 t(g) be the first derivative of -2*g**3/27 - 20*g**2/9 + 14*g/3 + 3874. Let t(m) = 0. Calculate m.
-21, 1
Let w = 212675 + -212673. Factor -3/2*j**4 + 5*j**3 + 36*j + 26*j**w + 16 - 1/2*j**5.
-(j - 4)*(j + 1)*(j + 2)**3/2
Let w = -251733/1910 - -659/5. Let k = 1523/1910 + w. Determine u, given that 0 - 4/5*u + 1/5*u**4 - k*u**2 + 1/5*u**3 = 0.
-2, -1, 0, 2
Let k(z) be the second derivative of 0 + 3/10*z**2 + 29/10*z**3 + 56/5*z**4 + 30*z + 147/25*z**5. Factor k(r).
3*(r + 1)*(14*r + 1)**2/5
Suppose 338*a - 252 = 331*a. Let q be a/(-90) + (-27)/(-30). Determine m, given that -1/2*m**2 - q*m + 1 = 0.
-2, 1
Let d(a) = -a**2 + a + 1. Let n(x) = 3*x**3 + x - 2. Let r be n(1). Let p(v) = v**4 + 11*v**3 + 33*v**2 + 27*v + 2. Let w(k) = r*d(k) - p(k). Factor w(g).
-g*(g + 1)*(g + 5)**2
Factor -406*i - i**2 + 259*i + 150*i.
-i*(i - 3)
Let t = 759/4 + -188. Let w(r) be the second derivative of 0 - 27/2*r**2 - 14*r + 3/20*r**5 + 15/2*r**3 - t*r**4. Factor w(b).
3*(b - 3)**2*(b - 1)
Suppose 3*h = -3*t + 12, -5*h + 20 = -4*t + 5*t. Suppose d - 98 = -4*b - 8, 411 = h*d - b. Factor 21*l**2 + 6 - d*l - 9*l**2 + 87*l - 3*l**3.
-3*(l - 2)*(l - 1)**2
Let v = -3859 - -3859. Let s(r) be the third derivative of -2/21*r**7 + 0*r + 1/3*r**5 - 5/24*r**4 + v*r**3 + 4*r**2 + 0 + 1/24*r**6. Let s(x) = 0. Calculate x.
-1, 0, 1/4, 1
Let d(z) = -40*z**3 - 12*z**2 - 80*z - 24. Let n(b) = -17*b**3 - 5*b**2 - 32*b - 10. Let i(g) = -5*d(g) + 12*n(g). Suppose i(q) = 0. What is q?
-2, 0, 2
Let v(j) be the first derivative of 5*j**4/4 + 95*j**3 - 585*j**2/2 + 295*j + 2689. What is w in v(w) = 0?
-59, 1
Let c(f) = f**3 - 2*f + 14. Let u be c(6). Find q such that -7 - u*q**2 + 69*q - 9*q - 5 + 143*q**2 = 0.
2/5
Let y(u) be the second derivative of u**4/3 + 194*u**3/3 - 396*u**2 + 343*u - 5. Let y(g) = 0. What is g?
-99, 2
Determine i, given that -2280/7*i + 3/7*i**2 + 433200/7 = 0.
380
Factor 105/4*k**2 + 441/2*k - 6*k**3 - 3/4*k**4 + 0.
-3*k*(k - 6)*(k + 7)**2/4
Suppose -60*j = -57*j + 30. Let f be (-276)/j - 6/10. Factor 18*p**3 - 78*p**3 - 6*p**2 + f*p**3.
-3*p**2*(11*p + 2)
Factor 272/3*i**2 - 578/3*i**3 + 1430/3*i + 676/3.
-2*(i - 2)*(17*i + 13)**2/3
Let d(c) be the first derivative of -3*c**4/8 - 307*c**3/2 - 17556*c**2 + 35574*c + 1853. Let d(r) = 0. What is r?
-154, 1
Let w be (74/222)/(171/540 - (-1)/(-4)). Let z(s) be the first derivative of 2*s**3 + 0*s + 0*s**2 - 16/5*s**w - 13/4*s**4 + 1/2*s**6 + 5. Factor z(l).
l**2*(l - 6)*(l + 1)*(3*l - 1)
Determine z so that 22/5*z**3 + 0*z - 21/5*z**4 + 0 - 1/5*z**5 + 0*z**2 = 0.
-22, 0, 1
Let n be 1 + (-18)/207 + 1392/138. Let q(f) be the second derivative of 1/4*f**4 + 2*f**3 - 6*f**2 + n*f + 0 - 3/20*f**5. Determine z, given that q(z) = 0.
-2, 1, 2
Let -1/2*r**3 + 259 + 260*r**2 - 1037/2*r = 0. What is r?
