, 1
Suppose -6*h**5 + 28560*h**2 - 712*h**4 - 2937*h**3 - 7200*h - 1369*h**3 - 16336*h**3 = 0. Calculate h.
-60, 0, 1/3, 1
Suppose 16*w - 32 = 48. Factor -5 + 10*b**2 + 57*b**5 - 4*b**4 + 10*b**3 - b**4 - 5*b - 31*b**w - 31*b**5.
-5*(b - 1)**2*(b + 1)**3
Let t(k) be the third derivative of -k**6/10 - 8*k**5/15 + 25*k**4/6 - 28*k**3/3 - 3895*k**2. Factor t(q).
-4*(q - 1)**2*(3*q + 14)
Let k = -5098 - -5098. Let a(y) be the first derivative of 1/2*y**4 + 0*y + 4/3*y**3 + k*y**2 + 14. Let a(o) = 0. Calculate o.
-2, 0
Let f(k) be the third derivative of 0*k**4 + 0*k**3 - 4/5*k**5 + 3*k**2 + 0*k + 1/14*k**8 - 16 - 2/3*k**6 + 2/105*k**7. Suppose f(l) = 0. What is l?
-3/2, -2/3, 0, 2
Let o(b) = b**2 - 23. Let c = 39 - 45. Let p be o(c). Suppose -2*r**4 + 84*r**5 - 79*r**5 + p*r**2 - 8*r**4 - 5*r - 3*r**2 = 0. What is r?
-1, 0, 1
Let y be 23/(1150/20) - 376/(-235). Factor 6/5*m**3 + 2/5*m - 2/5*m**4 + 0 - 6/5*m**y.
-2*m*(m - 1)**3/5
Let u(d) be the second derivative of -d**7/28 - 23*d**6/5 - 9507*d**5/40 - 24895*d**4/4 - 86359*d**3 - 645918*d**2 + 1229*d - 1. Factor u(t).
-3*(t + 7)**2*(t + 26)**3/2
Suppose 80 = 4*r + i, 592*r + 4*i = 591*r + 50. Let w(b) be the first derivative of 5*b**2 + 0*b + 5/3*b**3 + r. Factor w(q).
5*q*(q + 2)
Let o(h) be the second derivative of 3*h**5/80 + 19*h**4/24 + 155*h**3/24 + 25*h**2 - 57*h - 6. Suppose o(s) = 0. What is s?
-5, -8/3
Let s(l) be the third derivative of 5*l**8/336 + 3*l**7/14 + l**6 + 4*l**5/3 - 5739*l**2. What is p in s(p) = 0?
-4, -1, 0
Let i(p) be the second derivative of -7*p**6/90 + p**5/12 + 11*p**4/9 + 2*p**3/3 - 28*p + 10. Solve i(s) = 0.
-2, -2/7, 0, 3
Let c be (1 - (1 - 3))*28/12. Suppose c*n + 10 = 12*n. Suppose -186 - 5*p**n - 32*p - 15*p - 43*p - 219 = 0. What is p?
-9
Let c be (0*(-38)/1330)/(1 + 2*-1). Let o(p) be the second derivative of 0 + c*p**4 + 5*p - 2/21*p**6 + 1/35*p**5 + 4/49*p**7 + 0*p**3 + 0*p**2. Factor o(t).
4*t**3*(2*t - 1)*(3*t - 1)/7
Find b, given that 5/2*b**2 + 3*b**4 - 21/4*b**3 - 1/4*b**5 + 0*b + 0 = 0.
0, 1, 10
Factor 10 + 5*r**4 + 45*r**2 - 35*r + 566941*r**3 + 0*r**4 - 566966*r**3.
5*(r - 2)*(r - 1)**3
Suppose -3*p + 2*a + 159 = 0, -3*a - 165 = -3*p + a. Let n = 54 - p. Factor 3*o**2 + 4*o**3 + 0*o**3 - 3*o**4 + 9*o + 2*o**n - 15*o.
-3*o*(o - 2)*(o - 1)*(o + 1)
Let x(k) be the third derivative of k**8/84 - 4*k**7/105 - k**6/10 + 4*k**5/15 + 2*k**4/3 - k**2 - 321*k. Factor x(z).
4*z*(z - 2)**2*(z + 1)**2
Solve -82*x + 5*x + 1097*x**2 + 140 - 69*x - 1095*x**2 + 1324 = 0 for x.
12, 61
Let t(k) be the first derivative of k**6/15 - k**5/10 - k**4/2 + k**3/3 + 2*k**2 + 9*k + 188. Let s(n) be the first derivative of t(n). Factor s(q).
2*(q - 2)*(q - 1)*(q + 1)**2
Let s(i) be the first derivative of -i**5/30 - 532*i**4/3 - 2266319*i**3/9 - 754376*i**2 - 1508043*i/2 + 2112. Factor s(w).
