**6. Suppose q(w) = 0. Calculate w.
-5, -2, -1/3
Find r such that -484 - 1761/4*r**2 + 43/2*r**3 - 946*r - 1/4*r**4 = 0.
-1, 44
Let g be 40/(-20) + (2 - 0). Let z = -1208/19 + 3662/57. Factor g + 0*t + z*t**2.
2*t**2/3
Let b = -68 + 68. Suppose 5 = -j, 30*n - 29*n + 3*j + 15 = b. Solve n - 2/3*r**2 - 2/3*r = 0.
-1, 0
Let i = 574/1335 - 132/445. What is b in 2/5*b**3 - 16/5 + 104/15*b + 8/15*b**4 - i*b**5 - 68/15*b**2 = 0?
-3, 1, 2
Find b such that 24*b - 3*b**3 - 36*b**2 - 162 + 60*b - 219*b = 0.
-6, -3
Let i(t) be the first derivative of -t**5/60 + t**4/12 + 5*t**3/9 - 4*t**2 - 217*t - 142. Let c(m) be the first derivative of i(m). Factor c(o).
-(o - 4)*(o - 2)*(o + 3)/3
Let u be (-194)/(-38) - 3*(-8)/(-228). Suppose -17 - 11 = -7*f. What is d in 35*d**2 - 8*d**3 + f*d**4 - 9*d**4 - d**u - 39*d**2 = 0?
-2, -1, 0
Let 27 - 39/5*z**2 + 93/5*z + 3/5*z**3 = 0. What is z?
-1, 5, 9
Let m be 2*(-141)/(-312) + (-1)/(44/33). Find w, given that m*w**2 + 14/13 + 16/13*w = 0.
-7, -1
Let p(g) be the second derivative of -g**5/80 + 9*g**4/16 + 193*g**3/24 + 165*g**2/8 + 2224*g. Factor p(y).
-(y - 33)*(y + 1)*(y + 5)/4
Solve 43*o + 10*o**3 - 24*o**4 + 26*o**4 + 14*o**2 - 37*o = 0.
-3, -1, 0
Let t = 33781/15834 - -43/754. Determine i so that 4/3*i**2 - 8/21*i**4 - 8/21*i**5 + t*i**3 - 8/3*i + 16/21 = 0.
-2, 1/2, 2
Suppose -751*z + 55 = -756*z. Let n(c) = c**3 + 12*c**2 + 5*c - 64. Let a be n(z). Find s such that -1/3*s**5 + 0*s**a + 0*s - 1/3*s**3 + 0 + 2/3*s**4 = 0.
0, 1
Factor 21510*o**3 - 52*o**4 - 456 - 1456*o - 2*o**5 - 1634*o**2 - 22236*o**3 - 42*o**4.
-2*(o + 1)**3*(o + 6)*(o + 38)
Suppose p - 8*p - 2*p + 4*p = 0. Factor 1/2*h**2 + p*h + 0*h**3 - 1/4*h**4 - 1/4.
-(h - 1)**2*(h + 1)**2/4
Let p be 6/(300/(-3770)) + (-2)/(-5). Let l be (3/p)/((-3)/10)*147. Factor 2/5*k**2 - 28/5*k + l.
2*(k - 7)**2/5
Let s(p) = -20*p**3 + p**2 - 6*p - 7. Let o be s(-1). What is u in -25*u**2 - o*u**2 - 4*u**2 - 4*u + u**2 = 0?
-1/12, 0
Let r be -4*(-9 + 14)*(-2)/8. Let i be 14/(-1890)*-87 - 1/r. Factor 2/9*n**4 + i*n**2 + 0*n - 2/3*n**3 + 0.
2*n**2*(n - 2)*(n - 1)/9
Factor 594864*p - 722/5*p**5 + 11666*p**4 + 157464/5 - 313342*p**3 + 2775870*p**2.
-2*(p - 27)**3*(19*p + 2)**2/5
Suppose -17*d + 13*d + 8 = 0. Suppose 5 = i - 0*i - o, -3*i + 14 = -d*o. Factor 4*s**2 - 4 + i*s - s**2 + s - 4*s**2.
-(s - 4)*(s - 1)
Let a = -5741/18 - -319. Let s(k) be the second derivative of 1/180*k**6 - 1/24*k**4 + 0*k**5 + 16*k + 0*k**2 + a*k**3 + 0. Find w, given that s(w) = 0.
-2, 0, 1
Let u(g) be the second derivative of -5/2*g**4 + 166*g - 1/15*g**6 + 0 - 7/3*g**3 + 0*g**2 - 9/10*g**5. Solve u(w) = 0.
-7, -1, 0
Let p = 17 - 8. Let r(m) = p*m**3 + 10*m**2 + 18*m**2 - 16*m - 7*m**3. Let d(g) = -3*g**3 - 56*g**2 + 32*g. Let q(i) = 6*d(i) + 13*r(i). Factor q(n).
