t k = g + -269. Determine y, given that 4*y**k + 0 + 8/3*y**3 - 4/3*y**2 + 0*y = 0.
-1, 0, 1/3
Let l(i) be the third derivative of i**5/45 + 29*i**4/18 + 200*i**3/9 - 603*i**2. Suppose l(f) = 0. Calculate f.
-25, -4
Solve 258/11*h + 2/11*h**5 + 26/11*h**4 + 268/11*h**2 + 124/11*h**3 + 90/11 = 0 for h.
-5, -3, -1
Let l(t) be the first derivative of t**8/1680 + t**7/420 - t**6/360 - t**5/60 - 7*t**3/3 + 8. Let b(s) be the third derivative of l(s). Factor b(x).
x*(x - 1)*(x + 1)*(x + 2)
Let v(x) = x - 1. Let b(a) = a**2 + 7*a + 1. Let u be (-3)/2*(14 + -22). Let p(l) = u*v(l) - 4*b(l). Factor p(g).
-4*(g + 2)**2
Let y be (-3 - (-6)/1) + 1. Determine w so that 30*w**2 + y - 18*w - 2*w**3 - 23*w**3 + 0 + 6*w**4 + 3*w**3 = 0.
2/3, 1
Let p(m) be the first derivative of -m**6/24 + m**5/2 - 15*m**4/8 + 10*m**3/3 - 25*m**2/8 + 3*m/2 + 472. Factor p(z).
-(z - 6)*(z - 1)**4/4
Let s(c) = -c**2 - c + 1. Let q(t) = 5*t**2 - 28*t + 46. Let z(f) = -q(f) - 2*s(f). Find b such that z(b) = 0.
2, 8
Let d(r) be the first derivative of -98*r**5/5 - 35*r**4 + 104*r**3/3 - 8*r**2 + 100. Factor d(g).
-2*g*(g + 2)*(7*g - 2)**2
Suppose 3*w = -2*c - 2*w - 23, 0 = -2*c - 2*w - 8. Let u(f) be the first derivative of 2/3*f - 2/9*f**3 - c - 1/3*f**2 + 1/6*f**4. Factor u(v).
2*(v - 1)**2*(v + 1)/3
Let v = 4336/5075 - -2/725. Let -v + 33/7*u - 117/7*u**3 + 3/7*u**2 - 81/7*u**4 = 0. What is u?
-1, 2/9, 1/3
Let 1/2*s**5 - 3*s + 5/2*s**4 - 5/2*s**2 + 0 + 5/2*s**3 = 0. What is s?
-3, -2, -1, 0, 1
Let l(b) = -37*b**3 + 99*b**2 - 5*b - 99. Let w(h) = 16*h**3 - 49*h**2 + 2*h + 49. Let q(d) = 3*l(d) + 7*w(d). Factor q(a).
(a - 46)*(a - 1)*(a + 1)
Let z(u) = 2*u**3 + 21*u**2 - 45*u + 19. Let h(j) = -11*j**3 - 127*j**2 + 270*j - 115. Let n(g) = 6*h(g) + 34*z(g). Determine y so that n(y) = 0.
1, 22
Let u(p) be the third derivative of -p**6/540 + 2*p**5/135 - p**4/36 - 214*p**2. Factor u(t).
-2*t*(t - 3)*(t - 1)/9
Let i = 24 - 11. Factor 2*x - 2*x + i*x**3 - 11*x**3.
2*x**3
Suppose 4*l + 6*u - 211 = 5*u, 0 = 5*l - u - 266. Let d = 797/15 - l. Factor -4/15*j + 2/15 + d*j**2.
2*(j - 1)**2/15
Let l(o) be the first derivative of -o**5/130 + o**4/39 + o**3/39 - 2*o**2/13 + 18*o - 24. Let c(s) be the first derivative of l(s). Factor c(h).
-2*(h - 2)*(h - 1)*(h + 1)/13
Suppose -4*g = 88*c - 84*c + 24, -2*g + c = -6. Determine f, given that 0*f - 1/4*f**2 + g = 0.
0
Let d(r) = r**2 + 21*r + 26. Let i(b) = 3*b**2 + 84*b + 102. Let t(l) = -9*d(l) + 2*i(l). Let t(z) = 0. Calculate z.
-5, -2
Let k(t) = -3*t**3 - 2*t**2 - 6*t. Let f be k(-3). Suppose 20*u**4 - 24 - 16*u - 11*u**3 + 100*u**2 + 12*u - f*u**3 = 0. What is u?
-2/5, 1, 3
Let w(t) be the first derivative of -t**3 - 207*t**2 - 14283*t + 266. Factor w(v).
-3*(v + 69)**2
Let y(d) = -d + 1. Let v be y(0). Let r be 8*v - (-6 + 3 + 6). Factor -1/3*q**r + 0*q**2 - 2/3*q**4 + 0 - 1/3*q**3 + 0*q.
