(r) = 0. Calculate r.
0, 2/7, 1
Suppose 3*g = 2*w + 4, -g + 3*g = -3*w + 7. Factor 4 + 0*j**2 - 8 + 4*j**2 + 0*j**g.
4*(j - 1)*(j + 1)
Let m = 6 - 0. Suppose -m*f = -5*f - 7. Factor -v + f*v**3 + 5*v**3 + 2*v**2 - 9*v**3.
v*(v + 1)*(3*v - 1)
Let g be ((-176)/(-1452))/(2/33). Factor 0 + 1/2*a**4 - 5/2*a**g + 3/2*a + 1/2*a**3.
a*(a - 1)**2*(a + 3)/2
Let q(y) = 3*y**2 + 1. Let a(g) = -9*g**2 - 57*g + 248. Let f(l) = -a(l) - 4*q(l). Factor f(c).
-3*(c - 12)*(c - 7)
Let 48/11*j**3 + 4*j - 90/11*j**2 - 2/11*j**4 + 0 = 0. Calculate j.
0, 1, 22
Let q(n) be the first derivative of 1/16*n**4 - 1/4*n**3 + 0*n - 8 + 0*n**2. Let q(y) = 0. Calculate y.
0, 3
Let i(c) be the second derivative of 3*c**5/80 - 3*c**4/16 + 3*c**3/8 - 3*c**2/8 + 52*c. Determine p, given that i(p) = 0.
1
Let o(u) = 7*u - 1. Let m be o(5). Let h be 15/25 - m/(-10). Factor 3*w**3 + 24 - 18*w**2 - 9*w - 3*w**4 - 7*w + 6*w**h + 4*w.
3*(w - 2)*(w - 1)*(w + 2)**2
Let h(z) = 2*z**2 + z - 1. Let o(k) = -14*k**2 - 122*k + 124. Let w(r) = -12*h(r) - 2*o(r). Factor w(i).
4*(i - 1)*(i + 59)
Let c(v) be the first derivative of v**5/140 + v**4/84 - 5*v**3/42 + 3*v**2/14 + 15*v - 15. Let q(i) be the first derivative of c(i). Let q(l) = 0. What is l?
-3, 1
Let v(i) be the second derivative of -85*i**7/28 - 47*i**6/60 + 89*i**5/5 + 29*i**4 + 52*i**3/3 + 4*i**2 - 23*i - 1. Suppose v(t) = 0. What is t?
-1, -2/3, -2/5, -2/17, 2
Let d(p) be the second derivative of -5*p**7/14 + 4*p**6/3 - 3*p**5/2 + 5*p**3/6 + 248*p. Factor d(a).
-5*a*(a - 1)**3*(3*a + 1)
Let k = 116 + -578/5. Let g = -3443 - -17239/5. Factor g*i - 12/5*i**2 + k*i**3 - 16/5.
2*(i - 2)**3/5
Suppose -26*h = -21*h - 10. Factor w**h - 5 - 4*w + 9 - 1.
(w - 3)*(w - 1)
Let s(q) be the second derivative of 1/15*q**4 + 3/5*q**2 - 1/100*q**5 + 0 + 18*q + 11/30*q**3. Determine w so that s(w) = 0.
-1, 6
Let s(b) be the third derivative of -5*b**8/336 + 5*b**7/21 - 4*b**6/3 + 8*b**5/3 - 29*b**2 - 4. Factor s(d).
-5*d**2*(d - 4)**2*(d - 2)
Let l = -157 + 159. Suppose -20*w**2 + 4*w - 8 - 18*w**l - 18*w**2 + 60*w**2 = 0. What is w?
-2, 1
Let a(c) = -4*c**3 + 175*c**2 - 180*c + 3. Let k(h) = -28*h**3 + 1224*h**2 - 1256*h + 20. Let p(b) = -20*a(b) + 3*k(b). Suppose p(o) = 0. Calculate o.
0, 1, 42
Suppose -2*z - 3*p - 57 = -5*z, 4*z + 2*p - 46 = 0. Suppose 0 = -20*q + z*q. Determine w so that 2/7 + q*w**3 + 0*w + 2/7*w**4 - 4/7*w**2 = 0.
-1, 1
Let -62/9*r**3 + 88/9*r - 20/3*r**2 + 32/9*r**4 + 2*r**5 - 16/9 = 0. Calculate r.
-2, 2/9, 1
Let z(n) = -13*n + 135. Let k be z(10). Let w(x) be the first derivative of -1/12*x**6 + 0*x**4 + 0*x**3 - 2 + 0*x**2 + 0*x - 1/5*x**k. Factor w(p).
-p**4*(p + 2)/2
Let f(r) be the third derivative of r**8/191520 - r**6/6840 + r**5/12 + 10*r**2. Let p(c) be the third derivative of f(c). Suppose p(m) = 0. What is m?