1, 518
Let m(f) = -8*f - 10. Let p be m(-7). Let b = p + -41. Factor -4*z + z**2 + b - 1 + 4*z**3 - 5*z**2.
4*(z - 1)**2*(z + 1)
Let a be (-119)/(-14)*1170/3315. Let -9/4*t**a - 7/2 + 1/4*t**4 + 9/4*t + 13/4*t**2 = 0. What is t?
-1, 1, 2, 7
Let r = 7699/28196 - -51/4028. Factor r*n**2 + 68/7*n + 578/7.
2*(n + 17)**2/7
Let t = -2639 - -2639. Let r(x) be the first derivative of -2*x**3 + 3/4*x**4 + 0*x**2 + 4 + t*x. What is q in r(q) = 0?
0, 2
Solve 288/7*k + 102/7*k**2 + 0 + 2/7*k**3 = 0 for k.
-48, -3, 0
Suppose -193 = -9*g + 266. Find u, given that 4600*u - 36*u**2 + 3*u**3 - 21*u**2 - 6*u**3 - 4705*u - g = 0.
-17, -1
What is n in -5064355 + 3293*n - 3*n**2 + 3145*n + 1610368 = 0?
1073
Let c(z) be the second derivative of 0 + 202*z + 2/9*z**4 - 1/90*z**5 + 13/27*z**3 + 0*z**2. Let c(u) = 0. Calculate u.
-1, 0, 13
Let h = 714 - 709. Let t(g) be the second derivative of 1/10*g**2 - 9*g - 1/15*g**3 - 1/150*g**6 + 1/50*g**h + 0 + 0*g**4. Factor t(l).
-(l - 1)**3*(l + 1)/5
Suppose 760 = 24*o + 184. Let x be (-3)/(1800/(-305)) + (-9)/o. Find s, given that -x*s**2 - 2/5*s + 8/15 = 0.
-4, 1
Let z(y) be the second derivative of y**5/60 - 10*y**4/3 + 79*y**3/6 - 59*y**2/3 + 2*y + 154. Let z(r) = 0. What is r?
1, 118
Let m(q) = 275*q**2 + 7310*q - 280. Let u(x) = -273*x**2 - 7330*x + 280. Let p(y) = 4*m(y) + 5*u(y). What is n in p(n) = 0?
-28, 2/53
Let a(k) be the third derivative of 12167/2*k**3 + 0 + 1587/8*k**4 + 69/20*k**5 + 1/40*k**6 + 0*k - 76*k**2. Find g, given that a(g) = 0.
-23
Factor 0*f - 1/5*f**3 - 97/5*f**2 + 0.
-f**2*(f + 97)/5
Suppose -37*b + 32*b = -30. Factor b*t**2 + 7*t - 15 - 11*t**2 + 13*t.
-5*(t - 3)*(t - 1)
Let t(n) be the first derivative of 2*n**3/3 + 15*n**2 + 12*n + 15. Let b(s) = 5*s**2 + 59*s + 26. Let l(k) = -6*b(k) + 13*t(k). Factor l(r).
-4*r*(r - 9)
Factor -22/5*j**2 + 54 + 6/5*j + 2/5*j**3.
2*(j - 9)*(j - 5)*(j + 3)/5
Suppose 0 = -12*a + 445 - 349. Suppose a*b = -10*b. Factor -3/2*t + b - 3/4*t**2.
-3*t*(t + 2)/4
Factor -52*x**2 - 13*x**3 - 52*x**2 + 55*x**3 - 12*x**3 - 18*x**3 - 36*x.
4*x*(x - 9)*(3*x + 1)
Let c(o) = -2*o**3. Let v(s) = 344*s**2 + 347*s**2 - 695*s**2 + 4*s + 11*s**3. Let n(j) = -35*c(j) - 5*v(j). Let n(l) = 0. Calculate l.
-2, 0, 2/3
Suppose 0 = 6*b - 3*b - 4*q - 9, -5*q = -7*b + 8. Let u be ((-34)/(-18))/b - (-8 - -5). What is s in 0 + u*s + 2/9*s**2 = 0?
-5, 0
Let p = 1689 - 689. Find i, given that 3200000*i**2 + 512000000 + p*i**4 + 205*i**5 - 210*i**5 - 64000000*i - 94304*i**3 + 14304*i**3 = 0.
40
Factor 8/3*w - 1/3*w**2 + 128/3.
-(w - 16)*(w + 8)/3
Let x(z) be the third derivative of -2/175*z**7 + 0 + 0*z + 4/25*z**5 + 0*z**6 - 1/560*z**8 + 0*z**3 - 238*z**2 + 2/5*z**4. Solve x(s) = 0 for s.
