 1)/4
Factor 30/7*r**3 - 1/7*r**5 + 15/7 - 2/7*r**2 - 13/7*r**4 - 29/7*r.
-(r - 1)**3*(r + 1)*(r + 15)/7
Let c be -31 - (-5)/25*5. Let i be (c/126)/(-4 + 104/28). Factor 5/3*l - 5/6*l**2 - i.
-5*(l - 1)**2/6
Let j(x) be the third derivative of 29*x**6/60 + 143*x**5/30 - 46*x**4/3 + 4*x**3 + 473*x**2. Determine c so that j(c) = 0.
-6, 2/29, 1
Solve 0 - 1/4*x**4 + 5/4*x**3 + 0*x - 3/2*x**2 = 0 for x.
0, 2, 3
Let v(d) = 2*d**2 - 17*d + 15. Let p be v(7). Let r be 14 - ((p - -3) + 0). Factor 19*y**3 + 4*y**2 - r*y**3 + 6 - 6.
2*y**2*(y + 2)
Let r(y) be the third derivative of -y**6/360 - y**5/15 - 11*y**4/72 + 656*y**2. Determine g so that r(g) = 0.
-11, -1, 0
Suppose 0 + 9 = -3*q, 5*l - 3394 = -2*q. Let p be (-1)/(-4) + 238/l. Factor -3/5*n**2 + 3/5 + 3/5*n**3 - p*n.
3*(n - 1)**2*(n + 1)/5
Suppose -1931 + 2567 = 159*s. Suppose 0 + 4/3*w**s + 2/3*w**3 - 2/3*w**5 - 4/3*w**2 + 0*w = 0. Calculate w.
-1, 0, 1, 2
Let o(h) be the second derivative of 0*h**3 - 3*h - 14*h**2 + 1/70*h**5 + 0 + 1/280*h**6 - 3/56*h**4. Let w(a) be the first derivative of o(a). Factor w(y).
3*y*(y - 1)*(y + 3)/7
Let 6480/7*a + 8100/7 + 3/7*a**4 + 1431/7*a**2 + 114/7*a**3 = 0. What is a?
-15, -6, -2
Let h(s) = -5*s**2 + 9*s + 3. Let d = -69 + 69. Suppose 10*t + 17 + 13 = d. Let y(w) = 26*w**2 - 46*w - 16. Let z(l) = t*y(l) - 16*h(l). Solve z(i) = 0 for i.
0, 3
Let i(f) be the first derivative of -f**4/14 + 16*f**3/21 + 45*f**2/7 + 72*f/7 - 1512. Factor i(h).
-2*(h - 12)*(h + 1)*(h + 3)/7
Factor -62424 - 408*n - 2/3*n**2.
-2*(n + 306)**2/3
Factor 28*s**2 + 132 + 1937*s**3 + 49*s - 1933*s**3 - 213*s.
4*(s - 3)*(s - 1)*(s + 11)
Let n(y) be the third derivative of -y**10/68040 + y**9/4860 - y**4 + y**3/3 + 44*y**2. Let w(b) be the second derivative of n(b). Factor w(x).
-4*x**4*(x - 7)/9
Let d(v) be the second derivative of v**4/90 - 59*v**3/45 + 106*v**2/5 + 1359*v. Determine b so that d(b) = 0.
6, 53
Let a = 73794 + -73786. Factor -1/2*u**3 - 4*u - 7/2*u**2 + a.
-(u - 1)*(u + 4)**2/2
Solve -16*q + 2/5*q**2 + 120 = 0 for q.
10, 30
Let f(m) be the third derivative of 2*m**7/105 + 66*m**6/5 + m**2 + 400*m + 3. Factor f(h).
4*h**3*(h + 396)
Suppose 21*x - 12 = 7 - 19. Let z(b) be the first derivative of 4*b - 4/3*b**3 + 12 + x*b**2. Factor z(g).
-4*(g - 1)*(g + 1)
Let j be ((-216)/(-22))/3 + 0. Let k = 10690/6457 + -118/587. Solve 26/11*q + j*q**2 + k*q**3 + 6/11 = 0 for q.
-1, -3/4, -1/2
Let p(h) = 8*h**3 + 20*h**2 + 106*h + 58. Let i(z) = -7*z**3 - 21*z**2 - 103*z - 59. Let o(x) = -6*i(x) - 5*p(x). Determine f, given that o(f) = 0.
-8, -4, -1
Let x(m) be the third derivative of m**8/840 + 11*m**7/525 - m**6/60 - 11*m**5/30 + m**4/15 + 44*m**3/15 - 45*m**2 - 11. Suppose x(n) = 0. Calculate n.
