1
Let u = -52 - -56. Suppose 12 = -0*y + u*y. Factor 0 + 0*p**y + 0*p + 2/3*p**2 - 2/3*p**4.
-2*p**2*(p - 1)*(p + 1)/3
Let g be (-2)/12 + 39/18. Suppose 5*k - 4*q = 21, 0*k - g*q - 8 = -2*k. Factor 6*j**2 - k*j + j**3 - 6*j**3 + 4*j**2.
-5*j*(j - 1)**2
Let 981*t**3 - 62*t + 6*t**4 - 1031*t**3 + 21*t**2 + 82*t**2 - 9*t**2 + 12 = 0. Calculate t.
1/3, 1, 6
Factor 2/7*q**4 + 2/7*q**3 + 4/7 - 2/7*q - 6/7*q**2.
2*(q - 1)**2*(q + 1)*(q + 2)/7
Let i(k) be the third derivative of k**5/300 + 5*k**4/24 + 4*k**3/5 + 62*k**2. Find s such that i(s) = 0.
-24, -1
Let j = -48 + 46. Let x be j - 9/(18/(-8)). Factor 0*k - 2/3*k**3 + 0 + 0*k**x.
-2*k**3/3
Suppose 6*x - 4*x = 18. Let o be 6*10/(-15) + x. Determine l so that l**o + 3*l**5 + 2*l**2 - 3*l**4 + 1 + 2*l**3 - 3*l**5 - 3*l = 0.
-1, 1
Let u(j) be the first derivative of 2*j**5/5 + 11*j**4/2 - 26*j**3/3 - 11*j**2 + 24*j - 31. Factor u(f).
2*(f - 1)**2*(f + 1)*(f + 12)
Let u = 995/2318 - 1/122. Let o = 119/57 - u. Suppose -1/3*d**3 + o*d**2 - d + 0 - 1/3*d**4 = 0. Calculate d.
-3, 0, 1
Find t, given that 120/11 - 2/11*t**2 + 2*t = 0.
-4, 15
Let m(y) be the second derivative of 1/42*y**4 + 21*y + 2/7*y**2 + 0 - 5/21*y**3 - 1/35*y**6 + 1/14*y**5. Determine z, given that m(z) = 0.
-1, 2/3, 1
Let h(l) be the third derivative of l**5/45 + l**4/24 - 7*l**3/18 - 3*l**2 + 31*l. Factor h(j).
(j - 1)*(4*j + 7)/3
Let s(r) be the second derivative of -1/20*r**4 + 0*r**3 + 1/70*r**7 - 3/50*r**6 + 9/100*r**5 - 17*r + 0 + 0*r**2. Factor s(j).
3*j**2*(j - 1)**3/5
Let w be (-8 - (-3444)/432)*-6. Suppose -3*y + 17 = 4*j, j - 5*y + 19 = 3*j. Solve 1/2*d - 1/3*d**3 - 1/2*d**4 + 1/3*d**j + w - 1/6*d**5 = 0.
-1, 1
What is b in 44/3*b**4 + 200/3*b + 94*b**3 + 0 + 2/3*b**5 + 440/3*b**2 = 0?
-10, -1, 0
Let f(d) be the third derivative of d**8/672 + d**7/30 + 17*d**6/60 + 13*d**5/12 + 25*d**4/16 + 5*d**2 + 9. Factor f(p).
p*(p + 1)*(p + 3)*(p + 5)**2/2
Factor 18/5*c**3 - 64/5 + 2/5*c**4 + 0*c + 44/5*c**2.
2*(c - 1)*(c + 2)*(c + 4)**2/5
Let j = 14 + 2. Suppose f = 2*p - 2*f - 12, 4*f = 3*p - j. Find d such that p*d - 7*d - 2*d - 3 - 11*d**2 + 5*d**2 = 0.
-1, -1/2
Let o = -21876 + 87505/4. What is n in 3*n - o*n**2 - 9 = 0?
6
Let z(r) = -2*r + 44. Let l be z(10). Suppose -6*o = 2*o - l. Solve 1/3*j**o + 0 - 1/3*j**4 + 0*j + 2/3*j**2 = 0 for j.
-1, 0, 2
Let b = 357/6740 + -1/337. Let y(r) be the second derivative of 0*r**4 - 3*r - b*r**5 + 0*r**2 + 1/6*r**3 + 0. Factor y(p).
