t g(p) be the first derivative of -9/2*p**c + 6*p + 33 + 0*p**3 + 3/4*p**4. Factor g(i).
3*(i - 1)**2*(i + 2)
Let m(q) be the second derivative of -9*q**4/40 - 47*q**3/60 - q**2 - 915*q. Factor m(f).
-(f + 1)*(27*f + 20)/10
Let h(i) be the first derivative of i**4/2 + 24*i**3 - 291*i**2 + 860*i - 11328. Factor h(o).
2*(o - 5)*(o - 2)*(o + 43)
Solve 1/5*z**3 + 66/5*z + 21/5*z**2 - 224/5 = 0 for z.
-16, -7, 2
Let o(v) be the third derivative of 119*v**2 + 0*v + 1/15*v**5 - 1/60*v**6 + 0*v**3 + 0 + 1/4*v**4. Let o(g) = 0. What is g?
-1, 0, 3
Factor -770*k - k**2 + 219890 + 3*k**2 - 220662.
2*(k - 386)*(k + 1)
Let g(q) be the first derivative of 3*q**4/4 + 15*q**3 - 219*q**2/2 + 171*q + 1459. Factor g(o).
3*(o - 3)*(o - 1)*(o + 19)
Let j(k) = -29*k + 458. Let b(f) = 82*f - 1375. Let l(o) = 4*b(o) + 11*j(o). Let v be l(52). Factor -3/5*c**2 - 15 + v*c.
-3*(c - 5)**2/5
Let t be 2/((-14)/3)*-1. Let z be (35/49)/(((16 - 6) + 0)/12). Let z + t*b**2 + 9/7*b = 0. What is b?
-2, -1
Let o(h) be the third derivative of h**7/2310 - h**6/44 + h**5/5 - 89*h**4/132 + 25*h**3/22 + 2879*h**2. What is z in o(z) = 0?
1, 3, 25
Suppose -30*q - 48 = -26*q, 3*q = 2*y - 40. Let 12/5*d - 8/5*d**3 + y - 6/5*d**2 = 0. What is d?
-1, 5/4
Let g(a) be the first derivative of -2*a**2 - 1/5*a**5 + 1/4*a**3 - a - 40 + 11/16*a**4. Solve g(y) = 0.
-1, -1/4, 2
Let t(n) be the first derivative of 3*n**5/5 + 81*n**4 + 27197*n**3/9 + 25705*n**2/3 + 22472*n/3 + 2921. Let t(o) = 0. What is o?
-53, -4/3, -2/3
Let q(j) = j**2 - 27*j + 16. Let o be q(27). Suppose -x - 3*x + o = 0. Factor 8/3*i**x + 4/3*i**3 + 11/3*i - 2/3 - 6*i**2.
(i + 2)*(2*i - 1)**3/3
Let s(l) be the first derivative of -252 + 750*l**2 + 150*l**3 + 3/5*l**5 + 15*l**4 + 1875*l. What is k in s(k) = 0?
-5
Let u(m) = 7*m**2 - 2387*m - 2391. Let k(y) = 4*y**2 - 2392*y - 2394. Let t(o) = 3*k(o) - 2*u(o). Find i such that t(i) = 0.
-1200, -1
Let w(i) = -12*i - 84. Suppose -3*s + 46 = -6*s - 5*h, h - 23 = 4*s. Let y be w(s). Determine a so that 0 + 2/3*a + y*a**2 - 2/3*a**3 = 0.
-1, 0, 1
Let n(z) be the second derivative of 67*z - 1/8*z**4 + 34*z**3 - 3468*z**2 + 0. Determine k, given that n(k) = 0.
68
Let l = -540273 - -540275. Suppose 8/3*r**4 - 20/3*r**l + 2/3*r**5 - 8/3*r + 2/3*r**3 + 16/3 = 0. Calculate r.
-2, 1
Suppose -28044*p + 14 - 22 + 28054*p - 2*p**2 = 0. What is p?
1, 4
Suppose -15*y - 2200 = -11*y + 5*l, -l + 2176 = -4*y. Let z = -1585/3 - y. Factor 0 + 20/3*v**2 - 2/3*v**3 - z*v.
-2*v*(v - 5)**2/3
Let l be 9/45*-1*(-3)/54. Let k(n) be the third derivative of 1/450*n**5 + 0*n + 0 - l*n**4 + 1/45*n**3 - 10*n**2. Solve k(x) = 0 for x.
1
Suppose -696/7 + 706/7*v - 10/7*v**2 = 0. What is v?
1, 348/5
Let h(d) = d - 1. Let s(j) = -9*j**2 + 252*j - 75. Let u = -249 + 250. Let o(t) = u*s(t) + 12*h(t). Factor o(c).
