*s**2 - 18*s + 36 + 66.
-(s - 1)*(s + 5)*(s + 15)
Suppose 107 = 6*d + 77. Suppose -10*i**4 - 4*i**d + 136*i**2 - 52*i**4 + 60*i + 12*i**4 + 14*i**4 - 100 - 56*i**3 = 0. What is i?
-5, -1, 1
Factor 2699*j + 1753*j + 27*j**2 - 4450 + 15*j**2 - 44*j**2.
-2*(j - 2225)*(j - 1)
Let i(r) be the first derivative of -r**5/140 - 3*r**4/56 + 2*r**3/7 + 98*r**2 + 9. Let w(l) be the second derivative of i(l). Let w(q) = 0. Calculate q.
-4, 1
Let h = 940 - 1228. Let o be (-17)/14 + h/(-192). Let 1/7*k**3 + o + 4/7*k**2 + 5/7*k = 0. What is k?
-2, -1
Let i(u) be the second derivative of u**5/5 - 7*u**4/3 + 20*u**3/3 - 1567*u - 1. Solve i(m) = 0 for m.
0, 2, 5
Let d(r) be the first derivative of r**4/6 - 8*r**3/3 - 61*r**2/3 - 32*r - 1312. Determine s so that d(s) = 0.
-3, -1, 16
Suppose -4*j + 10*w = -2*j + 80, j + w - 32 = 0. Factor j*v - 45/4*v**2 + 5.
-5*(v - 2)*(9*v + 2)/4
Let i be (1495/(-650) + 28/8)/(42/10). What is c in -i*c**2 - 1058/7 - 92/7*c = 0?
-23
Let x(u) = 5*u - 220. Let h(o) = -5*o + 221. Let f(j) = -3*h(j) - 2*x(j). Let a be f(45). Factor -2/3 + 0*w**a - w + 1/3*w**3.
(w - 2)*(w + 1)**2/3
Let -768568 - 4*x**3 + 768568 + 92*x**2 + 432*x = 0. What is x?
-4, 0, 27
Let a = -81810 + 81813. Factor 0 - 2/3*m**a + 28/3*m**2 + 0*m.
-2*m**2*(m - 14)/3
Let j(k) be the second derivative of k**4/96 - 45*k**3 + 72900*k**2 + 4881*k. Factor j(c).
(c - 1080)**2/8
Suppose -11 = -4*p + o, 14 = p + 4*p - o. Suppose -3*s + 9 + p = 0. Let -4/5*y**2 + 0*y + 0 - 2/5*y**3 + 2/5*y**s = 0. Calculate y.
-1, 0, 2
Let d(y) be the third derivative of -43*y**5/150 + 259*y**4/120 - y**3/10 + 235*y**2 - 12*y. Let d(r) = 0. Calculate r.
1/86, 3
Let g = 16266 - 16266. Let r(x) be the second derivative of g - 3/5*x**5 + 0*x**2 + 2/75*x**6 - 50/3*x**3 + 5*x**4 + 18*x. Factor r(n).
4*n*(n - 5)**3/5
Let f(l) be the first derivative of 1/20*l**5 + 5/8*l**2 - 3/4*l**3 + 0*l + 3/16*l**4 - 28. Let f(o) = 0. What is o?
-5, 0, 1
Solve -4*k**2 - 18785*k + 39543*k - 18282*k = 0.
0, 619
Let p(z) be the second derivative of -9*z**2 - 4/5*z**6 + 3*z - 1/14*z**7 - 17/2*z**4 + 0 - 23/2*z**3 - 18/5*z**5. Factor p(v).
-3*(v + 1)**3*(v + 2)*(v + 3)
Let t(s) be the second derivative of -s**4/48 + 51*s**3 - 611*s**2/2 + 80*s - 1. Factor t(y).
-(y - 1222)*(y - 2)/4
Let c(l) be the second derivative of 0*l**2 - 4/33*l**3 - 8*l - 1/165*l**6 - 1/22*l**5 - 4/33*l**4 - 2. Suppose c(q) = 0. What is q?
-2, -1, 0
Suppose 0 = 3*u - 12 - 3. Suppose 3*o = 2*g - 21, u*g + 6*o = 3*o. Determine l, given that -1 - 15*l**2 + 354*l - 349*l - 5*l**g + 16 = 0.
-3, -1, 1
Suppose -5*r = -c - 13, 4*c + 2 = -0*c - 5*r. Let a be 4*(c/(-30) - (-6)/15). Factor 4*i**3 - 227*i**2 + 227*i**a + 4*i**4.
4*i**3*(i + 1)
Solve -162*l**5 - 3*l**3 + 324*l**5 - 158*l**5 + 3*l - 11*l**4 - 4*l**3 + 11*l**2 = 0.
