/3*k**3. Find b, given that g(b) = 0.
2/7, 1, 2
Suppose 2*h + 4 = j, -10 = 2*h - 0*j - 4*j. Let q be h - (-15)/3 - -16. Factor -2 + 3*p - 60*p**2 - 8 - q*p**3 - 48*p.
-5*(p + 2)*(2*p + 1)**2
Factor 18/5*x**3 + 32/5*x - 48/5*x**2 - 2/5*x**4 + 0.
-2*x*(x - 4)**2*(x - 1)/5
Let p be 4 + -1 - (4 - (-3 + 6)). Factor 0*b + 8*b + 640*b**2 - 635*b**p + 0*b**3 - 48 - b**3.
-(b - 4)**2*(b + 3)
Suppose -16 = -4*q + n, 2*q + 16*n - 18 = 14*n. Let l be 4 + (1 - q) - -3. Find z, given that -9/4*z**2 - 1 - l*z = 0.
-2/3
Let t(g) be the second derivative of g**5/20 - g**4/3 - 29*g**3/6 - 12*g**2 + 1136*g. Factor t(o).
(o - 8)*(o + 1)*(o + 3)
Let q(f) be the third derivative of f**7/1260 - 1487*f**6/360 + 2211169*f**5/360 + 12*f**2 - 3*f - 33. Suppose q(v) = 0. Calculate v.
0, 1487
Let s(i) = -4*i**2 + 6*i + 123. Let c be s(6). Let d be (-4 + (3 - -1))/(c - 12). Solve 0*j - 4/11*j**3 - 6/11*j**4 - 2/11*j**5 + d + 0*j**2 = 0.
-2, -1, 0
Suppose 52 = -5*m - 3*s, -2*m + 2*s - 19 = -11. Let g be 69/24 + (126/(-16) - m). Factor 0*f**g + 0*f + 2/13*f**4 + 0 - 2/13*f**2.
2*f**2*(f - 1)*(f + 1)/13
Let h = 21247/303 - 6914/101. Find z such that -1/6*z**2 - 11/6*z - h = 0.
-10, -1
Let m = -5875 + 17641/3. Let h(x) be the first derivative of -m*x - 40/3*x**2 - 7 - 76/9*x**3 + 5*x**4. What is r in h(r) = 0?
-2/5, -1/3, 2
Let i(p) = p**3 + 9*p**2 + 2. Let f(h) = -2*h**2 - 5*h + 3. Let n be f(-4). Let k be i(n). Suppose 0*w - 4*w**3 + 4*w**2 - k*w + 6*w + 9 - 13 = 0. Calculate w.
-1, 1
Let g(w) be the third derivative of w**5/90 - 127*w**4/3 + w**2 + 1579*w. Factor g(q).
2*q*(q - 1524)/3
Let h be (-4)/(2 + -6) - 2. Let u be h + -1 + 4 + 2. Determine n so that -6*n**3 + 18 + 160*n**2 + 12 + 115*n + 20*n**u + 101*n**3 = 0.
-2, -1, -3/4
Solve 216/11 - 24/11*z**2 - 2/11*z**3 + 18/11*z = 0 for z.
-12, -3, 3
Suppose 14345115 - 4238107 - 5129*r - 3863*r + 2*r**2 = 0. Calculate r.
2248
Let d(u) be the second derivative of u**5/120 + u**4/6 - 5*u**3/3 + 9*u**2 - 133*u. Let n(y) be the first derivative of d(y). Solve n(b) = 0 for b.
-10, 2
Let c(q) be the third derivative of -q**6/240 + 49*q**5/80 + 67*q**4/12 + 77*q**3/8 - 12*q**2 - 10. Factor c(f).
-(f - 77)*(f + 3)*(2*f + 1)/4
Let g(r) = r**3 - 53*r**2 - 110*r. Let d be g(55). Let t(u) be the first derivative of d*u + 0*u**2 + 1/2*u**4 + 12 - 2*u**3. Factor t(v).
2*v**2*(v - 3)
Let c be (4/(-14) + (-2)/(-7))/(-1). Suppose 2*v + c = 4*s - 8, -4*s + 24 = 2*v. Factor 0*i + 5 + 4*i**2 - 13 + s*i.
4*(i - 1)*(i + 2)
Let a(y) = -y**3 - 16*y**2 - 4*y + 13. Let h be a(-10). Let o = h + 550. Factor -2/5 + 3/5*b - 1/5*b**o + 0*b**2.
-(b - 1)**2*(b + 2)/5
Let k = -3865 + 19327/5. Let b(f) be the first derivative of -1/4*f**2 + k*f**5 - 1/12*f**6 + 0*f - 3/4*f**4 + 11 + 2/3*f**3. Let b(r) = 0. Calculate r.