-3*(c - 29)*(3*c - 1)
Let n(h) = 3*h - 37. Let a be n(16). Suppose 2*s + a*s - s = 0. Factor -3/2*y**2 + s - 3/4*y**5 + 3/2*y**4 + 0*y**3 + 3/4*y.
-3*y*(y - 1)**3*(y + 1)/4
Let m(u) be the first derivative of -u**4/18 - 85*u**3/9 + 86*u**2/3 - 25*u - 84. Let z(v) be the first derivative of m(v). Suppose z(i) = 0. Calculate i.
-86, 1
Let j(r) be the third derivative of r**8/480 + r**7/105 - r**6/90 + r**4/12 - 3*r**3 - 41*r**2. Let u(c) be the second derivative of j(c). Factor u(n).
2*n*(n + 2)*(7*n - 2)
Let t(b) be the third derivative of b**8/84 + 4*b**7/105 - 13*b**6/30 + 2*b**5/3 - 678*b**2 + 2*b. Find j such that t(j) = 0.
-5, 0, 1, 2
Let s be (-52)/182 + (-1292)/(-3934). Let c = s - -4998/1405. Factor -c + 12/5*a - 2/5*a**2.
-2*(a - 3)**2/5
Let m(r) be the third derivative of 0*r - 1/270*r**5 + 0*r**3 - 3*r**2 - 2/27*r**4 + 3. Factor m(t).
-2*t*(t + 8)/9
Let q = -3273 + 3273. Let y(b) be the third derivative of 1/40*b**6 - 1/70*b**7 + 0*b + 0*b**3 + q + 1/4*b**5 + 3/8*b**4 + 14*b**2. Factor y(f).
-3*f*(f - 3)*(f + 1)**2
Let l(j) be the second derivative of 343*j**7/9 - 1666*j**6/15 - 2269*j**5/10 + 290*j**4/9 - 4*j**3/3 - 4617*j. Find i, given that l(i) = 0.
-1, 0, 2/49, 3
Let j = 340214 - 340212. Determine w, given that -256/5*w - 156*w**5 + 24/5 - 638/5*w**4 + 338/5*w**j + 152*w**3 = 0.
-1, 3/26, 2/5, 2/3
Let p = 2965/18 + -329/2. Let q be (-4)/((-72)/(-14)) + (-3 - -4). Factor -p*a**2 + 0*a**3 + 0 + 0*a + q*a**4.
2*a**2*(a - 1)*(a + 1)/9
Suppose -3*w - 2*g = -47, -w - 5*g = -0*g - 20. What is m in 5*m**4 + 17*m**2 + 24*m - w*m**3 - 9*m - 22*m**2 = 0?
-1, 0, 1, 3
Suppose -4*f + 10 = -2. Suppose -d = w + f*d - 29, w + 3*d = 26. Determine j, given that -13*j + 3*j**2 - 10*j**2 + 4*j**3 - 24 + 57*j - w*j**2 = 0.
1, 2, 3
Factor 0 - 92*o + 1/3*o**2.
o*(o - 276)/3
Let s(f) be the third derivative of f**6/360 + f**5/20 + f**4/9 - 10*f**3/3 - 87*f**2. What is x in s(x) = 0?
-6, -5, 2
Let h be 18/21*((-87)/(-6) + -4). Let x be (h/(-216)*-8)/(1/6). Factor 3/5*g**3 + 24/5*g**x - 3/5*g - 24/5.
3*(g - 1)*(g + 1)*(g + 8)/5
Let h(m) = m**3 + 24*m**2 + 63*m - 2. Let j be h(-21). Let d be 190/57 + j/(-3). Factor 1/3*q**d + 0*q**3 - q**2 - 2/3*q + 0.
q*(q - 2)*(q + 1)**2/3
Let d(a) = -239*a**2 - 293*a + 311. Let l(n) = 37*n**2 + 49*n - 52. Let w(j) = -2*d(j) - 13*l(j). Factor w(q).
-3*(q - 1)*(q + 18)
Suppose 3*g - 171 = -h + 3*h, 3*g = -h + 162. Suppose g*t**2 + 8*t**4 + 10*t + 65*t**3 - 8*t**4 + 20*t**4 = 0. What is t?
-2, -1, -1/4, 0
Let b(g) be the second derivative of 34*g + 1/24*g**4 + 3 - 1/3*g**3 - 3*g**2. Suppose b(q) = 0. What is q?
-2, 6
Let m(h) be the second derivative of 1/12*h**5 + 0 - 8*h + 5/24*h**4 + 0*h**3 + 8*h**2. Let z(i) be the first derivative of m(i). Factor z(j).
