
Let y = -102827 - -719798/7. Factor 0 + 1/7*r**2 + y*r.
r*(r + 9)/7
Let o = -4333 - -13000/3. Let v(s) be the second derivative of -o*s**3 - s + 0*s**2 + 0 + 1/12*s**4. Factor v(m).
m*(m - 2)
Suppose 6*p + 2 - 14 = 0. Determine z so that -135*z**4 + 140*z**5 - 50*z**p - 46*z**2 - 7*z**3 - 8*z**3 + 106*z**2 = 0.
-2/7, 0, 1/4, 1
Let i(n) be the first derivative of -2*n**5/15 - 27*n**4/2 - 350. Find f, given that i(f) = 0.
-81, 0
Let x(u) be the third derivative of -u**5/300 + u**4/6 - 32*u**3/15 + 568*u**2. Factor x(l).
-(l - 16)*(l - 4)/5
Find i such that 34/7*i**3 - 48/7*i + 0 + 2/7*i**5 + 16/7*i**4 - 4/7*i**2 = 0.
-4, -3, -2, 0, 1
Let h(r) be the first derivative of -3*r**2 - 99*r + 47 - 1/33*r**3. Determine c so that h(c) = 0.
-33
Factor 378 + 58*j**2 + j**3 + 765 - 243 + 3*j**2 + 960*j.
(j + 1)*(j + 30)**2
Let o be 1359/81 + -13 - (-2)/9. Find l, given that -107*l**2 - 4*l - 5 - 3*l**4 + 113*l**2 + 2*l**4 + o*l**3 = 0.
-1, 1, 5
Let d(h) be the first derivative of h**3/3 - 51*h**2/2 + 50*h - 1970. Let d(y) = 0. Calculate y.
1, 50
Let -1/5*c**2 - 142/5*c + 0 = 0. What is c?
-142, 0
Let o(u) = 20*u - 116 + 41*u - 44 + 38. Let z be o(2). Solve -2/7*x**3 + 0*x + 2/7*x**4 + 0 + z*x**2 = 0 for x.
0, 1
Let j be ((276/207)/((-42)/9))/(2/(-14)). Let o(s) be the second derivative of -s + 1/8*s**3 - 3/4*s**j + 0 + 1/16*s**4. Let o(p) = 0. What is p?
-2, 1
Let i(j) be the third derivative of -j**6/132 - j**5/55 - 7*j**3/6 + 82*j**2 + 2. Let r(x) be the first derivative of i(x). Let r(u) = 0. What is u?
-4/5, 0
Let b(l) be the third derivative of -l**7/1155 - 2*l**6/55 - l**5/2 - 11*l**4/6 - l**2 - 6. Factor b(x).
-2*x*(x + 2)*(x + 11)**2/11
Let x(b) = 2*b**3 + 91*b**2 - 50*b - 181. Let s be x(-46). Let y be (-8 + 6)/(1 + -2). Factor -4/5 - 9/5*j - 6/5*j**y - 1/5*j**s.
-(j + 1)**2*(j + 4)/5
Let s(i) be the first derivative of -i**3/2 + 321*i**2 - 1281*i/2 + 208. Factor s(z).
-3*(z - 427)*(z - 1)/2
Let j(f) be the second derivative of 3*f**5/20 + 7*f**4/4 + f**3 - 60*f**2 - 1721*f. What is k in j(k) = 0?
-5, -4, 2
Let r = -13569/35279 + 389486416/189977415. Let o = 2/1795 + r. What is b in -4/3*b**4 + o*b - 4/3*b**3 + 2/3*b**2 + 2/3 - 1/3*b**5 = 0?
-2, -1, 1
Let m(k) be the first derivative of -2*k**6/3 + 124*k**5/5 + 66*k**4 + 8*k**3/3 - 130*k**2 - 132*k - 7507. Factor m(w).
-4*(w - 33)*(w - 1)*(w + 1)**3
Let y(n) = -n**2 + 39 - 16 - 21 - 7*n. Let g be y(-7). Suppose -v**3 - 3*v - g*v**2 - v**3 + 3*v = 0. Calculate v.
-1, 0
Factor -60 - 36*p**2 + 67*p - 4705*p**3 + 4709*p**3 + 25*p.
4*(p - 5)*(p - 3)*(p - 1)
Factor 2 + 2*r**3 - 32 + 370*r - 128*r**2 - 214.
2*(r - 61)*(r - 2)*(r - 1)
Let g be -6 + 13 - (-3 + 5). Let i(r) = 20*r**2 + 295*r - 300. Let z(x) = -23*x**2 - 295*x + 300. Let l(n) = g*z(n) + 6*i(n). Determine k so that l(k) = 0.
