/7
Suppose -106*c + 3*r + 14 = -102*c, 3*c + 3*r = 21. Let g be 2/c + ((-188)/(-30) - 4). Let 150*b**3 - 112/3*b - 110*b**2 - g = 0. Calculate b.
-2/15, 1
Let o be ((-4968)/(-69) - 72)*(2 + (-10)/4). Find j such that 13/4*j**3 - 3/2*j**4 + 1/4*j**5 + o + j - 3*j**2 = 0.
0, 1, 2
Let j(o) be the second derivative of o**5/70 + 11*o**4/42 + 8*o**3/7 + 1384*o. Factor j(g).
2*g*(g + 3)*(g + 8)/7
Let h = -375 - -529. Suppose -v - 6*v = -h. Factor -18*l**3 + 2*l**2 + v*l**2 - 9*l + 940*l**5 - 937*l**5.
3*l*(l - 1)**3*(l + 3)
Suppose 0 = 5*d - 4*r - 119, -d - 4*r = -4*d + 73. Let j be ((-2576)/d)/(-2 - -1). Factor -j*x + 4*x**2 + 563 + 113 + 8*x.
4*(x - 13)**2
Let j be 1/3*9*(-80)/(-24). Suppose j*z = -76*z. Let z + 1/7*u**3 - 3/7*u + 2/7*u**2 = 0. What is u?
-3, 0, 1
Let o(d) be the second derivative of -d**4/42 + d**3/21 + 20*d**2/7 + 7408*d. Factor o(k).
-2*(k - 5)*(k + 4)/7
Let p = -67199 - -268801/4. Factor -p*l**4 - 5/2 + 35/4*l + 25/4*l**3 - 45/4*l**2.
-5*(l - 2)*(l - 1)**3/4
Let g(q) be the third derivative of 11/2*q**4 + 52/15*q**5 + 8/35*q**7 + 1/84*q**8 + 19/15*q**6 + 118*q**2 + 16/3*q**3 + 0*q + 0. Factor g(j).
4*(j + 1)**4*(j + 8)
Let c(q) = -2*q + 1. Let g be c(-19). Let x = g + -37. Suppose -12*o**x + 2*o**2 + 4*o**2 - 2*o + 4*o = 0. Calculate o.
0, 1/3
Let h(v) be the first derivative of -v**6/30 + v**5/5 + 2*v**4/3 + 19*v**2 + 93. Let g(c) be the second derivative of h(c). Factor g(j).
-4*j*(j - 4)*(j + 1)
Suppose 0 = -l + 13 + 1. Let j(d) = -l*d + 21 - 6 + 9 + 38*d + 4*d**2. Let q(y) = -1. Let z(v) = j(v) + 4*q(v). Factor z(t).
4*(t + 1)*(t + 5)
Factor 83 + 59*u**2 - 141*u - 2*u**3 - u**3 + 16*u**2 - 14 + 0*u**3.
-3*(u - 23)*(u - 1)**2
Let a(m) = -6461*m - 271362. Let p be a(-42). Let l(b) = b**2 - 2. Let t be l(2). Let 4/9*x**t + p*x - 2/9*x**4 + 0 + 2/9*x**3 = 0. What is x?
-1, 0, 2
Let c(w) = -36*w**3 + 387*w**2 - 219*w - 8202. Let i(l) = 5*l**3 - 55*l**2 + 32*l + 1172. Let y(p) = -2*c(p) - 15*i(p). Let y(h) = 0. What is h?
-4, 7, 14
Let z = -35580/17 - -106774/51. Factor -4/3 + z*r**4 + 2*r**3 - 2*r + 2/3*r**2.
2*(r - 1)*(r + 1)**2*(r + 2)/3
Determine h, given that 1205*h**4 - 4316*h**5 + 646*h**3 + 2492*h**3 - 20 + 2440*h + 7427*h**3 + 791*h**5 - 10665*h**2 = 0.
-2, 2/235, 1/3, 1
What is w in -2880*w - 305*w**2 + 3160 + 2268*w + 301*w**2 = 0?
-158, 5
Let h(q) be the first derivative of -2*q**4/3 + q**3/9 - 756. Factor h(p).
-p**2*(8*p - 1)/3
Let i(h) = -2*h**5 + 13*h**4 + 6*h**3 - 22*h**2. Let t(x) = x**5 - 6*x**4 - 3*x**3 + 10*x**2. Let b(p) = -6*i(p) - 13*t(p). Determine d, given that b(d) = 0.
-1, 0, 2
Let r(t) be the first derivative of 0*t - 12/5*t**5 + 16*t**3 - 16*t**2 - 2*t**4 + 2/3*t**6 + 87. Suppose r(q) = 0. What is q?