-(w + 1)**2*(w + 2127)**2/6
Let k(w) = 20*w**2 + 25*w + 5. Let d be (3 - 1)/1 + -7. Let n(b) = 31*b**2 + 38*b + 8. Let p(a) = d*n(a) + 8*k(a). Solve p(h) = 0 for h.
-2, 0
Suppose 5 + 7 = 2*g - 3*h, g + h = 1. Let a be (-88)/(-96) - 2/g. Factor 0 - 3/4*f + a*f**2.
f*(f - 3)/4
Factor -2/7*u**2 - 6393888/7 - 7152/7*u.
-2*(u + 1788)**2/7
Let p = 170483 - 170479. Let -12/5*j**4 - 20*j + 20*j**3 + 32/5 - p*j**2 = 0. What is j?
-1, 1/3, 1, 8
Let d(u) be the second derivative of -u**4/30 + 592*u**3/3 - 438080*u**2 + 2655*u. Factor d(b).
-2*(b - 1480)**2/5
Suppose -q + 13 = 3*j, -j = -25 + 22. Let k(s) be the first derivative of 8/27*s**3 + 0*s**2 + 5/9*s**q + 0*s + 4/15*s**5 - 11. Solve k(d) = 0 for d.
-1, -2/3, 0
Let r = 82 - 55. Let u be -21*-3*3/r. Factor -8*x + 3*x**4 - u*x**4 - 16*x**3 - 104*x**2 + 84*x**2.
-4*x*(x + 1)**2*(x + 2)
Let j(d) be the first derivative of 8/15*d**3 + 14/5*d**2 + 99 - d**4 + 0*d. Factor j(u).
-4*u*(u + 1)*(5*u - 7)/5
Suppose -96 = -17*w + 14*w. Find g such that -15*g**3 + 2*g**4 + 5 + 36*g**2 + w*g + 5 + 31*g**3 = 0.
-5, -1
Let s(k) = -5*k + 104. Let u be s(20). Find m, given that 6*m**2 + 2*m**2 + 10 - 16*m - 6*m**2 + u*m = 0.
1, 5
Suppose 10*a - 15*a - 245 = 0. Let z = a - -52. Solve 20*c + 46*c**2 - 5*c**4 - 60 - 4*c**2 + z*c**2 = 0.
-2, 1, 3
Let m be ((-54)/(-12) - 4)/((12 - 5)/42). Let u(v) be the first derivative of -9/5*v**5 + 2/3*v**3 + 28 - v - 2*v**2 + m*v**4. Factor u(q).
-(q - 1)**2*(3*q + 1)**2
Let a(v) = 10*v**2 + 2855*v + 34585. Let p(y) be the second derivative of y**4/12 + 119*y**3/3 + 1441*y**2 - 2*y + 3. Let r(q) = 2*a(q) - 25*p(q). Factor r(k).
-5*(k + 24)**2
Let t be 2/22 + 1129440/(-5005). Let n = -225 - t. Let 0 + 12/7*d - n*d**2 = 0. Calculate d.
0, 3
Let x = 978 - 976. Let n(p) be the first derivative of 8 - 1/40*p**4 + 1/50*p**5 + 0*p + 0*p**x + 0*p**3. Factor n(b).
b**3*(b - 1)/10
Let s(w) = -63*w**3 + w**2 + 2*w + 2. Let y be s(-1). Factor 315*p**2 - 95*p**3 + 4 + 106 - y*p - 261*p - 5*p**4.
-5*(p - 1)**3*(p + 22)
Let w(l) be the third derivative of l**7/70 + 549*l**6/40 + 137*l**5/5 + 5*l**2 - 3*l - 20. Factor w(k).
3*k**2*(k + 1)*(k + 548)
Let t be 627/(-1710)*63/(-198). Let r(u) be the third derivative of t*u**5 + 0*u**3 + 16*u**2 + 0*u + 1/4*u**4 + 0 + 1/120*u**6. Factor r(w).
w*(w + 1)*(w + 6)
Let s be -34 + 27 - 115/(-14). Let d = s + -22/21. Suppose -d*l**3 + 1/2*l**2 - 2/3 + 0*l = 0. Calculate l.
-1, 2
Let n(b) be the first derivative of -b**8/3696 + b**6/264 - b**4/66 + 46*b**2 - 10. Let f(x) be the second derivative of n(x). Solve f(g) = 0.
-2, -1, 0, 1, 2
Let o(l) be the first derivative of 4*l**5/5 - 10*l**4 - 52*l**3/3 + 44*l**2 - 293. Let o(f) = 0. Calculate f.
