 d(k) be the first derivative of -55*k**3 - 155*k + 5/4*k**4 - 68 + 315/2*k**2. Factor d(i).
5*(i - 31)*(i - 1)**2
Let f(w) = w**4 + 7*w**3 - 81*w**2 + 61*w. Let a(x) = -x**4 - x**3 - 3*x**2 - x. Let i(p) = -2*a(p) + f(p). Solve i(n) = 0 for n.
-7, 0, 1, 3
Solve -2*q**2 + 436 + 893*q + 918*q + 428 - 2*q**2 - 1835*q = 0 for q.
-18, 12
Find r such that -7*r**3 - 1/9*r**5 - 106/9*r**2 - 56/9*r + 0 - 14/9*r**4 = 0.
-7, -4, -2, -1, 0
Factor 0 - 18/11*n**2 + 16/11*n**3 + 2/11*n**4 + 0*n.
2*n**2*(n - 1)*(n + 9)/11
Find d, given that 0 + 13/2*d - 2*d**2 = 0.
0, 13/4
Let i be (42/(-14) - (-111)/12)/(60/24). Let s(y) be the first derivative of 14 + 0*y + i*y**4 + 0*y**2 + 25/3*y**3 + 1/5*y**5. Factor s(o).
o**2*(o + 5)**2
Suppose 494*w + 15 = -498*w + 997*w. Let -w*t**3 - t**5 - 7/3*t**2 - 4/3 + 4*t + 11/3*t**4 = 0. What is t?
-1, 2/3, 1, 2
Let m(p) be the second derivative of -841/9*p**2 + 58/27*p**3 - 3 + p - 1/54*p**4. Find c, given that m(c) = 0.
29
Let z(c) be the second derivative of 1/30*c**5 - 2/3*c**2 + c - 2 - 7/27*c**3 + 1/18*c**4 - 1/135*c**6. Determine k, given that z(k) = 0.
-1, 2, 3
Let r(l) be the first derivative of l**4/30 - 14*l**3/15 + 49*l**2/5 + 38*l - 46. Let t(q) be the first derivative of r(q). Factor t(p).
2*(p - 7)**2/5
Let k = -188 + 213. Suppose 421*g**3 - 25*g**2 - 416*g**3 - 2*g + k + 3*g - 6*g = 0. Calculate g.
-1, 1, 5
Let f(l) = -16*l**2 + 76*l - 225. Let t = 187 + -194. Let c(k) = -11*k**2 + 50*k - 150. Let d(i) = t*c(i) + 5*f(i). Factor d(j).
-3*(j - 5)**2
Let t(s) be the second derivative of -1/4*s**5 - 38 - s - 25/6*s**3 + 5/3*s**4 + 5*s**2. Factor t(z).
-5*(z - 2)*(z - 1)**2
Let j = -304 - -555. Suppose -4*t**2 + 11*t - 5*t**3 + j + 4*t**3 - 257 = 0. Calculate t.
-6, 1
Let k be 58 + 15611/(-268) + ((-92)/(-48))/1. Factor 5/3*v + k*v**4 - 5/3*v**3 + 0 - 5/3*v**2.
5*v*(v - 1)**2*(v + 1)/3
Suppose 2*x + 0*u = 4*u - 734, 3*x + 5*u + 1046 = 0. Let g = x - -359. Factor 36/17*j**3 - 26/17*j**g + 4/17*j + 0.
2*j*(2*j - 1)*(9*j - 2)/17
Let c(g) = 93*g + 121. Let d be c(-3). Let i = d + 158. Solve 4/3*a + i - 2/3*a**2 = 0 for a.
0, 2
Let j be -11 + (21829/(-664) - -45). Factor -9/8*n**3 - 1/8*n**2 + j*n + 0 + 1/8*n**4.
n*(n - 9)*(n - 1)*(n + 1)/8
Suppose -5*g - 3*p = -79, -7 = -3*p + 2. Determine u so that -29*u**2 + 16*u**2 + u**5 + 3*u**3 + g*u**2 + 3*u**4 = 0.
-1, 0
Let y(p) be the first derivative of 0*p - 5/12*p**3 + 1/4*p**2 - 98. Factor y(t).
-t*(5*t - 2)/4
Let h(c) be the second derivative of -c**4/12 - 160*c**3 - 115200*c**2 + 2297*c. Factor h(b).
-(b + 480)**2
Factor -4/3*a**2 + 18 - 1/3*a**3 + 17*a.
-(a - 6)*(a + 1)*(a + 9)/3
Let r(u) be the second derivative of 3/5*u**5 - 2*u + 0*u**3 - 2/15*u**6 - 4 + 4/3*u**4 + 0*u**2. Find f, given that r(f) = 0.