-p*(p - 1)*(p + 1)
Let z be (-3)/(-3) - 5/(4 + 1). Let x(b) be the first derivative of 0*b**2 + 0*b + 6 + z*b**3 + 1/2*b**4. Factor x(r).
2*r**3
Let 0*j + 0 + 2/3*j**2 + 16/3*j**4 + 11*j**3 = 0. Calculate j.
-2, -1/16, 0
What is g in -1/5*g**4 + 0 + 23/5*g**3 - 168/5*g**2 + 396/5*g = 0?
0, 6, 11
Let f(s) = 3*s - 5. Let t be f(3). Suppose 42*n**4 + 8*n**2 + 20*n**3 - 10*n**t + 4*n**5 - 16*n**4 = 0. What is n?
-2, -1, 0
Let c = -20932 - -20934. Find d such that -2/13*d - 4/13*d**c + 0 - 2/13*d**3 = 0.
-1, 0
Let v(l) = l**2 + l - 1. Let n(z) = -z**4 + 7*z**3 - 12*z**2 + 4*z + 1. Let y(g) = 5*n(g) + 5*v(g). Factor y(w).
-5*w*(w - 5)*(w - 1)**2
Let g = -33221 + 33223. Factor -o**4 - 27/4*o**g - 19/4*o - 5/4 - 17/4*o**3.
-(o + 1)**3*(4*o + 5)/4
Let w(j) be the third derivative of j**7/525 + j**6/150 - 19*j**5/150 - 17*j**4/15 - 4*j**3 + 110*j**2. Factor w(d).
2*(d - 5)*(d + 2)**2*(d + 3)/5
Let o(v) be the first derivative of -2/27*v**3 + 1/6*v**4 - 2/45*v**5 - 32 - 1/3*v**2 + 4/9*v. Solve o(n) = 0.
-1, 1, 2
Let c = -1222/15 + 23/3. Let q = 74 + c. Solve 0*y - 1/5*y**2 + 1/5*y**4 + q*y**5 - 1/5*y**3 + 0 = 0 for y.
-1, 0, 1
Let y(i) = -2 + i - 4*i + i**2 - 1. Let r be ((-2)/(-6))/(32/(-480)). Let b(m) = 1. Let k(f) = r*b(f) - y(f). Factor k(j).
-(j - 2)*(j - 1)
Suppose z + 24 = 13*z. Let n be 11/(-44) + z/8. Factor 3/7*j**3 + 1/7*j - 1/7*j**4 + n - 3/7*j**2.
-j*(j - 1)**3/7
Let u(c) be the second derivative of 1/24*c**4 + 0*c**2 + 1/24*c**3 + 0*c**5 - 16*c + 0 - 1/60*c**6 - 1/168*c**7. Factor u(t).
-t*(t - 1)*(t + 1)**3/4
Suppose 0 + 1/7*c**2 + 4/7*c**3 - 1/7*c**4 - 4/7*c = 0. Calculate c.
-1, 0, 1, 4
Let b(o) be the second derivative of 0*o**5 + 1/2*o**4 + 0 - 20*o - 3/2*o**2 + 0*o**3 - 1/10*o**6. Factor b(k).
-3*(k - 1)**2*(k + 1)**2
Factor -11 - 1 + 11*i**2 + 167*i + 32 + 10.
(i + 15)*(11*i + 2)
Let x(q) be the third derivative of q**5/120 + q**4/16 - 16*q**2 + q. Solve x(l) = 0 for l.
-3, 0
Let t = 124/135 - 23/27. Let p(z) be the third derivative of 1/105*z**7 + 0*z + 0*z**4 + 0 - t*z**5 + 1/3*z**3 + z**2 + 0*z**6. Let p(r) = 0. What is r?
-1, 1
Find h such that 2/3*h**2 + 0*h**3 - 2/3*h**4 + 0*h + 0 = 0.
-1, 0, 1
Let y(o) be the second derivative of -o**6/6 + 41*o**5/4 - 185*o**4/2 + 1070*o**3/3 - 700*o**2 + 32*o. Find v such that y(v) = 0.
2, 35
Let l(g) = 11*g**2 + 4*g + 9. Let q be l(5). Suppose 3*j - 303 = 3*s, -88 + q = 2*j + 5*s. Find w such that -2*w**3 - 97*w**4 + 11*w**3 - 3*w**5 + j*w**4 = 0.
-1, 0, 3
Let t(v) be the third derivative of -v**2 + 0*v**3 + 1/12*v**5 + 0 - 5/6*v**4 + 0*v. Suppose t(f) = 0. What is f?