-q**3*(q + 1)**2/3
Let d(c) = 3*c + 4. Let i be d(8). Find w, given that 125*w**2 - 8 + i - 103*w + 3*w = 0.
2/5
Let x = -1766/105 - -86/5. Let k = x + 2/7. Suppose -2/3*u - k*u**2 + 0 = 0. What is u?
-1, 0
Let m(w) be the second derivative of 0 + 19*w + 1/6*w**4 + 4*w**3 + 0*w**2. Let m(a) = 0. What is a?
-12, 0
Let f(b) = b**5 - 6*b**4 - 14*b**3 + 4. Let w(o) = 6*o**5 - 29*o**4 - 71*o**3 + 22. Let l(z) = 33*f(z) - 6*w(z). Factor l(j).
-3*j**3*(j + 2)*(j + 6)
Let p = 1 - -4. Suppose 0 = 2*o - 3*v + 8*v + 12, -v - 24 = -p*o. Factor 15*q + 11*q**3 - 3 + 5*q - 15*q**2 - 31*q**3 + 20*q**o - 2.
5*(q - 1)*(q + 1)*(2*q - 1)**2
Let b be ((-4)/(-14))/(24/14) + 33/18. Factor 1/9*p + 0 + 1/9*p**4 - 1/9*p**b - 1/9*p**3.
p*(p - 1)**2*(p + 1)/9
Let c(z) be the third derivative of z**6/216 + z**5/24 - 5*z**4/18 - 3*z**3/2 + 8*z**2. Let r(p) be the first derivative of c(p). Factor r(k).
5*(k - 1)*(k + 4)/3
Let d(u) = -1. Suppose -5*p = -3*p + 4. Let v be 4/(p*(-3)/(-33)). Let z(c) = c**2 - 3*c - 9. Let a(y) = v*d(y) + 2*z(y). Let a(r) = 0. Calculate r.
1, 2
Let v(g) = g**2 - 3*g + 2. Let r be v(3). Let s be -1*r/2 + 6. Let -9*d**3 - 3*d**5 + s*d**4 + 6*d**4 - 2*d**4 + 3*d**2 = 0. What is d?
0, 1
Suppose -2*k + m + 5 = 0, -4*k + 11 = -m - 0. Suppose x - i + 1 = k*i, -5*x = i - 16. Factor 27*o**2 + 22*o**4 - 17*o**x - 19*o**4 - o**3.
3*o**2*(o - 3)**2
Suppose 5*j - 13*h - 18 = -12*h, 0 = -4*j + 3*h + 21. Suppose 3/7*p**2 - 12/7*p + 3/7*p**j - 12/7 = 0. Calculate p.
-2, -1, 2
Let s(i) = 155*i**3 - 575*i**2 - 2130*i - 1655. Let c(f) = -11*f**3 + 41*f**2 + 152*f + 118. Let z(d) = 85*c(d) + 6*s(d). Find k such that z(k) = 0.
-2, -1, 10
What is y in 2/7*y + 0 - 4/7*y**3 + 2/7*y**5 + 0*y**4 + 0*y**2 = 0?
-1, 0, 1
Let o be (0 + -1 - 1)*-2. Suppose -p - 3*d = -10, o*p - 10 = 2*p - d. Factor -2*l + p*l + 6*l**3 + 0*l + l**3 - 9*l**2.
l*(l - 1)*(7*l - 2)
Let u(a) = -14*a**3 + 7*a**2 + 44*a - 37. Let r(q) = 12*q**3 - 8*q**2 - 40*q + 36. Let k(c) = -5*r(c) - 4*u(c). Factor k(w).
-4*(w - 4)*(w - 1)*(w + 2)
Let s be (-3 + 3)/(-3 + (-4)/(-2)). Suppose 0*q - 8*q**3 + 4*q**3 - q**2 + s*q = 0. What is q?
-1/4, 0
Let o = -3/2315 + 4639/6945. Find z such that o*z**2 - 2/3*z**5 + 0 + 2/3*z**3 + 0*z - 2/3*z**4 = 0.
-1, 0, 1
Let l = 94 + -83. Suppose 3*n = 1 + l. Factor -1/4*i + 1/4*i**n + 1/4*i**3 + 0 - 1/4*i**2.
i*(i - 1)*(i + 1)**2/4
Let q(u) be the second derivative of -u**8/560 - u**7/140 + u**5/20 + u**4/8 - 17*u**3/6 - 11*u. Let p(o) be the second derivative of q(o). Factor p(l).
-3*(l - 1)*(l + 1)**3
Let i = 213 + -213. Let w(o) be the second derivative of i*o**2 + 1/50*o**5 + 1/15*o**4 + 0 + 2*o - 1/5*o**3. What is t in w(t) = 0?