-2, 0, 1, 11
Suppose 55*o = 58*o - 15, 0 = 3*d - 3*o - 9. Suppose 0 = -3*s - n + d, -3*s + 5*n + 11 + 21 = 0. Solve -1/3 - 4*r**3 + 5/2*r + 8/3*r**s - 23/6*r**2 = 0.
-1, 1/4, 2
Let g(t) = -3*t**3 - 233*t**2 - 2028*t - 1796. Let b(h) = -h**3 - h**2 - h - 2. Let k(y) = 2*b(y) + g(y). Factor k(s).
-5*(s + 1)*(s + 10)*(s + 36)
Let u = -41 + 33. Let d be (-102)/u + -1 - (-3)/(-4). Factor -12 - 2*x - 5*x**2 + 4*x**2 + d*x + 4*x**2.
3*(x - 1)*(x + 4)
Suppose 0 = 157*k - 103*k + 65 - 173. Let c(x) be the first derivative of 80*x + 5/3*x**3 - 26 - 20*x**k. Factor c(w).
5*(w - 4)**2
Let k(j) = -3*j**3 + 18*j**2 + 48*j + 6. Let q(v) = v**2 + 12*v - 6. Let t be q(-12). Let z(b) = 1. Let p(r) = t*z(r) + k(r). Factor p(l).
-3*l*(l - 8)*(l + 2)
Let m(c) be the first derivative of c**6/21 + 4*c**5/35 - c**4/2 + 8*c**3/21 + 4036. Solve m(x) = 0.
-4, 0, 1
Let s be (-23)/(-15) - ((-1344)/240)/(-28). Solve -s*r**3 + 2/3*r**5 + 2/3 + 2/3*r - 4/3*r**2 + 2/3*r**4 = 0 for r.
-1, 1
Let n(q) = -q**3 + 2*q. Let y = -495 - -496. Let j(f) = -4*f**4 + 42*f**3 - 168*f**2 + 220*f - 84. Let v(x) = y*j(x) - 6*n(x). Factor v(r).
-4*(r - 7)*(r - 3)*(r - 1)**2
Suppose -32 = -4*h + 2*x, h + 10 = x - 5*x. Suppose 0 = -g + 3*y, -h*y = -8*y. Determine z so that 0*z**2 + 0 + 2/7*z**4 + g*z + 2/7*z**3 = 0.
-1, 0
Let m(b) be the second derivative of -b**5/5 - 11*b**4 + 80*b**3/3 + 408*b**2 - 353*b. Factor m(g).
-4*(g - 3)*(g + 2)*(g + 34)
Let -2/21*l**2 + 10/7*l + 152/21 = 0. What is l?
-4, 19
Let t = -100830686216/249165 - -19828926/49. Let h = 2/1017 - t. Factor 36/5*g**3 - h*g**4 - 3/5 + 18/5*g - 39/5*g**2.
-3*(g - 1)**2*(2*g - 1)**2/5
Let b be 1 + 27/(9/1). Solve 6 + 33 + 25 - 87*l**3 - 45*l**2 - 7*l**4 + 87*l - 10 - 2*l**b = 0 for l.
-9, -1, -2/3, 1
Factor -9/2*y**2 + 3/4*y**3 + 0 + 15/4*y.
3*y*(y - 5)*(y - 1)/4
Let t(a) be the first derivative of -14*a**3/15 + 212*a**2/5 - 24*a - 1925. Factor t(n).
-2*(n - 30)*(7*n - 2)/5
Let l be (-2)/9 - (84/(-162))/((-35)/(-42)). Factor -l*v**3 - 8/15*v**2 + 8/3*v + 64/15.
-2*(v + 2)**2*(3*v - 8)/15
Let o(x) be the second derivative of -1/15*x**4 + 2/25*x**5 + 0 + 1/25*x**6 - 1/5*x**2 - 4/15*x**3 + 47*x. Determine j so that o(j) = 0.
-1, -1/3, 1
Find j such that 41*j + 3*j**3 + 43*j - 9326*j**4 - 78*j**2 + 9347*j**4 - 6*j**5 - 24 = 0.
-2, 1/2, 1, 2
Let x = 124 + 16. Suppose 5*c - o - 140 = 0, x = -2*c + 7*c - 5*o. Factor 2*p**3 - 46*p - c*p + 10*p**2 + 88*p + 6.
2*(p + 1)**2*(p + 3)
Let v(k) = -3*k**2 + 422*k - 274. Let z be v(140). Determine m, given that 3/4*m**2 + z*m + 45/4 = 0.
-5, -3
Let g be 96*5*(-8)/(-12). Suppose g = 8*a + 312. Find q, given that 1/3*q**2 + a + 4/3*q = 0.
-3, -1
Let 4*s**3 - 50928*s - s**3 - 3*s**3 + 348*s**2 + 51936*s + 4*s**3 = 0. What i