0, 4
Let s(o) = -600*o**2 + 112*o + 20. Let k(t) = -t**2 + 2*t + 1. Let h(f) = -44*k(f) + 2*s(f). Factor h(r).
-4*(17*r - 1)**2
Let b(a) be the second derivative of 9*a**6/10 - 21*a**5/20 - a**4/2 - 2*a + 106. Find y, given that b(y) = 0.
-2/9, 0, 1
Let f(o) be the second derivative of -o**8/1120 + o**7/560 + o**6/120 - 23*o**3/6 - o. Let k(v) be the second derivative of f(v). Factor k(z).
-3*z**2*(z - 2)*(z + 1)/2
Let z(t) be the second derivative of t**5/80 + 11*t**4/12 + 16*t**3 - 288*t**2 - 804*t. Factor z(f).
(f - 4)*(f + 24)**2/4
Let t(z) be the third derivative of -z**8/2520 - z**7/420 + z**5/45 + 11*z**3/6 - 7*z**2. Let g(k) be the first derivative of t(k). Factor g(h).
-2*h*(h - 1)*(h + 2)**2/3
Let w = -31226 + 31228. What is g in -w*g - 4/3 + 2/3*g**3 + 0*g**2 = 0?
-1, 2
Let f be 50/(-120) + -2 + 8/3. Let t = 343 - 341. Factor 7/4*q + f + 2*q**3 + 7/2*q**t.
(q + 1)*(2*q + 1)*(4*q + 1)/4
Suppose 15*o = 16*o + 112. Let f = -110 - o. Factor -f*q**3 + 0 - 4/3*q**2 + 0*q + 2/3*q**5 + 0*q**4.
2*q**2*(q - 2)*(q + 1)**2/3
Let l(g) be the second derivative of -g**5/5 - 4*g**4 + 2*g**3/3 + 24*g**2 - g - 10. Factor l(a).
-4*(a - 1)*(a + 1)*(a + 12)
Suppose k - 4*u - 10 = 0, -4*k + 0*u - 28 = u. Let m be ((-5)/(-3))/((-2)/k). Solve 2*g - 4*g**3 - 2*g**m + 0*g**5 - g**5 + 5*g**5 = 0 for g.
-1, 0, 1
Let c(m) be the first derivative of 17 - 1/3*m**4 + 2/9*m**6 + 0*m + 32/15*m**5 - 32/9*m**3 + 0*m**2. Let c(p) = 0. Calculate p.
-8, -1, 0, 1
Let p(h) be the third derivative of -17/140*h**5 + 0*h + 0 + 2/7*h**4 - h**2 - 3/14*h**3 + 1/70*h**6. What is k in p(k) = 0?
1/4, 1, 3
Let a be (7 + 315/(-60))*(-24)/(-28). Factor 1/4*i**2 + 7/4*i + a.
(i + 1)*(i + 6)/4
Let o(v) be the second derivative of 0 + 49/15*v**3 + 7/15*v**4 + 7*v + 0*v**2 + 1/50*v**5. Determine n, given that o(n) = 0.
-7, 0
Let r(x) be the third derivative of x**6/240 + 13*x**5/120 + 23*x**4/48 + 11*x**3/12 - 148*x**2. Factor r(s).
(s + 1)**2*(s + 11)/2
Let l(f) = -21*f + 106. Let w be l(5). Let y = w - 3/4. Suppose 0 - 1/4*r**3 + 0*r + 1/4*r**2 + y*r**5 - 1/4*r**4 = 0. Calculate r.
-1, 0, 1
Let t(l) = 1477*l + 55. Let f be t(6). Find m such that 5*m**2 - f*m + 8917*m = 0.
0
Let j(p) = p**2 + 15*p + 31. Let f be j(-13). Let k**f - 19*k - k**4 + 5*k**2 - 2*k**3 + 17*k - k**3 = 0. What is k?
-2, 0, 1
Let m(h) be the second derivative of h**4/36 - 31*h**3/18 + 5*h**2 + 441*h. Determine v so that m(v) = 0.
1, 30
Factor 153 + 159/2*p + 3/2*p**2.
3*(p + 2)*(p + 51)/2
Factor 0*j + 1/3*j**3 + 0 - 1/6*j**4 + 1/2*j**2.
-j**2*(j - 3)*(j + 1)/6
Suppose 3587 = n + 163. Factor -2*g + 3424 - 6*g**2 - n.
-2