7. Let w(y) = 20*y - 940. Let b be w(r). Factor 10/11*h**2 + b + 2*h**3 + 14/11*h**4 + 2/11*h**5 + 0*h.
2*h**2*(h + 1)**2*(h + 5)/11
Let b = 958/3 - 1277/4. Let m(h) be the third derivative of -b*h**6 - 1/42*h**7 + 6*h**2 + 0*h**4 + 0*h + 0*h**3 + 0 + 1/4*h**5. Factor m(f).
-5*f**2*(f - 1)*(f + 3)
Let c be ((-559)/26)/(2/(-12)). Let i = c - 81. Factor -2 + 27*g - 4 - 15*g**2 - i*g.
-3*(g + 1)*(5*g + 2)
Let y(v) be the third derivative of v**6/300 - 107*v**5/25 + 34347*v**4/20 - 3007*v**2. Determine m so that y(m) = 0.
0, 321
Let j be 192/(-9)*(-72)/6912. Factor -152/9*h - j*h**2 - 2888/9.
-2*(h + 38)**2/9
Suppose 404*l - 4596 = 402*l. Let b = l + -2296. Let 8/3*j**b + 0 + 0*j - 2/3*j**3 = 0. What is j?
0, 4
Suppose -6*q - 48 = -78. Factor 213 + 5*n**2 - q*n**2 - 217 + 4*n**2.
4*(n - 1)*(n + 1)
Let z(m) be the first derivative of -m**6/180 - m**5/60 + m**4/6 + 56*m**3/3 - 26. Let w(f) be the third derivative of z(f). Factor w(c).
-2*(c - 1)*(c + 2)
Suppose 8 = 2*d - 0. Suppose 0 = -4*x - d, 4*p - 4*x + 2*x = 34. Factor -p*n**4 + 19*n + 8 - 175*n**2 + 18*n - 9*n + 8*n**3 - 4*n**5 + 207*n**2.
-4*(n - 2)*(n + 1)**4
Suppose 0 = 5*o - 0*r - 2*r + 17, 5*o = r - 21. Let m be ((-8)/(-50))/(o + 154/30). Suppose 0*n + m*n**2 - 8/5 + 2/5*n**3 = 0. Calculate n.
-2, 1
Let y(k) be the third derivative of -k**6/160 + 97*k**5/240 + 85*k**4/16 + 37*k**3/3 - 84*k**2 - 4. Let y(b) = 0. Calculate b.
-4, -2/3, 37
Let c(u) be the first derivative of -u**3/18 - 177*u**2/4 - 265*u/3 + 2242. Determine o so that c(o) = 0.
-530, -1
Solve 172/9*s + 40/9*s**4 + 16*s**3 + 16/3 + 232/9*s**2 + 4/9*s**5 = 0.
-4, -3, -1
Let i(o) = 175*o**2 - 3671*o - 54. Let h be i(21). Let h - 3/2*n**2 + 12*n = 0. What is n?
-2, 10
Let i(u) be the third derivative of u**5/60 - 79*u**3/6 + 4*u**2 - 4. Let a be i(9). Suppose 4/9*w - 4/9*w**3 + 2/9*w**4 - 2/9 + 0*w**a = 0. Calculate w.
-1, 1
Let d(b) be the first derivative of b**6/180 - b**5/5 + 35*b**4/12 + 145*b**3/3 - 146. Let t(n) be the third derivative of d(n). Factor t(a).
2*(a - 7)*(a - 5)
Let a(j) be the third derivative of j**7/70 + 3*j**6/10 + 9*j**5/5 - 21*j**2 + 77. Suppose a(t) = 0. What is t?
-6, 0
Let r(f) be the second derivative of 3/40*f**6 - 3/80*f**5 + 1/4*f**3 + 0*f**2 - 2 - 2*f - 1/56*f**7 - 3/16*f**4. Solve r(h) = 0.
-1, 0, 1, 2
Let p = -131/79 - -6863/1185. Factor p*l**4 + 520/3*l**2 + 0 + 2/15*l**5 + 44*l**3 + 400/3*l.
2*l*(l + 1)*(l + 10)**3/15
Let v(m) be the third derivative of -m**7/1050 + m**6/600 + m**5/12 - 5*m**4/24 + 3*m**2 + 63. Factor v(h).
-h*(h - 5)*(h - 1)*(h + 5)/5
Suppose 0 = 3*l - 4*d - 9, -3*l - 2*d + 15 = 6. Factor 45*y**2 + 16*y**3 - 44*y**3 + 25*y**3 + l*y - 45.
-3*(y - 15)*(y - 1)*(y + 1)
Let q(a) = 770*a**2 - 58290*a - 12410. Let j(z) = -70*z**2 + 5299*z + 1128. Let s(f) = 65*j(f) + 6*q(f). Factor s(g).