-1, -1/4, 0, 1, 3
Let w(q) be the second derivative of q**4/30 - 7*q**3/3 + 286*q**2/5 - 6785*q. Factor w(n).
2*(n - 22)*(n - 13)/5
Let l(o) be the third derivative of o**8/896 + 5*o**7/112 + 113*o**6/160 + 207*o**5/40 + 81*o**4/8 - 108*o**3 + 382*o**2 - o. Let l(a) = 0. What is a?
-8, -6, 1
Factor 342 - 691 + 25*c - 2*c**2 + 265 + 61*c.
-2*(c - 42)*(c - 1)
Determine j so that 28/11*j**4 - 320/11 + 20*j**2 + 134/11*j**3 - 64/11*j + 2/11*j**5 = 0.
-5, -4, -2, 1
Let t(d) be the first derivative of 17*d**3/12 + 59*d**2/8 - 9*d + 4129. Determine b, given that t(b) = 0.
-4, 9/17
Let b(s) be the first derivative of s**4/42 + 4346*s**3/21 + 4721929*s**2/7 + 20521503434*s/21 - 13706. Factor b(q).
2*(q + 2173)**3/21
Let r(n) be the first derivative of n**3/6 - 19*n**2 - 2074. Determine x so that r(x) = 0.
0, 76
Let x be 2/(-3)*231/(-14). Let n = x + 1. Factor -t**2 - 16*t + n*t**3 + 8*t**4 - 8*t**2 - 4*t**5 - 7*t**2.
-4*t*(t - 2)**2*(t + 1)**2
Let d(a) be the first derivative of 0*a + 0*a**2 + 70 - 10*a**3 - 5/3*a**6 + 55/4*a**4 + 3*a**5. Find j, given that d(j) = 0.
-2, 0, 1/2, 3
Factor 0 + 0*v - 3/8*v**5 - 123/4*v**4 + 0*v**2 - 243/8*v**3.
-3*v**3*(v + 1)*(v + 81)/8
Let v(u) = -4*u**2 - 90*u + 1152. Let d(s) = s**2 - s. Suppose -11*z = 63 + 3. Let c(i) = z*d(i) - v(i). Factor c(x).
-2*(x - 24)**2
Let i be 1 + (-788)/(-220) - 31/(4092/24). Factor 6/5*p**2 - i*p + 12/5.
2*(p - 3)*(3*p - 2)/5
Let m = 9712 - 9708. Determine a so that 0*a + 0 + 1/3*a**m - 1/3*a**3 - 2/3*a**2 = 0.
-1, 0, 2
Let i(g) be the second derivative of 1/54*g**4 + 1/540*g**5 - 1/1620*g**6 - 9*g + 0 + 2/3*g**3 + 0*g**2. Let w(p) be the second derivative of i(p). Factor w(k).
-2*(k - 2)*(k + 1)/9
Factor -863/4*j - 1/4*j**2 + 865/2.
-(j - 2)*(j + 865)/4
Let c(p) be the third derivative of 1/24*p**4 + 4/105*p**7 + 0 - 2/15*p**5 + 0*p - 1/21*p**8 + 1/8*p**6 + 0*p**3 - 33*p**2. Let c(q) = 0. Calculate q.
-1, 0, 1/4, 1
Let m(t) = 612*t - 51. Let p be m(3). Let x be (-14)/(-10)*170/p. Factor 4/15 - 2/15*u**2 - x*u.
-2*(u - 1)*(u + 2)/15
Let p = -432 + 453. Let f be (6/4)/((252/32)/p). Determine q, given that 0*q + 1/2*q**3 + 0 + 3/4*q**f + 0*q**2 + 1/4*q**5 = 0.
-2, -1, 0
Let g = 3564/17 + -85519/408. Let x(k) be the third derivative of 0 + 0*k + 4*k**2 - 1/16*k**3 + 1/32*k**5 + g*k**4 + 1/240*k**6. Factor x(v).
(v + 1)*(v + 3)*(4*v - 1)/8
Let v(l) be the second derivative of l**6/6 + 55*l**5/2 + 535*l**4/12 - 545*l**3/3 - 9*l. Suppose v(i) = 0. What is i?
-109, -2, 0, 1
Factor -2/3*w**2 + 208/3*w - 800/3.
-2*(w - 100)*(w - 4)/3
Suppose 110*h - 107*h + 18 = p, 5*p = -4*h - 5. Let n(v) be the second derivative of 0 - 1/66*v**p + 1/220*v**5 + 21*v - 1/22*v**2 + 1/132*v**4. Factor n(f).
(f - 1)*(f + 1)**2/11
Let m(z) be the third derivative of 1/12*z**4 - 9 - 20/3*z**3 + 1/30*z**5 + 0*z - 6*z**2. Factor m(v).
