 = 0.
-9, 1, 4
Let t(r) = -r**2 + 9*r + 3. Let f(w) = 2*w**2 + 2572*w - 850220. Let s(l) = -f(l) - 4*t(l). Factor s(c).
2*(c - 652)**2
Let c(b) be the third derivative of -b**8/2016 + b**7/252 - b**6/90 + b**5/90 + 1555*b**2. Suppose c(z) = 0. Calculate z.
0, 1, 2
Let j be 2*(-2)/8*-1. Let h(u) = u**3 + 4*u**2 - 72*u - 358. Let c be h(-6). Determine v, given that v**c + 0 + 3/4*v**5 - 1/4*v - v**4 - j*v**3 = 0.
-1, 0, 1/3, 1
Let t = 11371/78029 - 32/11147. Factor 4/7*g + 6/7*g**4 + t*g**5 + 13/7*g**3 + 0 + 12/7*g**2.
g*(g + 1)**2*(g + 2)**2/7
Suppose 0 = -a - 27 + 28. Let f be 3 + 2 - 3 - (a - 2). Factor -4*b**4 + 4*b + 2 - b**f - 2 + 5*b**4 - 4*b**2.
b*(b - 2)*(b - 1)*(b + 2)
Let r(s) be the first derivative of -4/3*s**3 - 77 - 1/5*s**5 - 3/2*s**4 + 3*s**2 + 5*s. Solve r(l) = 0 for l.
-5, -1, 1
Let h(w) be the third derivative of -w**7/4620 + w**6/990 + w**5/165 - 2*w**4/33 + 5*w**3/3 + 32*w**2. Let r(t) be the first derivative of h(t). Factor r(y).
-2*(y - 2)**2*(y + 2)/11
Let l = 132 + -77. Let q(g) = 5 + 104*g**2 + 2*g**3 + g**4 - 57*g**2 - l*g**2. Let o(s) = -s**2 + 1. Let i(h) = 5*o(h) - q(h). Factor i(u).
-u**2*(u - 1)*(u + 3)
Suppose 2*v - 5*u = -10, 13*u = 5*v + 10*u + 6. Let k(g) be the second derivative of -3*g**4 + 0*g**2 + 4/3*g**3 + v + 7*g + 4/5*g**5. Solve k(z) = 0.
0, 1/4, 2
Suppose -x = 114 - 9. Let v be 0 + (x/5 - -5)/(-22). Factor -v + 8/11*d - 2/11*d**2.
-2*(d - 2)**2/11
Factor -26*x + 38/3 + 14*x**2 - 2/3*x**3.
-2*(x - 19)*(x - 1)**2/3
Suppose 40 - 376 = -7*x. Suppose -38*c**2 - 42*c**2 - x*c + 53*c**2 - 6 + 18 = 0. What is c?
-2, 2/9
Let q(s) = -8*s**3 + 2335*s**2 + 292*s + 3. Let m be q(292). Factor 0*d + 0 + 24/5*d**2 + 4/5*d**4 - 4*d**m.
4*d**2*(d - 3)*(d - 2)/5
Let u(m) be the second derivative of 0*m**2 + 243/56*m**7 + 30*m + 1/3*m**3 + 81/8*m**6 + 297/40*m**5 + 0 + 29/12*m**4. What is z in u(z) = 0?
-1, -2/9, 0
Let p(g) be the first derivative of -g**4/42 + 8*g**3/21 - g**2 - 12*g - 57. Let w(i) be the first derivative of p(i). Factor w(q).
-2*(q - 7)*(q - 1)/7
Let b be (105/12)/((-9)/12)*6. Let n = b - -72. Factor 2*x**5 + 22*x**2 - 4*x**4 - 18*x**n + 2*x - 4*x**5.
-2*x*(x - 1)*(x + 1)**3
Let j(f) be the third derivative of -f**8/20160 + f**7/1890 + 35*f**4/24 - f**3/3 - 47*f**2. Let i(h) be the second derivative of j(h). Let i(q) = 0. What is q?
0, 4
Suppose -19*v + 21*v + 3*g - 19 = 0, -5*v + 35 = 5*g. Find j such that j - 11*j**2 - j**5 - 16*j**2 + 25*j**v + 2*j**4 = 0.
-1, 0, 1
Let x(d) be the first derivative of d**4/4 - d**3/3 - d**2 + 2*d - 5. Let l be x(2). Solve 3/2*h + 1/2*h**2 - l = 0.
-4, 1
Let j = 504 - 520. Let n be (j - -16)*(1 + 0). What is z in -3/8*z**5 + 0*z**4 + n*z + 3/8*z**3 + 0*z**2 + 0 = 0?
