20*w**3/3 - 75. Let o(p) be the third derivative of l(p). Suppose o(t) = 0. Calculate t.
-1, 2
Let n = -27 + 33. Suppose -r + 1 = -2*z - 5, n = -2*z. Determine o so that -2*o + 1 + 3*o**2 + r - 3 + 1 = 0.
-1/3, 1
Let q(p) be the first derivative of -2*p**3/57 + 1338*p**2/19 - 895122*p/19 - 503. Factor q(c).
-2*(c - 669)**2/19
Let y(w) be the second derivative of -153*w**5/10 + 101*w**4 + 407*w**3/51 + 4*w**2/17 + 577*w - 4. Factor y(x).
-2*(x - 4)*(51*x + 1)**2/17
Let i(q) be the third derivative of q**7/42 + q**6/3 - 24*q**2 - 14. Factor i(x).
5*x**3*(x + 8)
Let k be (-20 + -5 - -23)*(4 - (-77)/(-14)). Factor -18/5*q**2 + 3/5*q**k + 3*q + 0.
3*q*(q - 5)*(q - 1)/5
Let o(x) be the second derivative of -x**6/20 + 41*x**5/20 - 559*x**4/24 + 235*x**3/3 + 225*x**2 + 2*x + 231. Suppose o(p) = 0. What is p?
-2/3, 5, 18
Let i(b) = 7*b**3 - 104*b**2 - 324*b + 48. Let k(o) = 45*o**3 - 625*o**2 - 1945*o + 300. Let c(s) = 25*i(s) - 4*k(s). Determine g so that c(g) = 0.
-16, -4, 0
Let p(y) be the second derivative of 0*y**3 + 0 + 1/270*y**5 + 9*y**2 - 5/108*y**4 - 6*y. Let z(u) be the first derivative of p(u). Suppose z(a) = 0. What is a?
0, 5
Let f(q) = q**2 + 1. Let o(y) = -y - 1. Let i be o(-4). Let m(v) be the third derivative of v**4/4 + v**3/2 + 2046*v**2. Let d(x) = i*f(x) - m(x). Factor d(s).
3*s*(s - 2)
Let s(w) be the first derivative of -2/33*w**3 - 98/11*w - 101 - 14/11*w**2. Factor s(c).
-2*(c + 7)**2/11
Let s = -10259 + 10283. Determine z, given that -2/3*z**3 + s - 32*z + 26/3*z**2 = 0.
1, 6
Let h = 69419 - 69416. Determine y so that 2/13*y**4 - 20/13*y**h + 72/13*y**2 - 108/13*y + 54/13 = 0.
1, 3
Let c(r) be the first derivative of r**7/105 - r**6/60 - 2*r**5/15 + r**4/3 - r**2/2 + 78*r + 278. Let d(x) be the second derivative of c(x). Factor d(s).
2*s*(s - 2)*(s - 1)*(s + 2)
Suppose 17*g - 50*g = -99. Suppose -48778 - 2*x**3 - 200*x - 39*x**2 + 4*x**g - 174*x**2 + 39*x**2 + 5246*x = 0. Calculate x.
29
Let a be 79*5 - (-18)/(-6). Suppose -5*c = 3*l - 8*c - 6, -3*l = 3*c - 12. Determine v, given that -2*v**3 + 3*v**3 - 394 + a - l*v = 0.
-1, 2
Let a(x) be the second derivative of x**6/120 - x**5/30 - x**4/6 - 14*x**3/3 - x + 6. Let s(d) be the second derivative of a(d). Solve s(c) = 0 for c.
-2/3, 2
Solve 2/5*g**2 - 768/5 - 766/5*g = 0.
-1, 384
Let f(u) = -u**3 + 42*u**2 + 141*u + 79. Let a be f(45). Suppose 331*d + 54 = a*d. Factor -2/3*o + 4/3*o**4 + 20/9*o**2 - 8/3*o**d - 2/9*o**5 + 0.
-2*o*(o - 3)*(o - 1)**3/9
Let v(l) = 15*l**2 + 246*l - 315. Let z(g) = g**2 + 10*g. Let c(w) = -v(w) + 18*z(w). Factor c(d).
3*(d - 15)*(d - 7)
Determine r so that -3604*r**2 + 1528*r + 1834*r**3 - 528*r**4 + 900*r**2 - 256 - 4*r**5 - 10*r**5 + 140*r**4 = 0.
-32, 2/7, 1, 2
Let g(h) = 37*h + 150 + 133 - 23*h. Let b be g(-20). Suppose -4/5*f**2 + 0 + 2/5*f**b + 0*f = 0. Calculate f.
0, 2
Let f(z) be the second derivative of -5*z**4/6 - 7*z**3/4 - z**2/4 - 28*z - 15. Factor f(t).
