g**6/90 + 1369*g**5/30 + g**4/2 + 105*g. Let c(m) be the third derivative of q(m). Factor c(f).
4*(f - 37)**2
Let d(q) = -24*q**3 + 130*q**2 + 160*q + 246. Let l(c) = c**3 - 5*c**2 - c - 3. Let t(m) = 2*d(m) + 44*l(m). Factor t(b).
-4*(b - 15)*(b + 2)*(b + 3)
Suppose -2*j = 5*y + 96, -j + 3*y + y - 22 = 0. Let t be 0/(0 + 1)*(-19)/j. Factor 0*z + t + 3/7*z**4 + 0*z**3 - 3/7*z**2.
3*z**2*(z - 1)*(z + 1)/7
Determine b so that -246/7*b - 1180/7 - 2/7*b**2 = 0.
-118, -5
Let c(t) be the second derivative of t**5/120 - 13*t**4/18 - 55*t**3/36 + 53*t**2/6 + 6*t + 170. Find g such that c(g) = 0.
-2, 1, 53
Suppose 10*o - 8*o + q = 3, -2*o + 2*q - 6 = 0. Let u(i) be the third derivative of 0 + 5*i**2 + 0*i**3 + o*i**5 + 0*i - 1/40*i**4 + 1/200*i**6. Factor u(n).
3*n*(n - 1)*(n + 1)/5
Let s = 102 + -102. Factor s - 3*m**2 + 13592*m**3 + 0 + 2*m - 13591*m**3.
m*(m - 2)*(m - 1)
Let q be 24/(-6) + (-16)/576*-156. Factor 1/3*v**4 - 4/3*v + 4/3*v**3 + 0 - q*v**2.
v*(v - 1)*(v + 1)*(v + 4)/3
Suppose 16*l - 13 - 55 = 12. Factor 4/3*i**4 + 8/3*i**3 - 4/3*i**l - 4/3*i + 4/3 - 8/3*i**2.
-4*(i - 1)**3*(i + 1)**2/3
Let h be (-3)/(-15)*(18 + -8). Find p such that -16*p - 190*p + 16*p - 5*p**h = 0.
-38, 0
Let x(k) = -k**2 - 903*k - 198450. Let b be x(-378). Let z(s) = 2*s**2 - 3*s. Let p be z(2). Factor -1/3*d**3 + 1/6*d**4 - 1/6 + b*d**p + 1/3*d.
(d - 1)**3*(d + 1)/6
Let y(t) be the first derivative of 5/3*t**2 + 4/3*t + 41 + 2/3*t**3. Factor y(q).
2*(q + 1)*(3*q + 2)/3
Suppose 230418*z - 4*z**3 + 60*z**2 + 420 - 229710*z + 224 = 0. Calculate z.
-7, -1, 23
Let u(g) be the first derivative of g**4/18 - 10*g**3/27 - 73*g**2/9 + 154*g/9 + 1733. Factor u(p).
2*(p - 11)*(p - 1)*(p + 7)/9
Let w(t) be the second derivative of 5/2*t**2 - 1/12*t**4 + 0 + 2/3*t**3 + 39*t. Suppose w(x) = 0. What is x?
-1, 5
Let h(v) be the third derivative of 3*v**5/20 + 11*v**4/8 - 17*v**3/3 - 215*v**2. Let u(k) = 40*k**2 + 133*k - 137. Let p(f) = -9*h(f) + 2*u(f). Solve p(g) = 0.
-32, 1
Suppose -137 = -5*h - 102. Let y be ((138/9)/(-23))/(h/(-3)). Factor 14 - 4*o + y*o**2.
2*(o - 7)**2/7
Let z be -2 + (0 - -1 - -1) - (-50 - -46). Let q(g) be the second derivative of 0 - 6*g + 5/6*g**z + 0*g**2 + 1/15*g**6 + 2/3*g**3 + 2/5*g**5. Factor q(s).
2*s*(s + 1)**2*(s + 2)
Suppose 2*r = 3*s - 1415, s + 17*r = 12*r + 500. Suppose 457 = -9*i + s. Suppose -1/7*y**i - 6/7 + y = 0. What is y?
1, 6
Let o = -907 - -965. Solve -7*m + o*m - 6*m**2 + 2*m**2 - 7*m = 0.
0, 11
Factor 252*w**3 - 1314*w**2 + 69 - 1260*w - 870 + 3*w**4 + 5270*w - 2150*w.
3*(w - 3)*(w - 1)**2*(w + 89)
Let x(n) = 4*n**2 + 3. Let v be x(0). Let i be -1 + -1 - (-4 - (3 - v)). Solve 5*h + 2*h**2 - 5*h**2 + 3*h + 5*h**i = 0 for h.