5*j*(j + 1)
Let v(j) = -j**2 - 2*j - 1. Let g(p) = 5*p**3 + 25*p**2 - 20*p - 10. Let d(s) = s**3 + 9*s**2 + 21*s + 8. Let i be d(-6). Let c(f) = i*v(f) + g(f). Factor c(r).
5*r**2*(r + 7)
Factor 34807*t**4 + 2*t**5 - 34799*t**4 + 137*t + 72*t**3 + 42 + 158*t**2 - 3*t**5.
-(t - 14)*(t + 1)**3*(t + 3)
Let s(o) = o**3 - 20*o**2 + 37*o - 14. Let b be s(18). Let g be 0 - b/(-36) - 0. Suppose 25/9 + g*v**3 + 11/9*v**2 + 35/9*v = 0. Calculate v.
-5, -1
Let c(z) be the first derivative of -2*z**3 + 878*z**2 - 1168*z + 304. Factor c(d).
-2*(d - 292)*(3*d - 2)
Let p = 141/5974 - -1336625/65714. Determine m, given that -168/11*m + p*m**2 + 14/11*m**4 - 102/11*m**3 + 32/11 = 0.
2/7, 1, 2, 4
Factor -43*x + 0 - 1/3*x**3 - 46/3*x**2.
-x*(x + 3)*(x + 43)/3
Let 0 - 854/3*z**2 - 2*z = 0. What is z?
-3/427, 0
Let -1056/5 - 8*r + 4/5*r**2 = 0. Calculate r.
-12, 22
Let w = -38714/3 - -13226. Let d = w - 320. Factor -2/3*c - 2/3*c**2 + d.
-2*(c - 1)*(c + 2)/3
Solve -251/6*y**4 - 306685/3*y**2 - 1/6*y**5 - 1164241/6*y - 10583/3*y**3 - 571787/6 = 0.
-83, -1
Let y(f) = 1121*f**2 - 6856*f + 10804. Let l(a) = -8*a**2 - 2*a + 3. Let h(o) = -8*l(o) - 2*y(o). Factor h(u).
-2*(33*u - 104)**2
Let r(o) be the third derivative of o**7/525 - 116*o**6/75 + 3619*o**5/10 - 17787*o**4/10 + 103*o**2 - 12. Determine b, given that r(b) = 0.
0, 2, 231
Let z(c) be the second derivative of -c**5/90 - 103*c**4/54 - 780*c. Suppose z(o) = 0. What is o?
-103, 0
Let c(w) = -3*w**2 + 11*w - 24. Let a be c(6). Let h = 68 + a. Suppose 12*o**3 + 20*o**h - 15 + 12 + o**2 + 6*o = 0. What is o?
-1, 1/4
Let b be 12 + 1 - (-21)/(-3). Factor 25 + b*t**2 + t**2 + 8*t**2 - 40*t**2 - 5*t**3 + 5*t.
-5*(t - 1)*(t + 1)*(t + 5)
Factor 33846156 + 2583*d**2 - 951*d**2 + 957612 + 443904*d + 1135770 + 2*d**3 + 4307758.
2*(d + 272)**3
Factor -2843*b**2 + 2825*b**2 + 0*b**4 + 44*b - 24*b**3 - 2*b**4.
-2*b*(b - 1)*(b + 2)*(b + 11)
Suppose -3*u + 29 = 4*t, 0 = -13*t + 18*t - 5*u + 25. What is z in -t + 1/3*z**2 + 5/3*z = 0?
-6, 1
Let k be (-6)/(-8) - ((-30195)/60)/33. Find d, given that -4/3*d**2 - 44/3*d + k = 0.
-12, 1
Let a = -2/77627 + -1354918/1009151. Let n = -8/11 - a. Let -56/13*t - 106/13*t**2 - 40/13*t**3 - n = 0. Calculate t.
-2, -2/5, -1/4
Let v(b) be the first derivative of 4/3*b**3 + 48*b + 14*b**2 + 17. Factor v(z).
4*(z + 3)*(z + 4)
Let q(h) be the first derivative of 16 + 1/3*h + 1/3*h**2 + 1/9*h**3. Solve q(x) = 0.
-1
Let y = 451509/13 + -34731. Let p = 2 - 0. Factor 8/13 + y*w - 2/13*w**p.
-2*(w - 4)*(w + 1)/13
Let k = 141119 + -141116. Solve 567/4*o**k + 198*o**2 + 355/4*o + 25/2 = 0 for o.
-5/9, -2/7
Let k(m) = -2*m**3 - 5*m**2 - 25*m - 82. Let o be k(-3). Let j(d) be the first derivati