-1, 0, 4
Let k(x) be the third derivative of -x**5/210 + 2*x**4/3 - 53*x**3/7 - 1023*x**2. Let k(i) = 0. What is i?
3, 53
Let o(s) be the second derivative of 0*s**2 + 0 + 3/20*s**4 - 1/210*s**7 + 11/100*s**5 - 1/3*s**3 - 3/50*s**6 + 72*s. Solve o(z) = 0 for z.
-10, -1, 0, 1
Let r(d) be the first derivative of -2*d**6/3 + 552*d**5/5 - 5025*d**4 + 71824*d**3/3 + 9513. Determine x, given that r(x) = 0.
0, 4, 67
Factor -1116*r + 467046 + 2/3*r**2.
2*(r - 837)**2/3
Let w = -931 - -933. Factor -6*s + 28/9 - 4/9*s**w.
-2*(s + 14)*(2*s - 1)/9
Let f(y) = -6*y**2 - 65*y - 11. Let n(b) be the first derivative of 2*b**3/3 + 11*b**2 + 4*b - 59. Let d(k) = 4*f(k) + 11*n(k). Solve d(v) = 0 for v.
-9, 0
Let u = -1389 + 1389. Suppose 65*i - 48 - 82 = u. What is s in 8*s - 16/3 - i*s**3 + 2/3*s**4 - 4/3*s**2 = 0?
-2, 1, 2
Let u be 13816/154 - 16/4. Let v = 603/7 - u. Factor 9/7*s**3 - 18/7 - 9/7*s**2 - 33/7*s + v*s**4.
3*(s - 2)*(s + 1)**2*(s + 3)/7
Suppose a - 28 = -3*f, -4*f + 84 = 4*a + f. Let g be (-10)/a*(-3 - -1 - 2). Find q, given that 2 - g*q + 1/2*q**2 = 0.
1, 4
Factor 0 + 50/3*f - 1/3*f**3 - 5/3*f**2.
-f*(f - 5)*(f + 10)/3
Let r(c) be the third derivative of 2*c**5/15 + 1027*c**4/12 + 256*c**3 - 4441*c**2. Factor r(v).
2*(v + 256)*(4*v + 3)
Let c(x) = x**3 - 54*x**2 + 123*x + 3853. Let d be c(50). Find f, given that 32*f - 624/7*f**2 - 594/7*f**4 - 32/7 + 864/7*f**d + 162/7*f**5 = 0.
2/3, 1
Let p(h) be the third derivative of h**5/360 - 5*h**4/48 + 3*h**3/2 + 8*h**2 - 205. Factor p(j).
(j - 9)*(j - 6)/6
Suppose -40 = 13*s - 107 + 41. Let b(a) be the first derivative of 22 - 4/19*a**4 - 2/95*a**5 - 32/57*a**3 + 0*a**s + 0*a. Determine q so that b(q) = 0.
-4, 0
Let q(j) be the second derivative of -17/10*j**5 + 14/15*j**6 + 0*j**2 - j + 27 + 0*j**3 + j**4 - 1/7*j**7. Solve q(m) = 0 for m.
0, 2/3, 1, 3
Let u(a) be the third derivative of -8*a**2 + 0 + 0*a**3 + 2/75*a**5 + 0*a - 1/5*a**4 - 1/900*a**6. Factor u(m).
-2*m*(m - 6)**2/15
Let k(f) = -f**4 - 138*f**3 - 484*f**2 + 4*f - 6. Let q(i) = -3*i**4 - 689*i**3 - 2422*i**2 + 22*i - 33. Let j(m) = 11*k(m) - 2*q(m). Factor j(n).
-5*n**2*(n + 4)*(n + 24)
Determine w, given that -8846/7*w**2 + 2/7*w**3 + 1396720*w + 1397984 = 0.
-1, 2212
Let r be 7 + 12/(-4) + (3 - 5). Let o(w) be the first derivative of 0*w + 2/7*w**r - 13 + 2/7*w**3 + 1/14*w**4. Factor o(s).
2*s*(s + 1)*(s + 2)/7
Factor 1/8*k**2 - 19/8*k - 5/2.
(k - 20)*(k + 1)/8
Let d(b) be the third derivative of -b**5/20 - 137*b**4/2 + 550*b**3 + 3*b**2 - 1575. Factor d(p).
-3*(p - 2)*(p + 550)
Let -1290/11*w + 18/11 + 23744/11*w**2 - 22472/11*w**3 = 0. What is w?
3/106, 1
Let t(x) be the second derivative of -x**5/90 + 4*x**3/9 - 16*x**2/9 - 388*x - 1. Factor t(l).