-1, 1
Let u(z) be the third derivative of z**5/160 + 31*z**4/64 - 2*z**3 + 179*z**2. Factor u(p).
3*(p - 1)*(p + 32)/8
Let r(o) be the first derivative of 3*o - 1/75*o**6 - 1/10*o**5 - 7/30*o**4 + 0*o**2 - 6 - 1/5*o**3. Let n(b) be the first derivative of r(b). Factor n(z).
-2*z*(z + 1)**2*(z + 3)/5
Let t(z) be the third derivative of -z**6/300 + 7*z**5/450 - 4*z**3/45 - 2*z**2 - 91*z. Find r, given that t(r) = 0.
-2/3, 1, 2
Factor 2/17*z**2 + 332/17*z + 13778/17.
2*(z + 83)**2/17
Suppose -13*f + 20 = -8*f. Let z be (-9)/((-135)/(-12))*(-10)/f. Solve -3/4*j**z + 0*j + 3/4 = 0.
-1, 1
Solve 9 + 0*b**2 - 2*b**2 + 7 - 2 + 12*b = 0 for b.
-1, 7
Let m = 67 + -199/3. Let s be 20/25 + 34/(-255). Suppose 2/3*l + m*l**2 - s - 2/3*l**3 = 0. Calculate l.
-1, 1
Let r be (-6)/(-4) + (-15)/(-10). Suppose -3*j = 4*u - 12, -2*u = j - r*u - 4. Determine m, given that 4*m**j - 12*m**2 - 3*m + 8 + 4*m - 5*m + 4*m**3 = 0.
-2, -1, 1
Let x(t) = -4*t**2 - 48*t - 80. Let i be x(-10). Factor 2/3*f**3 + i - 8/3*f + 0*f**2.
2*f*(f - 2)*(f + 2)/3
Factor 9*k**4 - 55*k**4 - 2000 - 2339*k - 18*k**4 - 722*k**3 - 2*k**5 - 2261*k - 3260*k**2.
-2*(k + 1)**2*(k + 10)**3
Let s(d) be the first derivative of d**4 + 32*d**3 + 384*d**2 + 2048*d + 112. Factor s(k).
4*(k + 8)**3
Let t = 349 - 344. Let q(c) be the third derivative of -1/9*c**3 - 1/18*c**4 - 1/90*c**t + 0 + 0*c + 4*c**2. Find f, given that q(f) = 0.
-1
Let y(u) = 313*u + 4103. Let x be y(-13). Let -32/7*r - 46/7*r**2 + x*r**4 + 134/7*r**3 + 8/7 + 14*r**5 = 0. Calculate r.
-1, 2/7
Let 150 - 4358*w - 14*w**2 + 11*w**2 + 4343*w = 0. Calculate w.
-10, 5
Let h(z) = -z**3 - 9*z**2 + 2*z. Let l be h(-10). Factor 4 - v**2 + 82*v - l*v - 4.
-v*(v - 2)
Determine z, given that 4*z**2 + 207 - 94 - 534 + 932*z - 373 - 142 = 0.
-234, 1
Suppose 0 = 62*k + 53*k - 112*k - 6. Factor -5/2*w**2 - 1/2*w**4 + w + 0 + k*w**3.
-w*(w - 2)*(w - 1)**2/2
Let u be (122/(-2))/(-6*(5 - 0)). Let t = u - -3/10. Find i, given that -2/3 - t*i - i**2 = 0.
-2, -1/3
Let t(k) be the third derivative of 26*k**4 + 0 - 21/16*k**8 - 41/5*k**7 + 0*k - 61/5*k**6 - 38*k**2 + 12*k**5 + 16*k**3. Suppose t(i) = 0. Calculate i.
-2, -2/7, 2/3
Let s be (-1 + (8 - 6))*2. Suppose -4*z + 12 = s*t, z + 0 - 1 = 0. Suppose 3/5*c**t - 6/5*c**3 + 6/5*c - 3/5*c**2 + 0 = 0. Calculate c.
-1, 0, 1, 2
Suppose -8 - 2 = -z + 2*v, -5*v = -4*z + 55. Suppose 2*a - 14 = -5*g, 4*a + 5*g - z + 2 = 0. Determine r so that -4*r**a + 6*r**2 + 2*r + 0*r = 0.
-1, 0
Factor -2/3*r**3 + 4*r**2 - 22/3*r + 4.
-2*(r - 3)*(r - 2)*(r - 1)/3
Let p(a) = a**3 - a**2 + a. Let d(l) = -18*l**3 + 3*l**2 - 30*l - 6. Let o(g) = d(g) + 15*p(g). Factor o(z).