0, 1
Suppose 0 - 2/15*q**4 + 24/5*q + 64/15*q**2 + 2/3*q**3 = 0. What is q?
-2, 0, 9
Factor 2/3*k**2 + 236/3*k - 762.
2*(k - 9)*(k + 127)/3
Let x be -12 + (-4 - (-25244)/1578). Let g = 87/263 - x. Factor -1/6*w**2 + g*w - 1/6.
-(w - 1)**2/6
Suppose 15*a + 279 - 1089 = 0. Suppose -12*j**2 + 45*j + a - 156*j**3 + 52*j**3 + 51*j**3 + 50*j**3 = 0. What is j?
-6, -1, 3
Let i = -324 - 316. Let a be (i/(-135) - 5)*-6. Let a*p**2 + 2/9*p**5 - 2/3*p**4 - 2/9*p**3 + 0*p - 8/9 = 0. Calculate p.
-1, 1, 2
Determine o so that -82*o**4 + 360 + 14/5*o**5 + 3218/5*o**2 + 2818/5*o**3 - 1488*o = 0.
-2, 2/7, 1, 15
Let t be 2 - 48/(-18) - 1/(-3)*-5. Let c(o) be the first derivative of -8/3*o**t + 6*o**2 - 4*o**4 + 2/3*o**6 + 8*o - 8 + 0*o**5. Factor c(y).
4*(y - 2)*(y - 1)*(y + 1)**3
Let t(v) be the first derivative of -v**4/4 - 1326*v**3 - 2637414*v**2 - 2331473976*v + 4332. Factor t(l).
-(l + 1326)**3
Factor -1/7*g**2 - 2*g + 1/7 + 2*g**3.
(g - 1)*(g + 1)*(14*g - 1)/7
Let h = -5174 - 454. Let f be 2/11 + 0 + h/(-1474). Factor -16/9*w**2 + 0 + 0*w - 4/3*w**f - 8/3*w**3 - 2/9*w**5.
-2*w**2*(w + 2)**3/9
Let r(h) be the first derivative of -h**3/3 - 20*h**2 + 129*h + 452. Factor r(c).
-(c - 3)*(c + 43)
Let n(m) = 9*m**2 - 150*m + 161. Let d(o) = 10*o**2 - 145*o + 160. Suppose u = -t + 5, -t - 20 = 3*u - 27. Let y(v) = t*d(v) - 5*n(v). Factor y(i).
-5*(i - 33)*(i - 1)
Let u(g) be the second derivative of 3*g**5/20 - g**4/2 - 19*g**3/2 + 30*g**2 - 25*g + 30. Factor u(k).
3*(k - 5)*(k - 1)*(k + 4)
Let d(k) be the third derivative of k**5/48 - 19*k**4/12 + 14*k**3 + 820*k**2. Factor d(x).
(x - 28)*(5*x - 12)/4
Factor 15*h**4 + 226*h**2 - 761*h + 195*h**3 + 539*h**2 + 1461*h + 5*h**3.
5*h*(h + 5)*(h + 7)*(3*h + 4)
Let s(t) be the second derivative of 20*t + 8*t**2 + 0 + 1/240*t**5 + 1/24*t**4 + 1/6*t**3. Let k(m) be the first derivative of s(m). Let k(f) = 0. What is f?
-2
Let o(h) be the third derivative of h**5/72 + 2315*h**4/72 + 1071845*h**3/36 - 3798*h**2. Suppose o(w) = 0. Calculate w.
-463
What is p in 0 + 20/9*p**4 - 20/9*p**2 + 2/9*p**5 - 8/3*p**3 + 22/9*p = 0?
-11, -1, 0, 1
Let d(a) be the second derivative of -4*a**6/105 + 173*a**5/70 + 243*a**4/14 - 1133*a**3/21 + 235*a**2/7 - 6204*a. Find y, given that d(y) = 0.
-5, 1/4, 1, 47
Let v = 260499/5084 - -14/1271. Let j = v - 203/4. Factor 9/2 + j*w**2 - 3*w.
(w - 3)**2/2
Let p be (-382)/(-60)*-38 + (-84)/(-63). Let t = 242 + p. Suppose -11/5*c**4 + 9/5*c**5 + 11/5*c**2 - t*c**3 + 0 - 2/5*c = 0. What is c?
-1, 0, 2/9, 1
Let r = 119 - 91. Solve -148*n**2 - 176*n - 68*n**3 - 100*n**2 + 64*n**4 - 17 + r*n**5 - 15 = 0.
-2, -1, -2/7, 2
Let t = -186 + 1308/7. Let b be 31/21 - 2283/1522*(-2)/(-9). Find p, given that 8/7 - 2/7*p**4 - t*p**2 - 8/7*p**3 + b*p = 0.