-2, 0, 1, 2
Let h(k) = 49*k + 111. Let r be h(6). Factor -32*a**3 - 84*a**2 + r*a**4 - 202*a**4 - 207*a**4 - 72*a.
-4*a*(a + 2)*(a + 3)**2
Let k(a) be the third derivative of a**5/30 - 7*a**4/4 + a**2 - 1131*a + 1. Factor k(z).
2*z*(z - 21)
Let v = 473/3420 + 53/380. Let g(r) be the first derivative of -7 - 4/3*r - 10/3*r**2 + v*r**6 + 7/15*r**5 - 31/9*r**3 - 13/12*r**4. Factor g(d).
(d - 2)*(d + 1)**3*(5*d + 2)/3
Let l(c) be the first derivative of c**5/25 + c**4/15 - 4*c**3/15 - 225*c + 66. Let s(w) be the first derivative of l(w). Factor s(n).
4*n*(n - 1)*(n + 2)/5
Let a = 1255/2 - 626. Let x(s) be the first derivative of a*s**2 - 1/4*s**4 + 0*s**3 + 2*s + 20. Suppose x(u) = 0. Calculate u.
-1, 2
Let s(v) = -90*v**2 - 1460*v + 480. Let f(l) = 46*l**2 + 731*l - 237. Let h(q) = 5*f(q) + 2*s(q). Factor h(p).
5*(p + 15)*(10*p - 3)
Let f(k) be the first derivative of k**7/1820 - 17*k**6/2340 + 11*k**5/390 - 2*k**4/39 + 17*k**3/3 - 3. Let g(q) be the third derivative of f(q). Factor g(m).
2*(m - 4)*(m - 1)*(3*m - 2)/13
Let o(d) be the first derivative of 5/16*d**4 + 25 + 1/20*d**5 + 1/12*d**3 - 21/8*d**2 - 9/2*d. Factor o(b).
(b - 2)*(b + 1)*(b + 3)**2/4
Let j(h) be the third derivative of -1/40*h**5 + 0*h + 0 - 11/2*h**3 - 59*h**2 - 23/16*h**4. Factor j(t).
-3*(t + 1)*(t + 22)/2
Let d(s) be the first derivative of -2*s**5/35 + 90*s**4/7 - 16904*s**3/21 + 31680*s**2/7 - 61952*s/7 + 130. Determine h, given that d(h) = 0.
2, 88
Suppose 4*c = 3*l - 274, 4*c = -2*l + 38 + 118. Let q = l - 84. Factor 43*p**3 + 4*p**4 - 43*p**3 + q*p**4 - 27*p**5.
-3*p**4*(9*p - 2)
Suppose -47*o + 276 = 15*o + 16*o + 120. Factor -6*f - 18 - 1/2*f**o.
-(f + 6)**2/2
Let v(i) be the third derivative of -i**8/224 - 19*i**7/560 + i**6/64 + i**5/2 + 11*i**4/16 - i**3 - 12340*i**2. Suppose v(r) = 0. Calculate r.
-4, -2, -1, 1/4, 2
Determine w, given that 242*w**4 - 14*w**4 + 2*w**5 - 12996 + 3179*w**3 - 688*w**2 - 19950*w + 3313*w**3 = 0.
-57, -1, 2
Suppose -837*m - 817*m + 1784*m - 68*m**2 + 2*m**3 - 64 = 0. What is m?
1, 32
Let a(w) be the second derivative of w**7/231 + 4*w**6/33 + 27*w**5/55 + 26*w**4/33 + 17*w**3/33 - 640*w. Find i, given that a(i) = 0.
-17, -1, 0
Let f(n) be the second derivative of -2 - 12*n**2 + 3*n**4 - 26/3*n**3 + 2*n**5 + 37*n. What is v in f(v) = 0?
-3/2, -2/5, 1
Let a(f) be the first derivative of 71 + 9/7*f**2 + 1/7*f**3 - 3/7*f**4 + 0*f + 3/35*f**5. Factor a(z).
3*z*(z - 3)*(z - 2)*(z + 1)/7
Let w(m) be the first derivative of m**7/42 + m**6/15 + m**5/20 + 46*m - 9. Let h(y) be the first derivative of w(y). Let h(v) = 0. What is v?
-1, 0
Let j(t) be the first derivative of t**3/12 + 23*t**2/8 - 1677. Determine b so that j(b) = 0.
-23, 0
Let x(m) be the first derivative of 4*m**5/25 - 21*m**4/5 + 16*m**3/3 + 1692. Factor x(c).
4*c**2*(c - 20)*(c - 1)/5
Let t be 1*4/(-6)*581/2. Let g = -2869/15 - t. Factor 2/5*a**2 + g - 14/5*a.