-3*(z + 1)**2*(z + 2)
Let d(i) = i**3 + 5*i**2 - 12*i - 31. Let g be d(-4). Suppose -f + g = 31. Solve -2*y**3 - y**f - 1/2 + 2*y + 3/2*y**4 = 0.
-1, 1/3, 1
Suppose 3*d - 5*b - 10 = 17, 4*b + 20 = 2*d. Suppose 0 = -i + d, -3*n + 0*n = 5*i - 29. Find q, given that -3*q**4 + n*q**4 + 4*q**4 = 0.
0
Let x = 7376/19 - 388. Find u such that -x + 6/19*u + 0*u**2 - 2/19*u**3 = 0.
-2, 1
Let x(t) = 23*t**3 + 271*t**2 + 8*t + 8. Let p(s) = -15*s**3 - 180*s**2 - 5*s - 5. Let m(w) = 8*p(w) + 5*x(w). Let m(c) = 0. Calculate c.
-17, 0
Suppose -2*d - y = -5*y + 40, -d - y - 35 = 0. Let r = d + 31. Factor g**3 + r - g - 1/4*g**4 - 3/4*g**2.
-(g - 2)**2*(g - 1)*(g + 1)/4
Let t(f) be the first derivative of 2*f**3/9 + 4*f**2/3 + 2*f + 126. Let t(q) = 0. Calculate q.
-3, -1
Let q = -87 + 89. Factor 20*l + 20 - 2*l**2 - 5*l**3 + 0*l**3 - 3*l**q.
-5*(l - 2)*(l + 1)*(l + 2)
Suppose -1576 = 16*i - 1624. Let y(k) be the first derivative of 1/21*k**i + 2/7*k**2 + 3/7*k - 11. Determine m so that y(m) = 0.
-3, -1
Let l(y) = -y**2 - 1. Let q be (3 - 1) + 42/14. Let p(u) = -30*u + 20. Let b(w) = q*l(w) - p(w). Solve b(g) = 0 for g.
1, 5
Let a be (5/9)/(-2*(-30)/72). Factor 8/15*s**2 + 0 + a*s - 2/15*s**3.
-2*s*(s - 5)*(s + 1)/15
Let q(o) = -3*o + 23. Suppose 4*m = 8 + 20. Let v be q(m). Factor 4/5*x**v - 4/5*x + 14/5*x**4 - 2/5 + 4/5*x**5 + 16/5*x**3.
2*(x + 1)**4*(2*x - 1)/5
Let z be 5*-1*(42/(-28) + 47/50). Suppose -2/5*d**2 + 0 + z*d = 0. What is d?
0, 7
Let t(d) = -d**2 + 3*d + 21. Let b be t(6). Let p(s) be the first derivative of s**b - 9/16*s**4 - 1/2*s**2 - 4 + 0*s. Factor p(m).
-m*(3*m - 2)**2/4
Let g(j) be the second derivative of 0 - 8*j - 1/12*j**4 + 2/3*j**3 - 2*j**2. Solve g(w) = 0 for w.
2
Solve 4*g**2 - 1/4*g**5 + 0*g + 5/4*g**4 + 11/2*g**3 + 0 = 0 for g.
-2, -1, 0, 8
Let l(d) = 7*d**2 - d + 1. Let a be l(-2). Find t, given that -35*t**4 - 4*t - a*t**3 + 39*t**2 - 20*t**3 - 4 + 55*t**3 = 0.
-1, -2/7, 2/5, 1
Factor 1 + 5/4*y**2 + 2*y + 1/4*y**3.
(y + 1)*(y + 2)**2/4
Let c(z) be the second derivative of -1/2*z**3 + 0*z**4 + 1/120*z**6 - 1/20*z**5 + 0*z**2 - 2*z + 0. Let y(q) be the second derivative of c(q). Factor y(j).
3*j*(j - 2)
Let i be -8*1 - (94/10 + -18). Factor 12/5 + 39/5*w**2 - 36/5*w - 18/5*w**3 + i*w**4.
3*(w - 2)**2*(w - 1)**2/5
Let b(r) be the first derivative of 0*r - 1/3*r**3 - 5 + 1/2*r**4 - 1/5*r**5 + 0*r**2. Factor b(c).
-c**2*(c - 1)**2
Let d(c) = c**4 + 3*c**3 + 9*c**2 - 11*c + 6. Let r = 63 + -68. Let v(a) = -2*a**4 - 3*a**3 - 9*a**2 + 10*a - 6. Let l(t) = r*d(t) - 4*v(t). Solve l(n) = 0.
-2, 1
Let w(q) be the first derivative of 3*q**5/100 + q**4/20 - q**3/10 - 3*q**2/10 + 28*q - 1. Let c(i) be the first derivative of w(i). Factor c(m).
3*(m - 1)*(m + 1)**2/5
Find o such that 35*o**2 + 115*o**3 - 45/2 - 105/2*o - 125/2