-2*(l - 2)**2*(l + 4)/9
Suppose 41*h - 45*h + 751 = -3*s, 0 = 2*s - 3*h + 502. Let q be ((-16)/(-45))/((-98)/s). Suppose 2/9*i**3 + 8/9*i**2 - 2/9*i**4 + 0 - q*i = 0. Calculate i.
-2, 0, 1, 2
Solve -111 + 148*z**4 + 219 + 140*z**3 + 24*z**5 - 120*z + 84*z**3 - 72 - 56*z**2 = 0.
-3, -1, 1/3, 1/2
Factor 114*u + 54 + 18 + 3*u**3 + 13887*u**2 - 13842*u**2.
3*(u + 1)*(u + 2)*(u + 12)
Let o(y) = -5*y**3 - 3*y**2 + 5*y + 7. Let s(p) = -6*p**3 - 4*p**2 + 6*p + 9. Let k be (88/(-48) - (-6)/(-9))*2. Let w(h) = k*o(h) + 4*s(h). Factor w(x).
(x - 1)**2*(x + 1)
Let n(a) be the third derivative of a**9/216 - 11*a**8/210 + a**7/35 + 56*a**3/3 + 15*a**2. Let t(o) be the first derivative of n(o). Factor t(m).
2*m**3*(m - 6)*(7*m - 2)
Let b(w) be the second derivative of -w**4/4 - 225*w**3 - 151875*w**2/2 - 1167*w - 1. Factor b(o).
-3*(o + 225)**2
Let d(z) be the third derivative of 21 + 0*z**3 + 9/4*z**4 - 9/10*z**5 - 1/105*z**7 + 3/20*z**6 - 4*z**2 + 0*z. Solve d(f) = 0.
0, 3
Let a(m) = m**2 + 3*m - 21. Let r be a(-9). Factor 27*n**2 - r*n + 8*n - 22*n**2 + 4 - 4.
5*n*(n - 5)
Factor 1315 - 1325/2*k + 5/2*k**2.
5*(k - 263)*(k - 2)/2
Let v(h) be the second derivative of -h**5/20 + 269*h**4/12 - 68*h + 4. Factor v(f).
-f**2*(f - 269)
Let q = 23164/7 - 3309. Let o(j) be the third derivative of 0 - 1/42*j**4 - 1/210*j**5 + q*j**3 + 0*j + j**2. Suppose o(a) = 0. What is a?
-3, 1
Let n(r) be the second derivative of 1/110*r**5 + 0 + 6/11*r**2 + 0*r**4 - 7/33*r**3 + 61*r. Let n(s) = 0. What is s?
-3, 1, 2
Let a(p) be the third derivative of 5/9*p**3 + 0 - 1/180*p**5 + 1/8*p**4 + 74*p**2 + 0*p. Solve a(o) = 0.
-1, 10
Let x(d) be the second derivative of 17/6*d**4 + 4/15*d**6 - 23/6*d**3 + 0 + 3*d**2 - 6/5*d**5 - 1/42*d**7 + 103*d. Find a, given that x(a) = 0.
1, 2, 3
Suppose 38 - 20 = 6*t. What is d in -48*d + d**2 - 7*d**2 + 2*d**2 + 40*d**t + 12*d**4 = 0?
-3, -4/3, 0, 1
Factor 3613*m + 338*m**2 + 251*m**2 + 505*m**2 - 1094 - 2*m**3 - 3611*m.
-2*(m - 547)*(m - 1)*(m + 1)
Suppose q + 2*q = q. Suppose -a - a - 4*w = 0, q = 4*a + 3*w - 5. Solve -1 + 4*r**2 + 9*r - 17*r**a + 3*r + 2*r**2 = 0 for r.
1/11, 1
Let y(p) be the second derivative of -5*p**7/378 + p**6/135 - 2069*p. Let y(r) = 0. Calculate r.
0, 2/5
Determine i, given that 2/25*i**3 + 28322 + 141134/5*i - 2378/25*i**2 = 0.
-1, 595
Let q = -11918 + 11918. Let p(h) be the second derivative of -1/35*h**5 + 0 + 0*h**4 + 0*h**2 - 1/105*h**6 + 10*h + q*h**3. Suppose p(t) = 0. Calculate t.
-2, 0
Let g be (-3)/(-10)*(7 + 4/(-12)). Determine y so that -24/5 - 8*y - 6/5*y**g = 0.
-6, -2/3
Suppose 216*w - 10 - 638 = 0. Let c(f) be the first derivative of 23 - 3/7*f**w + 3/14*f**2 + 9/7*f - 3/28*f**4. What is o in c(o) = 0?
-3, -1, 1
Suppose -51*n = -370*n + 957. Factor -1/8*g**4 + 3/8*g + 0