-4, 0
Let s(m) be the second derivative of m**7/56 - 9*m**6/10 + 1251*m**5/80 - 859*m**4/8 + 735*m**3/2 - 675*m**2 + 2*m - 234. Factor s(r).
3*(r - 15)**2*(r - 2)**3/4
Let d(s) = -2*s**2 + 138*s - 4624. Let i(f) = f**2 - 2*f. Suppose -3*j = -5*a + 9, -1 - 3 = 4*j - 4*a. Let g(h) = j*d(h) + 2*i(h). Factor g(n).
-2*(n - 68)**2
Let g(v) = 7*v**3 + 6*v**2 + 29*v + 36. Let d(x) = -5*x**2 + 43 - 5*x**3 - 30*x - 113 + 35. Let k(h) = 6*d(h) + 5*g(h). Factor k(u).
5*(u - 3)*(u + 1)*(u + 2)
Let u = 5360 + -5356. Let r(l) be the first derivative of u + 4/9*l + 2/27*l**3 - 1/3*l**2. Factor r(p).
2*(p - 2)*(p - 1)/9
Let z be (-272)/(80/(-5)) + -17. Let j(w) be the third derivative of 0*w + 0 - 1/60*w**5 + z*w**3 + 29*w**2 + 1/24*w**4. Factor j(c).
-c*(c - 1)
Let t be (1 - (-8 - -3)) + (-676)/2. Let u = t - -338. Factor u*q + 18 + 1/2*q**2.
(q + 6)**2/2
Let z = 296322 - 888962/3. Find j such that 1/9*j**3 - 20/9 + j**2 - z*j = 0.
-10, -1, 2
Let i(c) = -4 + 8*c**4 - 12*c**2 - 18*c**4 - 28*c**3 - 6*c**2. Let g(t) = t**4 + t**3 + t**2 + t - 1. Let q(l) = 4*g(l) - i(l). Solve q(n) = 0 for n.
-1, -2/7, 0
Suppose -350 = -3*s - 11. Let j = s + -113. Factor j + 0*p - 1/4*p**2 - 1/4*p**4 + 1/2*p**3.
-p**2*(p - 1)**2/4
Let z = 24051/1069 - -3/2138. Let w(s) be the first derivative of z*s**4 - 4*s - 118/3*s**3 - 81/20*s**5 + 20*s**2 + 16. Factor w(m).
-(m - 2)**2*(9*m - 2)**2/4
Factor 2*q**2 - 643 - 525 + 500*q + 1666.
2*(q + 1)*(q + 249)
Let i = 463 + -419. Let u be 11/i - 17/(-4). What is l in -u + 3*l - 1/2*l**2 = 0?
3
Let t be 22/(-4) + 8/((-80)/5). Let q be t/8*1/(-6). Factor 1/2 - 1/2*h + q*h**2.
(h - 2)**2/8
Suppose 8*b = 19*b + 15*b. Let n be (b + 0)/(8/(-4)). Let n - 18/11*k**2 - 72/11*k**4 - 32/11*k**5 - 2/11*k - 56/11*k**3 = 0. What is k?
-1, -1/2, -1/4, 0
Let f(j) = 27 + 73 + j**2 - 31*j - 49 + 37. Let p be f(3). Factor 30/13*y**3 - 18/13*y**2 + 2/13*y + 0 + 50/13*y**p.
2*y*(y + 1)*(5*y - 1)**2/13
Suppose 0 = 26862*j - 26863*j + 2. Let k(u) be the second derivative of -8/3*u**3 + 0*u**j + 11*u + 0 + 28/3*u**4 - 49/5*u**5. What is x in k(x) = 0?
0, 2/7
Let o = 1/5 + 3. Let v = -8/15 + o. Let -v - 2/3*y**3 - 10/3*y**2 - 16/3*y = 0. What is y?
-2, -1
Let o(b) be the third derivative of -3*b**6/40 + b**5/40 - 2*b**2 - 1632*b. Find m, given that o(m) = 0.
0, 1/6
Let h be -2*(-3)/(-8) - 475/(-420). Let f(l) be the second derivative of 16*l - 1/42*l**4 + 0 - 16/7*l**2 + h*l**3. Factor f(b).
-2*(b - 4)**2/7
Let d(s) = s**2 + 50*s - 153. Let n be d(-53). Let b be 3 + 5 + (0 - n). Factor 0*r - 2/9*r**5 - 2/3*r**3 - 2/3*r**4 + 0 - 2/9*r**b.
-2*r**2*(r + 1)**3/9
Let 58*v - 240 + 1/2*v**2 = 0. What is v?
-120, 4
Let q be 37 - ((-8 - -14) + -1). What is t in -66*t + q - 52*t**2 - 48*t**2 + 88 + 103*t**2 = 0?