-1, 0, 1
Suppose 7*c - 53 + 39 = 0. Solve 164*f**c + 181*f**2 + 20 + 45*f - 335*f**2 = 0 for f.
-4, -1/2
Suppose 27*g - 28*g = -16. Suppose 8*y - 3*y + 4*x - 26 = 0, g = 4*y + 2*x. Factor 6/7 - 2/7*a**y - 4/7*a.
-2*(a - 1)*(a + 3)/7
Let p(w) be the second derivative of 3*w**5/40 - 15*w**4/4 - 63*w**3/4 - 24*w**2 - w + 532. Suppose p(f) = 0. Calculate f.
-1, 32
Let k(h) be the first derivative of 4*h**3/21 - 194*h**2/7 + 384*h/7 - 36. Suppose k(q) = 0. Calculate q.
1, 96
Let k = 1070737 - 4282945/4. What is j in k*j + 0 + 1/4*j**2 = 0?
-3, 0
Let q(z) be the first derivative of -z**6/33 + 1126*z**5/55 - 80083*z**4/22 + 473762*z**3/33 - 235760*z**2/11 + 156800*z/11 - 1382. Let q(n) = 0. Calculate n.
1, 280
Suppose -4*v + 4*c = -96, 0*c + 20 = -4*c. Suppose 18*j = 901 - 847. Factor 32*g**3 + 4*g - 3 - 10*g + 15*g**2 - v*g**3 + 5*g**j.
3*(g + 1)*(2*g - 1)*(3*g + 1)
Let c(a) be the second derivative of 1/10*a**6 - 2 - 11/20*a**5 + 11/12*a**4 - a**2 - 1/6*a**3 - 4*a. Suppose c(n) = 0. What is n?
-1/3, 1, 2
Let x(v) be the first derivative of 2*v**3/9 + 884*v**2/3 + 390728*v/3 + 1583. Factor x(y).
2*(y + 442)**2/3
Let r = 2373 + -2373. Let m be -4 + (r - 2) + (-234)/(-27). Factor -4*n**2 + 8/3*n - 2/3*n**4 - 2/3 + m*n**3.
-2*(n - 1)**4/3
What is u in -118/23*u**3 + 358/23*u + 236/23 + 6/23*u**2 - 2/23*u**4 = 0?
-59, -1, 2
Let z(t) = -112*t - 4592. Let q be z(-41). Let v(o) be the third derivative of 23*o**2 - 9/2*o**3 + 0*o + 3/8*o**4 + q - 1/80*o**5. Solve v(s) = 0 for s.
6
Let i(d) be the third derivative of -1/12*d**4 + 10*d**2 + 0 + 0*d + 23/120*d**6 - 1/21*d**7 + 0*d**3 - 1/12*d**5. Suppose i(h) = 0. Calculate h.
-1/5, 0, 1/2, 2
Suppose 17*t - 41 - 10 = 0. Let i be (-7 - (-6 + -1)) + t. Factor 4/5*f**4 + 16/5*f - 4/5*f**i - 16/5*f**2 + 0.
4*f*(f - 2)*(f - 1)*(f + 2)/5
Suppose 0 = 5*m + m - 24. Suppose 51 + 69 = m*i. Determine y, given that 12*y**2 + 14*y**2 - 11*y - 5 - i*y**2 + 2*y = 0.
-5/4, -1
Solve 2635/4*d + 1315/2 + 5/4*d**2 = 0 for d.
-526, -1
Factor 90*j - 2/9*j**2 - 1612/9.
-2*(j - 403)*(j - 2)/9
Let a(u) be the first derivative of u**8/840 - 2*u**7/175 + 11*u**6/300 - u**5/25 - 55*u**2/2 - 34. Let d(c) be the second derivative of a(c). Solve d(t) = 0.
0, 1, 2, 3
Let s(k) be the second derivative of -1/30*k**4 - 8/5*k**2 + 0 - 8*k - 2/5*k**3. Suppose s(h) = 0. Calculate h.
-4, -2
Let x = -67 - -89. Let x*a + 26*a - 64*a - 3*a**2 - a**2 = 0. What is a?
-4, 0
Suppose -594 - 1070 = -104*u. Let n(i) be the first derivative of -3*i**6 + 24/5*i**5 + 31 + u*i - 12*i**2 + 23/2*i**4 - 12*i**3. Let n(f) = 0. Calculate f.
-1, 2/3, 2
Let g(f) be the first derivative of -f**3/2 + 4896*f**2 - 15980544*f - 3515. Factor g(v).
-3*(v - 3264)**2/2
Suppose 52*j + 167*j = 0. Solve j + 0*t + 1/7*t**3 - 2*t**2 = 0 for t.
0, 14
Factor -467*q**2 - 4621*q**2 - 272*q + 336*q + 101124*q**3.