-60, 1
Let m(o) be the first derivative of -2/9*o**3 - 70 + 2/3*o + 0*o**2. Factor m(t).
-2*(t - 1)*(t + 1)/3
Suppose 467*k - 898*k = -900 - 393. Factor -2/3*n**k - 30*n + 36 + 8*n**2.
-2*(n - 6)*(n - 3)**2/3
Let h(n) = -3*n**2 + 31*n - 33. Let t be h(9). Let s be (-4 - 0)*(-5)/(-20)*-2. Factor 2/5*c + 8/5*c**t - 7/5*c**s - 3/5*c**4 + 0.
-c*(c - 1)**2*(3*c - 2)/5
Let x(j) be the second derivative of -2/5*j**6 + 1 + 7/2*j**4 + 12*j**2 + 3/20*j**5 - 10*j**3 + 1/14*j**7 + 59*j. Determine q so that x(q) = 0.
-2, 1, 2
Let u = 3022 - 72523/24. Let g(o) be the third derivative of -u*o**4 + 0*o + 1/24*o**6 - 1/12*o**5 + 4*o**2 + 5/6*o**3 + 0. Solve g(z) = 0.
-1, 1
Let f(u) be the first derivative of -1/96*u**4 - 1/16*u**3 - 10*u - 39 - 1/8*u**2. Let v(k) be the first derivative of f(k). Factor v(p).
-(p + 1)*(p + 2)/8
Let y(d) be the second derivative of d**6/225 - 79*d**5/75 - 53*d**4/30 - 3*d - 543. Determine g, given that y(g) = 0.
-1, 0, 159
Let v = -9713044/17 + 571356. Let -8/17*l - 2/17*l**2 - v = 0. What is l?
-2
Let g(d) = -d**4 - 105*d**3 + 121*d**2 + 15*d - 5. Let j(t) = 2*t**3 + t**2 + 3*t - 1. Let v(c) = g(c) - 5*j(c). Factor v(s).
-s**2*(s - 1)*(s + 116)
Let a(f) be the first derivative of f**6/12 + 13*f**5/10 + 6*f**4 + 6*f**3 + 2309. Factor a(k).
k**2*(k + 1)*(k + 6)**2/2
Suppose y + 10 = 5*v, 4*v - 27 = 3*y - 30. Determine o so that -112/3*o - 32/3*o**4 + 268/3*o**v + 32/3 - 28*o**5 - 24*o**2 = 0.
-2, -2/3, 2/7, 1
Suppose 5*y + 4*b - 2034 = 0, -7*b + 3*b = 3*y - 1222. Let k = y - 1216/3. What is u in -2*u**4 + k + 2/3*u**5 - 2*u + 4/3*u**2 + 4/3*u**3 = 0?
-1, 1
Let s(v) be the second derivative of 11*v**2 + 3/2*v**4 - 1 - 1/10*v**5 + 40*v + 7*v**3. Find p such that s(p) = 0.
-1, 11
Suppose 15 = 3*t - 0. Let v(c) = c. Let w be v(t). Factor -w + 33*o + 10 + 5*o**2 - 43*o.
5*(o - 1)**2
Let v(z) be the first derivative of -2*z**3/15 - 20*z**2 + 408*z/5 - 2025. Let v(y) = 0. Calculate y.
-102, 2
Factor 1/10*r**5 - 121/2*r**4 + 122409/10*r**3 + 0 - 8363007/10*r**2 + 8120601/5*r.
r*(r - 201)**3*(r - 2)/10
Let r(t) be the first derivative of 24*t - 4*t**2 + 12 - 2/3*t**3. What is m in r(m) = 0?
-6, 2
Let g = 1737/10915 + 27/185. Let j = g - -310/531. Find v, given that -j + 2/9*v - 2/9*v**3 + 8/9*v**2 = 0.
-1, 1, 4
Let t(b) be the second derivative of -17/48*b**4 - 2*b + 73 - 1/120*b**6 - 17/24*b**3 - 7/80*b**5 - 3/4*b**2. Solve t(x) = 0.
-3, -2, -1
Let z(g) = 3*g**3 + g**2 - 3*g - 3. Let i(o) = -15*o**3 - 6*o**2 + 15*o - 11*o + 17 - o**3 + 12*o. Let c(j) = 2*i(j) + 11*z(j). Solve c(l) = 0 for l.
-1, 1
Let p(w) be the second derivative of 255/4*w**3 + 75/2*w**2 - 27/10*w**6 + 73/2*w**4 - 83*w + 0 + 39/20*w**5 + 1/4*w**7. Let p(g) = 0. Calculate g.