4*n*(n + 4)*(2*n - 1)
Suppose -5*k + 12 = -i, 2*k - k = -i. Let c(w) = -7*w**2 + 14*w + 109. Let g be c(5). Solve 27*u - 25*u - 5*u**2 + 3*u**2 + g - k*u**3 - 2 = 0 for u.
-1, 1
Suppose 49*z + 50 = 54*z. Factor 34*r**2 - z*r + 36 - 30*r**2 - 14*r.
4*(r - 3)**2
Let w = 10385639/459 + -339394/15. Let s = 1/459 + w. Suppose -4/5*f**4 + 1/5*f**5 + 2/5 + s*f**2 - f + 4/5*f**3 = 0. Calculate f.
-1, 1, 2
Let r(n) be the second derivative of n**6/30 + 179*n**5/60 - 629*n**4/36 + 23*n**3/6 + 63*n**2 + 4798*n. Let r(b) = 0. Calculate b.
-63, -2/3, 1, 3
Let t(v) = 2*v**3 - 24*v**2 + 4*v - 43. Let z be t(12). Determine d, given that 16*d**2 - 11*d**z - 30*d**4 - 24*d + 6*d**4 + 8*d**5 - 82*d**2 - 63*d**3 = 0.
-4, -2, -1, 0
Let n = -7848 - -7850. Let b(i) be the first derivative of 4/3*i**3 + 9 - 2*i**n - 8*i. Factor b(a).
4*(a - 2)*(a + 1)
Suppose 7*c - 83 = -97. Let a be 4 + 3 + c + -3. Solve 1/2*x**3 + 1/4 - 1/4*x**4 + 0*x**a - 1/2*x = 0.
-1, 1
Let y(d) be the second derivative of -d**5/50 + 3*d**4/5 + 119*d**3/3 + 2*d - 4130. Factor y(t).
-2*t*(t - 35)*(t + 17)/5
Suppose 0 = -2*h + 5*f - 386 + 356, -4*h - 2*f + 12 = 0. Factor -14/5*w - 2/5*w**2 + h.
-2*w*(w + 7)/5
Let i be -2 - (-16)/10 - 94/(-10). Let u(p) = -p**2 + 8*p + 12. Let w be u(i). Let 2221*y**2 - 10 + 5*y**4 + 10*y**3 + 5*y**w - 2216*y**2 - 15*y = 0. What is y?
-2, -1, 1
What is n in 10*n**4 - 352/3*n**3 - 512/3 - 512*n + 448*n**2 = 0?
-4/15, 4
Let s(h) = 8*h**4 + 258*h**3 + 4332*h**2 + 24568*h + 6. Let a(g) = 33*g**4 + 1033*g**3 + 17327*g**2 + 98273*g + 26. Let i(w) = 3*a(w) - 13*s(w). Factor i(p).
-5*p*(p + 17)**3
Let y(i) = i**3 - 53*i**2 - 1108*i + 278. Let l be y(69). Let 0 - 8/7*t**l - 4/7*t - 4/7*t**3 = 0. Calculate t.
-1, 0
Suppose 6 = i - 14. Suppose 4*b - 4*u - i = -b, -b + u = -4. Determine v so that 3*v**3 - 10*v**2 + v**3 + 11*v**3 - v - b*v = 0.
-1/3, 0, 1
Let g(k) be the second derivative of 14/9*k**3 - 111*k + 44/9*k**2 + 0 - 1/27*k**4. Solve g(p) = 0.
-1, 22
Find w, given that -5*w**3 - 4290*w + 19360 - 4848*w - 1223*w + 401*w + 1160*w - 430*w**2 = 0.
-44, 2
Let c be 2/(-6) - (-400)/75. Suppose 0 = 5*j + 5*a - 10, c*a + 1 - 3 = -3*j. Determine g, given that 2/7*g**5 + 0*g**2 - 2/7*g**j + 0*g - 4/7*g**3 + 0 = 0.
-1, 0, 2
Let o(k) = 2*k**4 + 3453*k**3 - 3974406*k**2 + 1524845954*k + 3. Let n(g) = g**4 - g**2 + g + 1. Let t(u) = 3*n(u) - o(u). Let t(x) = 0. Calculate x.
0, 1151
Find z, given that -5716/7*z - 4084082/7 - 2/7*z**2 = 0.
-1429
Let l be 131169/(-92) + 4/(-16). Let k = 1428 + l. What is n in k*n + 2/3*n**2 - 20/3 = 0?
-5, 2
Let u(o) be the first derivative of -9*o**5/25 + 291*o**4/20 - 32*o**3/5 - 3403. Let u(z) = 0. What is z?