4*q*(159*q - 4)**2
Let f = -23 - -41. Factor -20*t + 0*t**2 + 2*t**2 - 9*t**2 + 5*t**2 - f.
-2*(t + 1)*(t + 9)
Factor -3*b**3 + 0*b**3 - 5*b**3 - 2304 + 92*b**2 + 8*b**3 + 960*b + 2*b**3.
2*(b - 2)*(b + 24)**2
Suppose -3256 = -h - 2400. Let a = -5129/6 + h. Factor 0*y + a*y**2 - 2/3 - 1/2*y**3.
-(y - 2)*(y - 1)*(3*y + 2)/6
Let p(m) be the first derivative of 55*m**6/3 + 304*m**5/5 + 471*m**4/10 + 212*m**3/15 + 8*m**2/5 - 412. Determine z, given that p(z) = 0.
-2, -4/11, -1/5, 0
Let r(i) be the second derivative of 32*i**7/21 + 80*i**6/3 + 753*i**5/5 + 820*i**4/3 + 562*i**3/3 + 60*i**2 + 2*i - 288. Determine o, given that r(o) = 0.
-6, -5, -1, -1/4
Let k(g) be the second derivative of -3/2*g**3 + 119*g - 1/12*g**4 - 4*g**2 + 0. Factor k(i).
-(i + 1)*(i + 8)
Let i = 398 - 398. Factor -17*w + 12*w**3 + 2*w + i*w**5 + 4*w**5 - w**5 - 18*w**4 + 18*w**2.
3*w*(w - 5)*(w - 1)**2*(w + 1)
Let c = 565 + -563. Solve 2 + 10*f - 4107*f**c - 3 + 1 + 4532*f**2 = 0 for f.
-2/85, 0
Let g(w) be the first derivative of w**5/5 + 37*w**4/4 - w**3/3 - 37*w**2/2 + 127. Factor g(k).
k*(k - 1)*(k + 1)*(k + 37)
Suppose 3181*g = 3185*g. Let p(q) be the second derivative of 4/21*q**3 - 27*q + 1/21*q**4 + g + 2/7*q**2. Factor p(z).
4*(z + 1)**2/7
Let w = 5046 + -5040. Let j(t) be the second derivative of 0 + 5*t - 1/50*t**5 + 0*t**2 - 1/30*t**4 + 1/15*t**3 + 1/75*t**w. Suppose j(q) = 0. What is q?
-1, 0, 1
Let -11*u**2 + u**4 - 81*u + 117*u + 7*u**2 - 9*u**3 = 0. Calculate u.
-2, 0, 2, 9
Let b(k) be the first derivative of -81*k**5/10 - 1071*k**4/2 - 29258*k**3/3 - 12376*k**2 - 5408*k + 529. Factor b(t).
-(t + 26)**2*(9*t + 4)**2/2
Let h(f) be the first derivative of 33/14*f**4 + 384/7*f + 48/7*f**2 - 6/35*f**5 + 51 - 72/7*f**3. Find a such that h(a) = 0.
-1, 4
Let t(c) be the second derivative of 7/30*c**6 + 0 + 10*c**2 - 19/12*c**4 + 53*c - 8/3*c**3 + 7/20*c**5 + 1/42*c**7. Determine q, given that t(q) = 0.
-5, -2, 1
Suppose -3*r + 3*u + 0*u = -156, -r = 5*u - 70. Let q = -3 + 22. Factor -q*b**3 + 725*b**2 + r*b - 805*b**2 + 54*b**3 - 10.
5*(b - 1)**2*(7*b - 2)
Let z(r) be the third derivative of 1/6*r**4 - 1/84*r**8 + 0 - 2/15*r**5 + 4/105*r**7 - 119*r**2 + 0*r**3 + 0*r**6 + 0*r. Factor z(g).
-4*g*(g - 1)**3*(g + 1)
Factor -2952*x**4 + 2953*x**4 - 21*x**2 - 22*x**2 - 36*x**3 + 222*x.
x*(x - 37)*(x - 2)*(x + 3)
Let t = 227 - 227. Let f be (6 - 10) + (((-72)/30)/(-3) - -4). Factor 0*a + f*a**2 + t.
4*a**2/5
Factor -9/4*q**4 - 9/2*q**2 + 3/8*q**5 + 39/8*q**3 + 0 + 3/2*q.
3*q*(q - 2)**2*(q - 1)**2/8
Suppose 5 = -5*u, 0 = -3*v + 12*u - 17*u + 37. Suppose 9*b + v*b - 5*b = 0. Suppose -2/7*y + 0 + 2/7*y**3 + b*y**2 = 0. What is y?
-1, 0, 1
Let j(x) = -13*x**2 + 3*x + 