-2, 0, 2
Solve -381/4*b**2 + 9/8 - 2283/8*b = 0.
-3, 1/254
Solve -2/13*z**2 - 38/13*z - 120/13 = 0.
-15, -4
Let o(b) = 13*b**3 + 507*b**2 - 2*b - 76. Let i be o(-39). Solve 17/3*h - 2 + h**i = 0 for h.
-6, 1/3
Suppose 3*k - b + 11 = 5*k, 0 = -5*k + b + 45. Let l be ((-2)/2 - 0)*-2. What is y in k*y**l + 17*y**2 - 5*y**3 - 60*y + 4*y**2 + 40 + y**2 = 0?
2
Let f(z) be the first derivative of 4/5*z**5 - 44 - 2/3*z**6 - 32*z + 52*z**2 + 11*z**4 - 116/3*z**3. Suppose f(i) = 0. What is i?
-4, 1, 2
Determine i, given that 597/4*i - 3/4*i**2 - 1455/2 = 0.
5, 194
Let g(j) = -20*j**2 - 83*j - 95. Let c(f) = 11*f**2 + 42*f + 45. Let o(z) = 9*c(z) + 5*g(z). Solve o(h) = 0 for h.
-35, -2
Let a(f) be the first derivative of -4*f**3/21 - 288*f**2/7 - 572*f/7 + 1845. Determine j so that a(j) = 0.
-143, -1
Factor 7 + 2*h**3 - 138*h**2 - 102*h + 12 - 12*h**3 - 14 + 21.
-2*(h + 1)*(h + 13)*(5*h - 1)
Let v(f) be the second derivative of f**4/8 + 37*f**3/2 - 114*f**2 + 2814*f. Determine m, given that v(m) = 0.
-76, 2
Suppose -18*s + 14*s + 64 = 4*j, 5*j + 3*s = 68. Let b(m) be the first derivative of -j*m + 5/3*m**3 - 22 + 5/2*m**2. Find t, given that b(t) = 0.
-2, 1
Suppose 3*x = 2*a - 9 - 93, -a - 5*x = -51. Solve -58*y + 2*y**2 + a*y + 8 + y**3 - 4 = 0.
-4, 1
Let w = 1024 - 1035. Let r(t) = 2*t**3 + 100*t**2 - 80*t - 11. Let y(d) = 20*d**2 - 16*d - 2. Let j(f) = w*y(f) + 2*r(f). Factor j(u).
4*u*(u - 4)*(u - 1)
Let w(j) = -2*j**4 - 5*j**3 + 21*j**2 + 34*j + 5. Let z(u) = 3*u**4 + 8*u**3 - 31*u**2 - 52*u - 8. Let h(i) = -8*w(i) - 5*z(i). Factor h(s).
s*(s - 4)*(s + 1)*(s + 3)
Suppose 97*t - 654 = 91*t. Determine y, given that 67*y - 96 - 2*y**4 - 102*y**2 - 11*y**3 + t*y + 35*y**3 = 0.
1, 3, 4
Find g such that -63*g**4 + 12*g**2 + 59*g**4 + 2516*g - 2504*g + 4*g**3 + 8*g**2 = 0.
-1, 0, 3
What is m in 39*m**2 + 46*m**2 + 1464 - 11*m - 196*m + 40*m**2 - 122*m**2 = 0?
8, 61
Suppose 3*r - 9 = 2*r. Suppose -u + 6 + r = -3*t, 3*u = -4*t - 7. Suppose 16*j**4 + 2*j**5 - 14*j**5 + 4*j**u + 0*j**5 - 8*j**2 = 0. What is j?
-2/3, 0, 1
Let w(i) = -5*i**3 - 25*i**2 - 144*i - 320. Let c(y) = -19*y**3 - 99*y**2 - 576*y - 1280. Let m(t) = -4*c(t) + 15*w(t). Determine q, given that m(q) = 0.
-8, -5
Let v(u) be the first derivative of u**4 + 26*u**3/5 - 124*u**2/5 + 24*u/5 - 434. Factor v(i).
2*(i - 2)*(i + 6)*(10*i - 1)/5
Suppose -2*g = -15*g + 130. Let c be -4 + g + 0 - 2. Determine q, given that 6*q**3 + 8*q**2 + 15*q - 11*q - q**3 + q**c = 0.
-2, -1, 0
Factor -1/2*r**5 - 8*r - 1/2*r**3 + 0 + 3*r**4 - 12*r**2.
-r*(r - 4)**2*(r + 1)**2/2
Let m(h) be the first derivative of -1/12*h**4 + 3/2*h**2 - 9 - 27*h - 1/3*h**3. Let v(x) be the first derivative of m(x). Solve v(f) = 0.
-3, 1
Let a(k) be the first derivative of 2*k**3/