5*(g - 76)*(14*g + 3)
Factor 271 - 227 + 5*d - 670*d**2 + 282 - 5*d**3 + 344.
-5*(d - 1)*(d + 1)*(d + 134)
Let j = 27 + -103. Let o = -72 - j. Factor -12*r**3 + 11*r - 6*r - 4*r**2 + 7*r + o*r**4.
4*r*(r - 3)*(r - 1)*(r + 1)
Suppose -10*g - 6697 = -6777. Let t(n) be the first derivative of -1 - 7*n**2 + 5/3*n**3 - g*n + 1/2*n**4. Factor t(i).
(i - 2)*(i + 4)*(2*i + 1)
Let t(q) = 6*q**3 + 13*q**2 - 32*q + 18. Let x be t(1). Factor -4/3*b**x - 4/3*b**3 + 0*b + 0 + 0*b**2 - 8/3*b**4.
-4*b**3*(b + 1)**2/3
Let p(j) be the second derivative of 2*j**7/21 - 274*j**6/15 + 27*j**5 + 137*j**4/3 - 272*j**3/3 - 28*j + 15. Suppose p(t) = 0. What is t?
-1, 0, 1, 136
Let o(k) be the second derivative of -2*k**6/15 - 28*k**5/5 - 71*k**4 - 476*k**3/3 + 3136*k**2 + 27*k - 5. Determine w so that o(w) = 0.
-16, -7, 2
Suppose 61*d - 74*d + 5*l = -37 - 29, 5*d - 5*l = 50. Let f = 147 + -732/5. Find c such that -c**d + 2/5 - 1/5*c + 1/5*c**3 + f*c**4 = 0.
-1, 2/3, 1
Factor 0*z - 585/8*z**3 - 147/4*z**4 - 73/2*z**2 - 1/8*z**5 + 0.
-z**2*(z + 1)**2*(z + 292)/8
Let p be -3 - -8 - (7/56*-6)/((-47)/188). Determine s, given that 176/3*s**4 + 8/3*s**5 + 1130/3*s**3 + 200/3 + 1802/3*s**p + 1040/3*s = 0.
-10, -1, -1/2
Let u(y) = -9*y**3 + 2475*y**2 - 168084*y - 228510. Let d(g) = 18*g**3 - 4949*g**2 + 336168*g + 457026. Let o(j) = -3*d(j) - 5*u(j). Factor o(q).
-3*(q - 138)**2*(3*q + 4)
Let u be (528/81*6/(-8) + 5)*2. Let c(n) be the first derivative of u*n + 25 + 2/27*n**3 + 2/9*n**2. What is x in c(x) = 0?
-1
Suppose -2/15*r**3 - 75076/15 - 12878/5*r - 184/5*r**2 = 0. Calculate r.
-137, -2
Let 4/7*i**3 + 484/7*i + 496/7*i**2 - 984/7 = 0. Calculate i.
-123, -2, 1
Suppose 34 = 4*v - 2*c, -3*c - 32 = -2*v + c. Let r be (1/2)/(v/4). Factor -r*z**2 + 0 + z.
-z*(z - 3)/3
Suppose -2*y + 14 = -2*z, 4*y + 33 = z + 52. Factor 3*q**y + 2 + 1 + 37*q**3 + 102*q - 6*q**2 + 102 - 102*q**2 - 139*q**3.
3*(q - 35)*(q - 1)*(q + 1)**2
Let i(j) be the third derivative of -j**7/10 - 19*j**6/20 - 8*j**5/5 + 4*j**4 + 4*j**2 - 20. Determine n, given that i(n) = 0.
-4, -2, 0, 4/7
Factor 686*z**2 + z**4 - 224*z**2 - 251*z**2 - 350*z**2 + 11*z**3 + 125*z**3 - 274*z.
z*(z - 2)*(z + 1)*(z + 137)
Let f be (-2)/(-28)*(-770)/(-44). Let j(o) be the second derivative of 0*o**2 + 5/6*o**4 + 0 + 1/2*o**6 + 0*o**3 + f*o**5 + 5*o. Factor j(q).
5*q**2*(q + 1)*(3*q + 2)
Let n(f) be the third derivative of f**6/60 - 62*f**5/15 - 125*f**4/12 - 1813*f**2. Factor n(k).
2*k*(k - 125)*(k + 1)
Factor 0 + 4/3*n**3 - 176*n - 64/3*n**2.
4*n*(n - 22)*(n + 6)/3
Let f = 489/637 + 1/637. Let l be ((-3)/3)/((18 + -12)/(-12)). Factor f*n**l + 6/13*n**4 - 14/13*n**3 - 2/13*n + 0.