-3, 0, 1
Suppose -w = 13 - 15. Let -5*r**4 + 5*r**w + 1307*r**3 - 1307*r**3 = 0. Calculate r.
-1, 0, 1
Solve 12/5*s - 6*s**2 + 9/5*s**3 + 24/5 = 0.
-2/3, 2
Let y(g) be the second derivative of -2*g + 19/200*g**5 + 1/60*g**3 + 0 - 1/8*g**4 + 1/10*g**2 - 7/300*g**6. Find f, given that y(f) = 0.
-2/7, 1
Suppose a - 6 = -4*k + 11, -3*a = -15. Factor -24*w + 4*w**2 + 16 - 3*w**5 + 15*w**k - 3*w**4 - 4 - w**2.
-3*(w - 1)**3*(w + 2)**2
Let 36*d**4 - 120*d**3 - 16*d**2 - 259*d + 122*d + 108*d**5 + 169*d = 0. Calculate d.
-1, -2/3, 0, 2/3
Let l(w) be the second derivative of -9/2*w**2 + 1/2*w**3 - 3*w + 0 - 1/48*w**4. Let l(u) = 0. What is u?
6
Factor 21*b + 87/4 - 3/4*b**2.
-3*(b - 29)*(b + 1)/4
Let h = -60 + 63. Suppose 28 + 41*u - 9*u**h - 3*u**2 - 16 - 5*u = 0. Calculate u.
-2, -1/3, 2
Let g(s) be the third derivative of -1/75*s**5 + 5*s**2 - 2/15*s**3 + 4/525*s**7 + 0 + 0*s - 3/100*s**6 + 3/20*s**4. Determine l, given that g(l) = 0.
-1, 1/4, 1, 2
Let m(c) be the first derivative of -9/4*c**2 + 5/2*c**3 + 1/10*c**5 - 1 + 0*c - 7/8*c**4. Factor m(v).
v*(v - 3)**2*(v - 1)/2
Let f(o) = -o**2 + 3*o + 8. Let m(q) be the second derivative of q**3/2 + 9*q**2/2 + 11*q. Let h(t) = 3*f(t) - 2*m(t). Let h(p) = 0. Calculate p.
-1, 2
Let y(s) be the second derivative of -s**7/210 + s**6/75 + s**5/50 - 2*s**4/15 + 7*s**3/30 - s**2/5 - 66*s. Factor y(b).
-(b - 1)**4*(b + 2)/5
Let b(i) = -9*i**5 - 32*i**4 - 96*i**3 - 123*i**2 - 64*i. Let u(h) = 5*h**5 + 16*h**4 + 48*h**3 + 61*h**2 + 32*h. Let z(s) = -3*b(s) - 5*u(s). Factor z(f).
2*f*(f + 2)**4
Let g(f) be the third derivative of -f**6/270 + f**4/72 - f**3/54 + 118*f**2. Factor g(q).
-(q + 1)*(2*q - 1)**2/9
What is h in -1/2*h**4 - 59*h**2 - 81/2 - 10*h**3 - 90*h = 0?
-9, -1
Suppose 5*r = 24 - 14. Let h(i) = 3*i**2 - 5*i + 2. Let g be h(r). Find d such that 0 - 1/2*d**g + 0*d**2 - 1/4*d + 3/4*d**3 = 0.
-1/2, 0, 1
Suppose -255*u + 262*u - 28 = 0. Let p = -4 + 7. What is y in -y + u*y**p + 4*y**2 - 3*y + 0*y**2 - 4*y**4 = 0?
-1, 0, 1
Let f be (27/(-180))/(3/(-5)). Let n be (-4 - -1) + (39/(-4))/(-3). Determine v, given that -f*v + 0*v**2 + 0 + n*v**3 = 0.
-1, 0, 1
Let p(n) = -n**2 + 1. Let o(s) = s**3 - 3*s**2 - 4*s + 3. Let j be ((-10)/25)/(2/(-5)). Let t(i) = j*o(i) - 3*p(i). Let t(d) = 0. Calculate d.
-2, 0, 2
Let s(j) = -4*j - 53. Let m be s(-15). Let i(f) be the first derivative of 4/21*f**3 + m + 2/7*f**2 + 0*f. Factor i(v).
4*v*(v + 1)/7
Solve 28*b**5 + 58*b**3 - 156*b**4 - 78*b**5 - 8*b - 522*b**2 + 606*b**4 + 43 + 29 = 0 for b.
-1, -2/5, 2/5, 1, 9
Suppose -2*c = -5*h + 17, 4*c + 2*h = 17 + 9. Factor 9*m**4 - 75*m**2 - 13*m**c + 87*m**2 + 8*m.
-4*m*(m - 2)*(m + 1)**2
Suppose 4*u = 5*u + 3*f - 9, -5*u + 13 = -f. Determine l