-1, -2/7, 5
Let u(a) be the first derivative of -a**5 + 50*a**4 - 2170*a**3/3 + 1520*a**2 + 5415*a + 463. Suppose u(c) = 0. Calculate c.
-1, 3, 19
Let k(u) = -10*u**2 + 3243*u + 6533. Let h(c) = 15*c**2 - 4865*c - 9800. Let d(l) = -7*h(l) - 10*k(l). Factor d(b).
-5*(b - 327)*(b + 2)
Let l(z) = 2*z**2 + 2 - z**2 - 4 - 2*z**3 + 3*z**3 - 4*z. Let s be l(2). Factor -6/13*i**s + 12/13 - 14/13*i.
-2*(i + 3)*(3*i - 2)/13
Let x = 33076 + -429868/13. Determine k so that -x*k - 2/13*k**3 - 36/13*k**2 + 400/13 = 0.
-10, 2
Let b(w) be the second derivative of -5/2*w**2 - 55/6*w**4 + 0 - 115/6*w**3 + 118*w. Factor b(s).
-5*(s + 1)*(22*s + 1)
Let q(i) be the first derivative of -25*i**4/4 - 160*i**3/3 + 470*i**2 + 400*i + 806. Find x, given that q(x) = 0.
-10, -2/5, 4
Let r(i) be the first derivative of -31*i**4/7 + 2*i**3/21 - 1066. Factor r(c).
-2*c**2*(62*c - 1)/7
Let z = 105712/19 - 5565. Let p = 11/38 - z. Factor 9/2*l + 1/8*l**3 + 0 + p*l**2.
l*(l + 6)**2/8
Suppose 8 = -y + 25. Factor -4*k**5 + 100*k**2 + 28*k**4 - 76*k**3 - 15*k - 78 - 66*k + 94 + y*k.
-4*(k - 2)**2*(k - 1)**3
Let d(j) = -j**3 - 15*j**2 - 53*j - 23. Let t be d(-10). Suppose -43*c + t*c + 108 = 0. Let 16/15*l + 2/15*l**c + 2/3*l**2 + 8/15 = 0. What is l?
-2, -1
Let k(g) = -14561 + 32*g - 10*g + 19*g**2 + 14541. Let x(h) = -8*h**2 - 11*h + 10. Let p(m) = 3*k(m) + 7*x(m). Factor p(r).
(r - 10)*(r - 1)
Let w(t) be the third derivative of -t**7/840 - t**6/48 + 11*t**5/240 + 203*t**2. Factor w(g).
-g**2*(g - 1)*(g + 11)/4
Let t = 285/11 - -323/44. Let v = 67/2 - t. Factor -v*h**3 + 0 - h**2 - 3/4*h.
-h*(h + 1)*(h + 3)/4
Suppose 5*h + 4*f = 26, -4*f + 82 = -h + 68. Let s(r) be the third derivative of 3*r**h + 0*r**3 - 5/24*r**4 + 0 - 1/12*r**5 + 0*r. Factor s(v).
-5*v*(v + 1)
Let g be (-168)/(-392) + (-106)/(-14) + 9/(567/(-450)). Solve 31/7*a - 1/7*a**3 - g*a**2 + 36/7 = 0.
-9, -1, 4
Let v(u) be the first derivative of 10*u**3/9 - 52*u**2/3 + 40*u/3 - 225. Factor v(h).
2*(h - 10)*(5*h - 2)/3
Let r(i) = -i**3 - 4*i - 10. Let u(c) = c**2 - 1. Let s(z) = r(z) - 3*u(z). Let a be s(-3). Factor 2*x**2 - 8*x**5 + 2*x**4 - x + 9*x**a - 4*x**2.
x*(x - 1)*(x + 1)**3
Factor -2724*i**2 + 936*i + 2830*i**2 - 144*i + 2*i**3.
2*i*(i + 9)*(i + 44)
Factor -3466875/2 - 1/6*w**2 + 1075*w.
-(w - 3225)**2/6
Let b(a) = 2*a - 30. Suppose -234 + 90 = -9*u. Let w be b(u). Factor 0*m**2 - m**2 - w*m**4 - m**2 - 2*m**2 - 6*m**3.
-2*m**2*(m + 1)*(m + 2)
Let y(a) be the second derivative of a**6/150 - 69*a**5/100 + 337*a**4/15 - 896*a**3/5 + 2048*a**2/5 + 1783*a. Solve y(b) = 0.
1, 4, 32
Let t(n) be the second derivative of 3/160*n**5 + n + 42 - 1/16*n**4 + 1/16*n**3 + 0*n**2. Solve t(p) = 0 for p.
0, 1
Determine z so that -3/5*z**2 + 38/5*z**3 + 