2*(a - 6)*(a - 1)/5
Let a = -34/6557 - -236290/45899. Let 400/7 - 120/7*g - 2/7*g**3 - a*g**2 = 0. Calculate g.
-10, 2
Let s(b) be the second derivative of b**6/45 - 3*b**5/10 - 36*b**4 - 528*b**3 + 2*b - 3365. Factor s(i).
2*i*(i - 33)*(i + 12)**2/3
Let o(f) be the first derivative of -3*f**7/70 + 11*f**6/40 - f**5/4 - 3*f**4/8 + 3*f**2 - 130. Let q(h) be the second derivative of o(h). Factor q(v).
-3*v*(v - 3)*(v - 1)*(3*v + 1)
Let 15/2*f**2 + 4*f**3 - 6 - 3/2*f**4 - 16*f = 0. Calculate f.
-2, -1/3, 2, 3
Determine b so that -1577 + 3*b - 4*b**4 + 5*b + 788 + 789 + 4*b**2 - 8*b**3 = 0.
-2, -1, 0, 1
Let j be (43/(3784/110))/(-4 - (-69)/12). Let c be 2 - -2*5/(-14). Determine u so that -2/7 - 6/7*u**5 + c*u**2 + j*u - 11/7*u**3 - 19/7*u**4 = 0.
-2, -1, 1/3, 1/2
Let x(s) = -2*s**2 - s - 1. Let p(u) = -13*u**2 - 101*u - 5. Let j be (30/(-9))/(22/(-33)). Let z(o) = j*x(o) - p(o). Factor z(w).
3*w*(w + 32)
Let a be (-2 + -11 - -7)*28*(-5)/540. Factor -4/9 + 2*i - a*i**2.
-2*(i - 1)*(7*i - 2)/9
Let c(f) be the third derivative of -1/690*f**5 + 0 + 0*f**3 + 1/69*f**4 + 0*f - 60*f**2. Solve c(a) = 0.
0, 4
Suppose k + 5*j = 11, -25 - 3 = -5*k + 2*j. Factor -17*a + 8 + 28*a**2 - 6*a**2 + k*a + 59*a.
2*(a + 2)*(11*a + 2)
Let i(u) = -4 - 23*u**2 + 238*u**2 + 581*u + 612*u + 15*u**3 - 1151*u. Let d(a) = 60*a**3 + 861*a**2 + 168*a - 18. Let p(m) = 2*d(m) - 9*i(m). Factor p(n).
-3*n*(n + 14)*(5*n + 1)
Let m(i) be the third derivative of i**8/140 - 43*i**7/525 - 47*i**6/300 + 17*i**5/50 + 41*i**4/60 - 8*i**3/15 - 11*i**2 + 150*i. What is s in m(s) = 0?
-1, 1/6, 1, 8
Let c(r) = 9*r - 79. Let h be c(9). Factor -24*m + 154*m**4 - 80*m**h + 18*m**3 - 73*m**4 - 67*m**4.
2*m*(m - 2)*(m + 3)*(7*m + 2)
Let y(h) = -h**4 + h**3. Let k(x) = 3*x**5 - 7*x**3 + 3*x**4 - 26*x - 12*x**2 + x**3 + 38*x. Let n(r) = k(r) - 3*y(r). Determine a, given that n(a) = 0.
-2, 0, 1
Let v = 11313 - 11312. Let r(n) be the first derivative of -8/3*n**2 - 8/3*n - v + 2/15*n**5 + 1/3*n**4 - 2/3*n**3. Solve r(d) = 0.
-2, -1, 2
Determine i, given that 5960/3*i**3 - 65320*i**2 + 49665*i**4 - 80/3 - 2640*i + 16335*i**5 = 0.
-2, -2/99, 1
Suppose 2*r + 5*r - 21 = 0. Let k be (-2)/r - (55/(-15) - 0). Factor -3*o**k + 15*o + 15*o**2 + 12 - 24*o - 15*o.
-3*(o - 2)**2*(o - 1)
What is i in -6*i + 125*i - 10*i - 23*i**2 + 48*i**2 - 3*i**2 - 5 = 0?
-5, 1/22
Let v(c) = 4*c**2 + 42*c + 76. Let z(n) = 68*n - 94 - 4*n**2 - 49*n + 16 - 60*n. Let q(r) = -3*v(r) - 2*z(r). Factor q(o).
-4*(o + 2)*(o + 9)
Let c be (-8961)/(-1545) + -5 + 4. Factor 56/5*b + 12*b**2 + c*b**3 + 2/5*b**4 + 18/5.
2*(b + 1)**3*(b + 9)/5
Let m = -13268 - -13271. Let j(u) b