0, 1/3, 32
Let w(h) = -5*h**3 - 205*h**2 + 460*h - 320. Let o(j) = j**3 + 68*j**2 - 154*j + 106. Let s(g) = 10*o(g) + 3*w(g). Factor s(a).
-5*(a - 10)*(a - 2)*(a - 1)
Let o(t) be the third derivative of -t**7/210 + t**6/15 + t**5/15 - 4*t**4/3 - 2893*t**2. Determine q so that o(q) = 0.
-2, 0, 2, 8
Let t(k) be the second derivative of 3*k**7/14 + 7*k**6/10 - 15*k**5/4 - 63*k**4/4 - 9*k**3 - 5554*k. Let t(n) = 0. Calculate n.
-3, -2, -1/3, 0, 3
Suppose 10*y = 6*y - 4. Let t be y - (-12)/30*10. Factor 4/3*q**t - 8/9 + 8/3*q - 2/9*q**4 - 26/9*q**2.
-2*(q - 2)**2*(q - 1)**2/9
Let r(m) be the second derivative of -m**5/20 - m**4 - 10*m**3/3 + m**2 - 112*m. Let a be r(-10). Factor 9/5*u**a + 9/5*u**3 + 3/5*u**4 + 0 + 3/5*u.
3*u*(u + 1)**3/5
Let -4304*o**5 + 16*o**2 + 8605*o**5 + 8*o**3 + 1 - 4300*o**5 - 7*o**4 - 1 = 0. Calculate o.
-1, 0, 4
Let a(m) be the first derivative of -m**5/15 + m**4/6 + 11*m**3/9 - 2*m**2 + 1750. Factor a(t).
-t*(t - 4)*(t - 1)*(t + 3)/3
Suppose 0 = -2*y - 8*y - 30. Let q(j) = -9*j**3 + 5*j**2 - j - 3. Let k be q(y). Factor 20 + 324*b**2 + 51 + k*b - 7.
4*(9*b + 4)**2
Let o(x) be the second derivative of -x**7/630 + 37*x**6/180 - x**4/6 - 4*x**2 - 113*x. Let m(y) be the third derivative of o(y). Factor m(p).
-4*p*(p - 37)
Suppose 0 = -19*s + 9*s + 40. Let y be (3 - 2)*5 + -3. Factor -70 + 12*q + 33 + 29 - s*q**y.
-4*(q - 2)*(q - 1)
Suppose 13*w = 2*w + 22. Suppose 2*h - 22 = -4*g, -9 = -2*g - h + w*h. Find p such that 3*p**3 + 16*p + 9*p**2 + 3 + g*p - 12*p = 0.
-1
Factor -117*m**2 + 5*m**3 - 12*m**4 + 245*m**2 + 7*m**4 - 98*m**2.
-5*m**2*(m - 3)*(m + 2)
Suppose -5*p + 1266 = 4*w, -5*p + 629 + 640 = w. Let y = p - 252. Solve 0 - 11/3*u**3 - 2/3*u**y + 0*u = 0 for u.
-2/11, 0
Suppose 132*c = 129*c + 33. Let k(q) = 7*q**2 + 141*q - 46. Let t(v) = 21*v**2 + 424*v - 137. Let g(p) = c*k(p) - 4*t(p). Find z, given that g(z) = 0.
-21, 2/7
Let z = -25 - -27. Suppose 4*l + z*j = j + 14, -4*l = 5*j - 22. Factor -4*t**5 + 4*t**l + 0*t**3 + t + 4*t**3 - 5*t.
-4*t*(t - 1)**2*(t + 1)**2
Let y = -302 + -81. Let r = 1535/4 + y. Suppose -r*u**3 + 1/8*u**4 + 0*u + 0 + 9/8*u**2 = 0. What is u?
0, 3
Let h(g) be the third derivative of -g**8/560 + 3*g**7/25 - 517*g**6/200 + 399*g**5/25 - 361*g**4/10 + 104*g**2 + 1. Factor h(q).
-3*q*(q - 19)**2*(q - 2)**2/5
Let q = -18758 + 18761. Find y such that -1/3*y**5 - 8/3*y**3 - 2*y**2 + 0 + 2*y**4 + q*y = 0.
-1, 0, 1, 3
Let n = 11023/27595 - -3/5519. Factor 2/5*x**4 - 4/5*x**3 + 2/5*x + n*x**5 + 2/5 - 4/5*x**2.
2*(x - 1)**2*(x + 1)**3/5
Solve -40/13*n - 2/13*n**2 - 198/13 = 0.
-11, -9
Let n(x) = -8*x - 16. Let w(v) = -9*v - 16. Let q(z) = 3*n(z) - 2*w(z). Let g be q(-3). Factor 64 - 15*m**2 + 152*m + 6*m**g - 11*m**2.
-4*(m - 8)*(5*m + 2)
Let w(k) be the second derivative of 2*k**6/135 -