2*n*(n - 1)**2*(3*n - 1)/13
Suppose 5835*i - 1281*i = 22770. Find f, given that -237*f**2 - 102*f - 465/2*f**3 - 33/2*f**i - 102*f**4 - 12 = 0.
-2, -1, -2/11
Let c(m) = 41*m**2 - 128*m + 40. Let r(h) = -5*h**2 + 16*h - 5. Let x(z) = 8*c(z) + 68*r(z). Factor x(y).
-4*(y - 5)*(3*y - 1)
Let s(q) = 33*q**4 + 2*q**3 - 71*q**2 + 9*q + 17. Let j(f) = -f**5 + 2*f**4 - f**2 - 2. Let m(u) = 15*j(u) - 3*s(u). What is d in m(d) = 0?
-3, -3/5, 1
Suppose -75 - 66 = -29*x - 25. Let y(v) be the first derivative of -2/25*v**5 + 0*v**2 - 1/5*v**x - 2/15*v**3 + 0*v + 12. Factor y(h).
-2*h**2*(h + 1)**2/5
Determine i so that 227 + 850 - 126*i + 424 - 301 - 3*i**2 = 0.
-50, 8
Determine j, given that -656/5*j + 16/5 - 273*j**4 - 3184/5*j**2 - 4156/5*j**3 = 0.
-2, -2/3, -2/5, 2/91
Let x be (-28)/126 - 169/(-234). Let f(d) be the first derivative of 2/15*d**3 - 2/25*d**5 + 8/5*d + 1/15*d**6 + 8/5*d**2 - x*d**4 + 39. Factor f(n).
2*(n - 2)**2*(n + 1)**3/5
Let v(k) be the second derivative of -3*k**5/5 - 15*k**4/8 + k**3/2 + 6*k + 121. Factor v(s).
-3*s*(s + 2)*(8*s - 1)/2
Let s(f) be the second derivative of -5/36*f**4 + 19*f - 2 + 1/6*f**5 - 5/9*f**3 + 1/18*f**6 + 0*f**2. Suppose s(w) = 0. Calculate w.
-2, -1, 0, 1
Let w(y) be the second derivative of -1 - 2*y**3 + 11/6*y**4 + 15*y - 2/5*y**5 - 1/15*y**6 + 0*y**2. Factor w(c).
-2*c*(c - 1)**2*(c + 6)
Let h(u) be the third derivative of -u**6/1080 + 11*u**5/180 - 7*u**4/24 - 25*u**3/2 + 86*u**2. Let q(j) be the first derivative of h(j). What is m in q(m) = 0?
1, 21
Let u(i) be the second derivative of i**4/4 - 60*i**3 - 744*i**2 - 153*i - 6. Let u(x) = 0. What is x?
-4, 124
Suppose -2*j + 8 = 2. Let i(n) be the first derivative of n**j + 15 - 3*n + 3*n**3 + 6*n**2 - 6*n - 5*n**3. Factor i(h).
-3*(h - 3)*(h - 1)
Let r(a) be the second derivative of a**5/40 + 29*a**4/24 + 46*a**3/3 + 84*a**2 + a - 96. What is t in r(t) = 0?
-21, -4
Let z = 889 - 887. Suppose -2*g + z = 5*s, g + 8*g + 46 = 5*s. Determine h so that -2/3*h**s - 8/3 + 1/3*h**4 + h**3 - 4*h = 0.
-2, -1, 2
Suppose 5*i + 7 = 17. Suppose -i*v + 14*m + 9 = 19*m, -7 = -3*v - m. Determine t so that -10/3*t - 2/3*t**v + 0 = 0.
-5, 0
Let n = 610 - 607. Factor 5*w**n + 4*w + w**3 - 5*w**3 - 8*w**2 + 32 - 8*w.
(w - 8)*(w - 2)*(w + 2)
Suppose -14/5*f**4 - 164/5*f**3 + 18/5 + 98/5*f**5 + 66/5*f - 4/5*f**2 = 0. What is f?
-1, -3/7, 1
Let p(k) be the third derivative of -k**6/30 - 2*k**5/15 - k**4/4 + 2*k**3/3 + 2*k**2. Let i be p(-5). Factor 340*z - i*z - 4 - 4*z**2 + 2*z**2.
-2*(z - 2)*(z - 1)
Let g = -82 - -85. Suppose 6*f = -g + 15. Factor 10*x + 0*x - 6*x + 4*x**5 - 4*x**f - 20*x**3 + 28*x + 4*x**4 - 16.
4*(x - 1)**3*(x + 2)**2
Let u(z) be the first derivative of z**4/16 + 53*z**3/4 - 81*z**2/4 - 80*z + 1196. What is x in u(x) =