-(t + 1)*(20*t + 1)/2
Let s(i) be the second derivative of 2*i + 0*i**2 - 1/45*i**6 + 1/20*i**5 - 1/126*i**7 + 18 + 0*i**3 + 0*i**4. Factor s(f).
-f**3*(f - 1)*(f + 3)/3
Let s(c) = -26*c**5 + 106*c**4 - 39*c**3 - 65*c**2 + 72*c + 1. Let o(h) = -h**5 + 4*h**4 + h**3 + h**2 + h + 1. Let b(m) = 35*o(m) - 5*s(m). Solve b(d) = 0.
-1, 2/19, 1, 3
Let -2/17*a**3 + 20/17*a**2 - 180/17 + 162/17*a = 0. What is a?
-6, 1, 15
Let n be 0/(17 + -2 - (-1694)/(-121)). Factor 11/2*m**2 - 3*m**3 + m + n.
-m*(m - 2)*(6*m + 1)/2
Solve -1682/5 - 116/5*s - 2/5*s**2 = 0 for s.
-29
Let b be (-8)/(-14)*(-363)/(-66)*(-14)/(-22). Factor -162*c**3 - 24 - 81/2*c**4 - 216*c**b - 120*c.
-3*(c + 2)*(3*c + 2)**3/2
Suppose -15*i = 34*i - 1176. Suppose -32*s + 20*s + i = 0. Factor -2*z**s + 0 + 0*z - 4/3*z**3 + 2/3*z**4.
2*z**2*(z - 3)*(z + 1)/3
Let r = -183 - -185. Factor -42*n - 56*n + 81*n**r - 2*n**3 - 148*n**2 + 39*n**2.
-2*n*(n + 7)**2
Let k(z) = -4*z**5 - 148*z**4 + 2179*z**3 - 2051*z**2 + 6*z - 3. Let g(v) = -2*v**5 - 6*v**4 + v**3 - v**2 + 2*v - 1. Let s(q) = -3*g(q) + k(q). Factor s(p).
2*p**2*(p - 32)**2*(p - 1)
Let c(w) = -6*w**2 - w. Let t(f) = -25*f**2 - 30*f - 133. Let x(n) = 4*c(n) - t(n). Let x(k) = 0. Calculate k.
-19, -7
Let m = 1059183 + -9532579/9. Factor m*f**2 + 2/9*f**4 + 16/3*f + 22/9*f**3 + 0.
2*f*(f + 1)*(f + 4)*(f + 6)/9
Suppose 0 = 32*s - 897 + 129. Solve -2*n**3 + 24*n**5 + 52*n**4 + s*n**3 - 8*n + 2*n**3 - 7*n**2 - 5*n**2 = 0.
-1, -2/3, 0, 1/2
Let z(m) be the second derivative of m**4/6 - 308*m**3/3 + 23716*m**2 + 4*m - 140. Let z(a) = 0. What is a?
154
Let w(o) be the third derivative of 8 + 1/40*o**6 + 1/10*o**5 + 0*o**3 - 3/112*o**8 + 0*o + 0*o**4 - 2/35*o**7 + 2*o**2. Determine n so that w(n) = 0.
-1, 0, 2/3
Suppose -8*d + 23*d = 315. Let z be ((-30)/d)/5 + (-310)/(-350). Factor 3/5*f**2 - z*f - 6/5.
3*(f - 2)*(f + 1)/5
Let y(u) be the third derivative of -u**6/600 - 13*u**5/150 - 167*u**4/120 - 119*u**3/15 + 8*u**2 - 144. Factor y(i).
-(i + 2)*(i + 7)*(i + 17)/5
Let m be 0/((8 - 3)/1). Suppose g + 1 = m, 8*g - 10*g - 14 = -4*v. Factor -1/3*f**2 + 1/3 + 1/3*f - 1/3*f**v.
-(f - 1)*(f + 1)**2/3
Factor 7860*r**4 + 134*r**3 + 5*r**5 - 5*r + 14*r**3 - 7945*r**4 + 75 - 150*r + 2*r**3 + 10*r**2.
5*(r - 15)*(r - 1)**3*(r + 1)
Suppose -478571*g = -478596*g + 75. Let -3 - 1/4*h**g - 5*h - 9/4*h**2 = 0. What is h?
-6, -2, -1
Let w(o) be the first derivative of 0*o + 49 + 2/21*o**3 - 3/14*o**2 + 1/28*o**4. Factor w(g).
g*(g - 1)*(g + 3)/7
Let t(w) = 6*w - 188. Let p(v) = -26*v - 72. Let r be p(-4). Let q be t(r). Let 2/3*d**3 - 50/3*d - 14*d**2 - 4 + 2*d**q = 0. Calculate d.