-11, -2, -1, 1, 2
Factor 142 - 86 + 105*t**3 + 107 - 645*t - 65*t**2 + 5*t**4 + 220*t**2 + 217.
5*(t - 1)**2*(t + 4)*(t + 19)
Factor 216/13*o**2 + 0*o + 0 - 6/13*o**4 + 646/13*o**3.
-2*o**2*(o - 108)*(3*o + 1)/13
Factor 89*d**3 - 5*d**2 - 73*d**3 + 45*d - 21*d**3 + d**2 - 25 - 11*d**2.
-5*(d - 1)**2*(d + 5)
Let p(w) be the first derivative of -w**3/18 + 9*w**2/4 - 1042. Find g, given that p(g) = 0.
0, 27
Let u(f) = 6*f**2 + 261*f + 257. Let x be u(-1). Solve 2/9*q**x + 100/9*q + 1250/9 = 0 for q.
-25
Let y(o) be the second derivative of -5*o**4/12 + o**3/3 - 2*o**2 - 9*o + 7. Let i(f) = 6*f**2 - 3*f + 5. Let z(w) = 4*i(w) + 5*y(w). Factor z(u).
-u*(u + 2)
Let o be (-45)/(-27) - (-390)/9. Factor -594 + o*s - 3*s**3 + 350 + 352 - 6*s**2.
-3*(s - 4)*(s + 3)**2
Let p be (0 - 16/6)/((-5492)/4119). Factor 15/2 - 33/2*c - 3/2*c**3 + 21/2*c**p.
-3*(c - 5)*(c - 1)**2/2
Let f(g) be the first derivative of g**5/5 - 207*g**4/4 + 10606*g**3/3 + 5616*g**2 - 21632*g - 935. Solve f(b) = 0.
-2, 1, 104
Let h(q) be the second derivative of -16*q**6/21 - 68*q**5/35 - 23*q**4/14 - 3*q**3/7 + 214*q. Factor h(r).
-2*r*(4*r + 3)**2*(5*r + 1)/7
Let f = 3/21257 - 47849516/63771. Let z = f + 751. Factor 0 + 8/3*p - z*p**2.
-2*p*(p - 4)/3
Let q(f) = -f**3 - 12*f**2 + 3*f. Let v(w) = 9*w + 30. Let b be v(-4). Let s(o) = 2*o**3 + 12*o**2 - 2*o. Let t(j) = b*q(j) - 5*s(j). Factor t(n).
-4*n*(n - 2)*(n - 1)
Let d(b) = 11*b**2 - 3013*b - 149961. Let y(p) = -3*p**2 + 1004*p + 49988. Let h(g) = -4*d(g) - 13*y(g). Let h(s) = 0. What is s?
-100
Let d = 1012 + -434. Let m = d - -310. Determine j, given that -4*j**2 + m*j - 1 + 5 - 888*j = 0.
-1, 1
Let h(i) be the first derivative of -i**8/1344 + i**7/105 + 3*i**6/160 - 123*i**2/2 + 94. Let w(g) be the second derivative of h(g). What is q in w(q) = 0?
-1, 0, 9
Let d(b) = b**3 - b**2 - b + 7. Let y be d(0). Let h(r) = -13*r**2 - r - 7. Let j(o) = -9*o**2 - o - 5. Let f(p) = y*j(p) - 5*h(p). Find c, given that f(c) = 0.
0, 1
Let r = 2696/55 + -18707/385. Solve r*n**4 + 0 + 45/7*n**2 - 3*n**3 - 27/7*n = 0 for n.
0, 1, 3
Suppose -113*u + 891 = -86*u. Suppose u*y = 42*y - 18. Let -14/23*t**3 + 4/23*t**4 + 18/23*t**y - 10/23*t + 2/23 = 0. What is t?
1/2, 1
Determine t so that 20 + 5/3*t**4 - 15*t**3 + 5/3*t**5 - 25/3*t**2 + 80/3*t = 0.
-3, -1, 2
Let s = 21 + -19. Suppose -25 = -s*f - 9. Factor f*a**2 + 2*a - 14*a - 16 - 4*a**2.
4*(a - 4)*(a + 1)
Let f(x) = -x**3 - 2*x + 1. Let t be (-6)/(-14)*(15 + -8) + -4. Let o(k) = 13*k**3 - 4*k**2 - 3. Let s(u) = t*o(u) - 3*f(u). Find r, given that s(r) = 0.
-3/5, 0, 1
Factor -12/7*x + 60/7 + 3/7*x**3 - 15/7*x**2.
3*(x - 5)*(x - 2)*(x + 2)/7
Let z(j) be the third derivative of -j**6/540 + 2*j**5/135 + j**4/4 - 10*j**3/3 + 59*j**2. Factor z(y).