2, 20
Let c be (-4 - 316/(-78))/((-10)/105). Let p = c + 113/65. Determine w so that -2/5*w**2 - 4/5 + p*w = 0.
1, 2
Let x(k) be the second derivative of 0*k**3 + 2209/30*k**4 - 2303/50*k**5 + 19/15*k**6 + 0 - 1/105*k**7 - 17*k + 0*k**2. Factor x(s).
-2*s**2*(s - 47)**2*(s - 1)/5
Let i(p) be the second derivative of 147*p**5/20 + 55*p**4/4 - 46*p**3 - 18*p**2 + 282*p. Let i(m) = 0. Calculate m.
-2, -6/49, 1
Let p(h) be the first derivative of 3*h**4/28 + 75*h**3/7 + 2592*h**2/7 + 33792*h/7 - 3152. Let p(y) = 0. What is y?
-32, -11
Let c(m) be the third derivative of m**6/24 - 499*m**5/60 + 395*m**4/24 + 33*m**3/2 + 801*m**2. Factor c(j).
(j - 99)*(j - 1)*(5*j + 1)
Suppose 2/5*q**2 + 32/5 - 114/5*q**3 - 34/5*q**4 + 6/5*q**5 + 108/5*q = 0. Calculate q.
-2, -1, -1/3, 1, 8
Let t(h) = h**2 - h - 1. Let o be t(-2). Let g = -1319 - -1325. Solve 3 - o + i**2 + g - 4*i = 0.
2
Let r(k) be the second derivative of -k**7/147 - 8*k**6/105 + 61*k**5/70 - 26*k**4/21 + 738*k. Let r(p) = 0. What is p?
-13, 0, 1, 4
Let g(q) be the third derivative of -1/6*q**4 + 4/5*q**3 + 0*q + 1/30*q**6 + 150*q**2 - 2/525*q**7 - 1/15*q**5 + 0. What is h in g(h) = 0?
-1, 1, 2, 3
Let h be 4/(-8) + 496/32 + -11. Let m(g) be the first derivative of 1/25*g**5 + 0*g**h + 0*g - 28 - 1/5*g**3 - 1/5*g**2. Factor m(p).
p*(p - 2)*(p + 1)**2/5
Let x(r) be the third derivative of -r**6/70 - 26*r**5/105 - 15*r**4/14 + 12*r**3/7 - 1556*r**2. Suppose x(b) = 0. What is b?
-6, -3, 1/3
Let m be (-15647)/(-300) - (-35)/42. Let k = -406/25 + m. Find u, given that 21/4*u**2 + 1/4*u**3 + k*u + 343/4 = 0.
-7
Let 203*q + 60*q**2 + 463*q - 4*q**3 + 44*q + 26*q = 0. What is q?
-8, 0, 23
Let t = 214506 - 126947. Factor -370*k**2 - t + 195*k**3 - 15*k**4 + 87439 + 340*k - 35*k**4 + 5*k**5.
5*(k - 3)*(k - 2)**3*(k - 1)
Let t(p) be the first derivative of -p**7/2940 + 11*p**6/1260 - p**3/3 - 29*p + 85. Let z(s) be the third derivative of t(s). Factor z(b).
-2*b**2*(b - 11)/7
Let w(v) be the second derivative of -27*v**5/100 - 8511*v**4/20 - 5671*v**3/10 - 567*v**2/2 + 36*v - 1. Suppose w(s) = 0. What is s?
-945, -1/3
Let f(t) be the third derivative of -4*t**7/315 - t**6/36 + t**5/30 + 5*t**4/36 + t**3/9 - 8*t**2 + 19*t. What is q in f(q) = 0?
-1, -1/4, 1
Suppose -28 - 44 = -6*k. Factor 41*l**4 + 32*l - 16 - 20*l**4 - 8*l**3 - 17*l**4 - k*l**2.
4*(l - 2)*(l - 1)**2*(l + 2)
Let z(b) = 18*b**5 - 68*b**4 + 82*b**3 - 32*b**2 - 28. Let u(w) = 7*w**5 - 27*w**4 + 33*w**3 - 13*w**2 - 11. Let s(l) = 28*u(l) - 11*z(l). Solve s(q) = 0 for q.
-6, 0, 1
Let v be (400/528 - (-3)/(-33))*-6. Let h be (v + 7 - 5/2)/1. Suppose -h*l**2 - l - 1/2 = 0. What is l?
-1
Let j(s) be the third derivative of -s**8/84 - 46*s**7/105 + s**6/10 + 67*s**5/15 - 23*s**4/3 + 63*s**2 - 9. What is x in j(x) = 0?
-23, -2, 0, 1
Suppos