-2, -1, -1/3, 3
Factor 1292/5*j - 1296/5 + 4/5*j**2.
4*(j - 1)*(j + 324)/5
Suppose h - 4*r = 8, 7*r + 10 = 4*h + 2*r. Suppose h = -4*p - 12, -11*n + 2*p = -14*n. Factor 1/2*c**3 + 5/2*c**n - 1/2*c**4 + 0 + 3/2*c.
-c*(c - 3)*(c + 1)**2/2
Let l(f) = -135 - 75 - 43*f - f**2 + 27 + 252*f. Let w(m) = m**2 - 104*m + 93. Let q(v) = 2*l(v) + 5*w(v). Find j, given that q(j) = 0.
1, 33
Let a(m) be the third derivative of m**8/2688 + m**7/1008 - 61*m**4/24 - 14*m**2 - m. Let p(t) be the second derivative of a(t). Let p(o) = 0. What is o?
-1, 0
Suppose 0 = -248*x + 242*x + 12. Let l be (4/(-3))/(x/(-2 + -14)). What is q in l - 56/3*q + 20/3*q**2 = 0?
4/5, 2
Suppose 2*q - 6 = -14, -k - q - 260 = 0. Let n be (-213)/142*k/42. Let -96/7*d**3 + n*d + 8*d**2 - 36/7*d**4 + 12/7 = 0. Calculate d.
-3, -1/3, 1
Suppose -r = -10*b + 9*b - 659, -b + 1309 = 2*r. Let h = r - 652. Factor -h*g**3 + 2/3*g**4 + 8*g**2 - 20/3*g + 2.
2*(g - 3)*(g - 1)**3/3
Let y = -1257546/35 + 179658/5. Suppose 0 + 12/7*q**2 + 4/7*q**4 - y*q**3 - 4/7*q = 0. What is q?
0, 1
Suppose 71*l - 24154 = 97*l. Let g = -929 - l. Solve g + 0*i - 2/3*i**2 = 0.
0
Let u = 98 + -90. Suppose 0 = -2*l - 2*l + u. Let 1/5 - 4/5*d**5 - 4*d**3 + 0*d - 3*d**4 - 2*d**l = 0. Calculate d.
-1, 1/4
Solve 124/5*g**2 + 0 + 332/5*g**3 - 336/5*g + 4/5*g**5 - 124/5*g**4 = 0 for g.
-1, 0, 1, 3, 28
Suppose -t = 24*k - 20*k - 41, -k = -6. Suppose 9 = -2*z + 5*z. Find r such that 12*r - t*r**4 - 6*r**z + 14*r**4 - 4*r**3 + r**3 = 0.
-2, 0, 1
Let l(z) = 29*z - 113. Let t be l(4). Let 200*r**4 + 6*r**t - 88*r**2 + 3*r**3 - 24*r + r**3 = 0. Calculate r.
-2/5, 0, 3/4
Let p be (2/(-20))/((-36)/(-2250)*-25). Let s(f) be the third derivative of -1/2*f**3 + 0 - 33*f**2 - 1/20*f**5 + p*f**4 + 0*f. Factor s(o).
-3*(o - 1)**2
Suppose -5/4*w**2 - 7805/4 + 3905/2*w = 0. Calculate w.
1, 1561
Let s be 12/48 - ((-750)/8)/(-3). Let h = s - -34. Factor -h*n + 4*n**3 + 22*n**5 + 2*n**3 - 25*n**5.
-3*n*(n - 1)**2*(n + 1)**2
Let w(x) be the second derivative of -x**5/160 - 7*x**4/24 - 9*x**3/16 + 131*x - 2. Factor w(s).
-s*(s + 1)*(s + 27)/8
Find y such that -348*y**2 + 6*y**4 - 73 + 669*y**3 - 1335*y + 625 - 181 + 637 = 0.
-112, -3/2, 1
Let a(q) = q - 27. Let d be a(27). Let h be (-3)/(36/6)*d. Solve 6/13*g**3 + 2/13*g**4 + h - 2/13*g**2 - 6/13*g = 0.
-3, -1, 0, 1
Suppose -47*r = -3 - 132 - 6. Let t(l) be the third derivative of 0 - 25*l**2 + 1/20*l**5 + 0*l + 2*l**r - 5/8*l**4. Factor t(k).
3*(k - 4)*(k - 1)
Let a = -174 + 184. Determine s so that 2*s - a*s - 42*s**3 + 24*s**3 - 82*s**3 + 52*s**2 + 56*s**4 = 0.
0, 2/7, 1/2, 1
Let d = 11520 - 11515. Let v(f) be the second derivative of 8*f - 3/5*f**d - 4/15*f**6 + 0 + 2/21*f*