-2, -1, 1
Factor 1/3*x**4 + 0*x + 1/3*x**2 + 2/3*x**3 + 0.
x**2*(x + 1)**2/3
Let y be 1/51*2913 + (-10)/85. Suppose 0 = y*m - 42*m. Solve -18/5 + 2/5*t**2 + m*t = 0 for t.
-3, 3
Let d(t) be the second derivative of 9*t**5/50 + 37*t**4/15 - 404*t**3/15 + 88*t**2 - 12*t + 10. Factor d(w).
2*(w - 2)**2*(9*w + 110)/5
Let a be -1*((-36)/96)/(2/(-16)). Let h be (-3*(-6)/54)/((-2)/a). Factor h*t**2 + 0 - 2*t.
t*(t - 4)/2
Let p = 182 + -179. Let -6*w**4 + 52*w - p*w - 17*w + 3*w**5 + 6*w**2 - 23*w - 12*w**3 = 0. What is w?
-1, 0, 1, 3
What is j in -131 + 1325*j**3 + 45 - 82*j**2 - 1323*j**3 - 170*j = 0?
-1, 43
Suppose 26*p = -13 + 117. Let l be 30/35 + (p - 91/49). Find k such that 0 + 16/15*k**2 + 0*k - 2/15*k**l = 0.
0, 8
Let o = 556090 - 2780396/5. Solve o - 12*k + 6/5*k**2 = 0.
1, 9
Let i(v) be the first derivative of 90601*v**5/5 + 451801*v**4/4 - 549622*v**3/3 + 3622*v**2 - 24*v - 1705. Factor i(y).
(y - 1)*(y + 6)*(301*y - 2)**2
Suppose -91*j + 9 + 225 + 130 = 0. Suppose 52/3*v**3 + 35*v**2 + 16/3 + 5/3*v**j + 74/3*v = 0. What is v?
-8, -1, -2/5
Let a(n) be the second derivative of n**5/10 - 5*n**4/2 + 4*n**3 + 28*n**2 + 5*n + 16. Determine w, given that a(w) = 0.
-1, 2, 14
Let q(f) be the second derivative of -1/210*f**7 + 0*f**2 + 9/50*f**5 - 3 - 2*f + 4/3*f**3 + 1/150*f**6 - 13/15*f**4. Solve q(k) = 0.
-5, 0, 2
Let -3*o**4 + 11*o**4 + 6*o**5 + 3*o**5 - 10*o**3 - 2*o**5 - 5*o**5 = 0. Calculate o.
-5, 0, 1
Let y(p) = -553*p + 7192. Let u be y(13). Factor 0 + w**u + 1/2*w**5 + 3/2*w**4 + 0*w**2 + 0*w.
w**3*(w + 1)*(w + 2)/2
Suppose 1791*c - 2205 = 1782*c. Let n be 406/c - (-30)/(-35). Factor 0*w - n*w**2 + 4/5.
-4*(w - 1)*(w + 1)/5
Let w(j) be the third derivative of j**5/12 + 1805*j**4/2 + 3909630*j**3 + j**2 + 2128*j. Factor w(c).
5*(c + 2166)**2
Let n = 559 + -524. Factor -13*q + q**2 + 22 - q + n - 21 - 3*q**2.
-2*(q - 2)*(q + 9)
Let o = -13/32 - -37/32. Let r = 46/3 - 89/6. Factor -o - r*b - 1/2*b**3 + 7/4*b**2.
-(b - 3)*(b - 1)*(2*b + 1)/4
Determine x so that -3*x**2 - 805*x - 816*x - 811*x + 2423*x = 0.
-3, 0
Let i(a) be the third derivative of a**6/96 - 387*a**5/16 + 748845*a**4/32 - 96601005*a**3/8 + 37*a**2 - 4*a. Find r such that i(r) = 0.
387
Let v(n) be the first derivative of -2*n**5/45 + 19*n**4/6 - 722*n**3/9 + 6859*n**2/9 - 3027. Suppose v(s) = 0. What is s?
0, 19
Let i(b) be the third derivative of b**8/23520 + b**7/8820 + b**4/24 - 5*b**3/6 + 15*b**2 + b. Let l(f) be the second derivative of i(f). Factor l(v).
2*v**2*(v + 1)/7
Let n = 417 - -1708. Determine z so that 3*z**2 + n*z - 5*z**2 - 1993*z - 2178 = 0.
33
Let n(t) be the first derivative of -t**6/45 + 224*t**5/75 - 108*t**4/5 + 512*t**3/9 - 848*t**2/15 + 1065. Factor n(p).
-2*p*(p - 1