-2*(y - 6)*(y - 3)*(y + 5)/9
Suppose x = -12*x - 13. Let h be 8*x + -27 + 35. Factor 1/2*t**2 - 1/2*t**4 + 1/4*t**5 + 0*t + h - 1/4*t**3.
t**2*(t - 2)*(t - 1)*(t + 1)/4
Let q = 300 + -297. Suppose -2*t - 2 = -i - q*t, -5*t - 22 = -3*i. Find s, given that 1/2*s**5 - 6*s**2 - s**3 + 2*s**i + 9/2*s + 0 = 0.
-3, 0, 1
Let u(h) be the first derivative of -11*h**7/189 - h**6/15 + h**5/45 + 52*h + 47. Let i(o) be the first derivative of u(o). Factor i(g).
-2*g**3*(g + 1)*(11*g - 2)/9
Let b = 17738 + -17732. Let x(m) be the third derivative of 0 - 13*m - 1/27*m**4 - 1/270*m**b + 0*m**3 + 2*m**2 - 1/45*m**5. Determine j, given that x(j) = 0.
-2, -1, 0
Let u(k) be the second derivative of -k**6/10 + 39*k**5/10 - 91*k**4/4 + 33*k**3 - 2406*k. Let u(o) = 0. What is o?
0, 1, 3, 22
Let b(p) be the first derivative of 8*p**3/3 - 160*p**2 - 20*p - 18. Let r(w) = -w**2 + 46*w + 3. Let a(h) = -3*b(h) - 20*r(h). What is y in a(y) = 0?
0, 10
Let j = 4729/9 + -4726/9. Find w, given that -13/3*w + 22/3 + j*w**2 = 0.
2, 11
What is b in -2*b**2 + 0 + 36/11*b + 2/11*b**3 = 0?
0, 2, 9
Let s(r) = -7*r**2 + 38*r - 8. Let v be s(5). Determine p so that -4*p**3 + 12*p - 3*p**4 - 12*p**3 - v*p**3 + 14*p**3 = 0.
-2, 0, 1
Factor -3/7*u**4 - 40359/7*u**2 + 78660/7*u - 38988/7 + 690/7*u**3.
-3*(u - 114)**2*(u - 1)**2/7
Let h(y) = -2*y**3 + 428*y**2 + 871*y - 1508. Let j be h(216). Suppose -2/13*r**j + 6/13*r - 14/13*r**2 + 10/13*r**3 + 0 = 0. Calculate r.
0, 1, 3
Let i = -240 - -242. Solve 28*f - 10*f + 34 + i*f**2 + 2 = 0 for f.
-6, -3
Suppose -3*d - c = 9, -1835*c + 36 = -d - 1839*c. Solve 0 + 0*j**2 + 20/3*j**3 - 16/3*j + d*j**4 - 4/3*j**5 = 0 for j.
-2, -1, 0, 1, 2
Suppose 7*y + 4*y - 2 = 64. Let x - y*x**2 + 1/4*x**4 + 5/4*x**3 + 8 = 0. What is x?
-8, -1, 2
Let d(q) be the third derivative of q**5/180 + 3*q**4/8 - 209*q**3/9 + 3309*q**2. Factor d(m).
(m - 11)*(m + 38)/3
Suppose w + 4 - 16 = 0. Let v be 64/w*54/252. Determine x so that v*x + 24/7*x**2 + 24/7*x**5 - 6*x**3 - 34/7*x**4 + 0 = 0.
-1, -1/4, 0, 2/3, 2
Let -133 + 2*b**2 - 132*b**3 + 373 - 39*b - 4*b**4 - 5*b**2 + 407*b + 7*b**2 + 4*b**5 = 0. Calculate b.
-5, -1, 2, 6
Let k(r) be the first derivative of 0*r - 1/3*r**3 - 25/2*r**2 + 116. Let k(p) = 0. What is p?
-25, 0
Let l(i) be the second derivative of i**7/10080 - 23*i**6/2880 - 103*i**4/12 - 63*i. Let h(x) be the third derivative of l(x). Find u such that h(u) = 0.
0, 23
Let f(p) be the first derivative of 0*p**3 + 0*p + 0*p**2 + 2/3*p**5 - 1/9*p**6 - 58 + 0*p**4. Factor f(i).
-2*i**4*(i - 5)/3
Suppose -12*k**5 + 2*k**5 - 296*k**3 + 472*k**2 + 8*k**5 + 38*k**4 + 192 + 92*k**3 - 496*k = 0. Calculate k.
1, 2, 12
Factor 72963 - 341*h + 6*h**2 - 4*h**2 + 8645 - 467*h + 0*h**2.
2*(h - 202)**2
Let u(w) be the second derivative of