2*(v - 4)*(v + 5)
Suppose 54*r**2 + 31*r - 10*r**4 + 54*r + 30*r - 151*r + 16*r**3 = 0. What is r?
-2, 0, 3/5, 3
Let f = 4 + -2. Suppose -35 = 216*o - 582 - 317. Factor -13/9*m**3 - 10/3*m**f - 4/9*m**5 - m + 20/9*m**o + 0.
-m*(m - 3)**2*(2*m + 1)**2/9
Suppose 0 = 5*i - 2*v - 58, -3*i - v + 35 = -2*v. Suppose 3*j + i = 6*j. Let -3*c**3 + 5*c**4 - 6*c**j + 0*c**2 - 2*c**2 = 0. Calculate c.
-2, -1, 0
Let i(w) = -49*w**3 - 3*w**2 + 4*w + 24. Let v(d) = -8*d**3 - d. Let c(o) = i(o) - 6*v(o). Let c(h) = 0. What is h?
-4, -2, 3
Factor -50582*a**2 + 6996*a**2 - 2316*a + 7635*a**2 - 6 - 38547*a**2 - 12.
-2*(193*a + 3)**2
Let x = -312 - -4682/15. Let o(a) be the first derivative of x*a**3 - 13 + 0*a + 0*a**2. Find b, given that o(b) = 0.
0
Let m(d) = -54*d**2 + 2233*d - 506. Let k(n) = 27*n**2 - 1116*n + 252. Let b(r) = 7*k(r) + 3*m(r). Factor b(a).
3*(a - 41)*(9*a - 2)
Suppose 11*y - 7791 = 32*y. Let u be 3392/y + 9 + 1. Factor 160/21*d + 8/3 - u*d**3 + 34/7*d**2.
-2*(d - 7)*(3*d + 2)**2/21
Let a(f) = -3*f**2 + 57*f - 208. Let j be a(14). Let t(y) be the first derivative of 0*y + 1/3*y**3 + 3 + y**j. Factor t(h).
h*(h + 2)
Let w = -54948 + 608544/11. Let u = w + -374. Suppose 2/11*g**2 - 4/11 + u*g = 0. What is g?
-2, 1
Let q(m) = -19*m**4 + 110*m**3 - 3018*m**2 - 10559*m + 13450. Let w(o) = -6*o**4 - o**3 - 2*o**2 - o - 2. Let n(i) = -3*q(i) + 9*w(i). Factor n(a).
3*(a - 58)**2*(a - 1)*(a + 4)
Suppose 26*w - 35*w = -8181. Factor 5*d**4 + w*d**3 - 447*d**3 - 447*d**3.
5*d**3*(d + 3)
Suppose 84 = 21*n - 7*n. Suppose 15*d - 2*d**4 + 4*d**5 + 44*d**2 - 17*d**3 + n*d**4 - 31*d - 19*d**3 = 0. Calculate d.
-4, 0, 1
Let y be -1 - (3 - 7) - (-9275)/(-3025). Let c = 314/1089 + y. Determine t so that c*t**2 - 4/9 + 2/9*t = 0.
-2, 1
Factor -688/9*a - 686/9 - 2/9*a**2.
-2*(a + 1)*(a + 343)/9
Let h(c) be the second derivative of 0*c**2 - 1/10*c**6 + 2/3*c**3 + 0 + 2/3*c**4 + 1/20*c**5 - 20*c. Factor h(s).
-s*(s - 2)*(s + 1)*(3*s + 2)
Suppose 389*q = -363*q + 772*q - 40. Factor 24/5*u**q + 0 - 4*u - 4/5*u**3.
-4*u*(u - 5)*(u - 1)/5
Let a(f) = -4*f**2 - 1523*f - 13018. Let k be a(-372). Find q such that -2 - k*q**2 + 1/3*q**3 + 11/3*q = 0.
1, 2, 3
Let b(w) = 18*w**3 - 141*w**2 + 873*w - 582. Let p(k) = k**3 + k**2 + 6. Let x(u) = b(u) - 21*p(u). Factor x(v).
-3*(v - 4)*(v - 1)*(v + 59)
Let y = -530218 + 5302181/10. Factor 1/10*b**3 + 3/5*b**2 - 4/5 - 2/5*b - y*b**4.
-(b - 2)**2*(b + 1)*(b + 2)/10
Factor 29364*n**4 + 5859691 - 8519680*n - 616811 + 3573450*n**2 + 113441*n**4 + 1618230*n**2 - 1406080*n**3.
5*(13*n - 32)**4
Let o(g) = -g**3 + 6*g**2 - 42*g + 58. Let z(f) = 2*f**3 - 8*f**2 + 42*f