r = 20/3 + q. Solve -2/3*y**3 + 0 + 4/9*y - 14/9*y**4 + r*y**2 - 2/3*y**5 = 0.
-1, 0, 2/3
Let w be 2072/814 - (-12)/(-22). Let p(o) be the first derivative of 4 - 1/12*o**3 + 1/2*o**w - 3/4*o. Factor p(h).
-(h - 3)*(h - 1)/4
Let b = 0 + -84. Let j be (-8)/b*28/6. Find y, given that 2/3*y + 2/3*y**4 - 4/9*y**2 - j*y**3 - 2/9*y**5 - 2/9 = 0.
-1, 1
Let n(a) be the third derivative of 0*a - 19/10*a**5 + 9/70*a**7 - 2*a**2 - 3/10*a**6 - 5/2*a**4 + 0 - 3/2*a**3. Factor n(y).
3*(y - 3)*(y + 1)*(3*y + 1)**2
Suppose 4*c + 3*d + 20 = 2*c, -3*c - 8 = -d. Let b be (24/(-7) - c) + 0. Factor -2/7*k - 2/7*k**3 + 0 - b*k**2.
-2*k*(k + 1)**2/7
Let i = -2335542/7 - -334266. Solve 1200/7*a**3 - 5184/7 + i*a**2 + 4320/7*a + 6/7*a**5 + 20*a**4 = 0 for a.
-6, 2/3
Let m be (8/(-2))/(-1 - 1). Suppose 0 = -2*j + 5*j - 6. Find g, given that 9*g - g**m - 2*g**j + g**2 - 5*g = 0.
0, 2
Let i(z) be the second derivative of -z**6/90 - 7*z**5/150 - z**4/15 - z**3/2 - 6*z. Let o(k) be the second derivative of i(k). Solve o(u) = 0 for u.
-1, -2/5
Let k = 2 - -1. Suppose 4 = 3*g - u, -5*u + 17 = -8. Solve w**3 + 3*w - k - 4*w**3 + g*w**2 + 0 = 0.
-1, 1
Let a(u) be the first derivative of -u**2 + 2/9*u**3 + 0*u - 5. Determine s so that a(s) = 0.
0, 3
Suppose 0 = 435*a - 328*a - 214. Factor 24/7 + 6/7*w**a + 48/7*w + 6/7*w**5 - 6/7*w**4 - 30/7*w**3.
6*(w - 2)**2*(w + 1)**3/7
Let k(f) = -70*f**3 + 125*f**2 + 1765*f + 1570. Let t(a) = -5*a**3 + 9*a**2 + 126*a + 112. Let d(l) = -4*k(l) + 55*t(l). Factor d(i).
5*(i - 6)*(i + 1)*(i + 4)
Let i(r) be the first derivative of 23 - 5/4*r**2 - 3*r + 1/4*r**4 + 1/2*r**3. What is y in i(y) = 0?
-2, -1, 3/2
Suppose -52*y - 81 + 185 = 0. Factor -3 + 5/3*c**y - 1/3*c**3 - c.
-(c - 3)**2*(c + 1)/3
Factor 227 + 91*d + 54 - 167*d + 4*d**2 - 1.
4*(d - 14)*(d - 5)
Let b(s) = -3215*s + 25720. Let v be b(8). Factor v*a + 4/5*a**2 - 2/5*a**4 + 0 - 2/5*a**3.
-2*a**2*(a - 1)*(a + 2)/5
Let f = -6816 + 6816. Factor 0*p**2 - 2/13*p**5 + f*p**4 + 4/13*p**3 + 0 - 2/13*p.
-2*p*(p - 1)**2*(p + 1)**2/13
Solve -98/3*z + 0 + 0*z**2 + 2/3*z**3 = 0.
-7, 0, 7
Suppose -4*t = 33 + 15. Let d be ((-10)/(-20))/(-1*3/t). Suppose 4/3*g - 4/3*g**d + 0 = 0. What is g?
0, 1
Let j(g) be the third derivative of 0*g**5 - 6*g**2 + 0*g + 1/60*g**6 - 1/210*g**7 + 0*g**3 + 0*g**4 + 0. Factor j(c).
-c**3*(c - 2)
Let t(g) be the first derivative of -g**6/6 + 3*g**4/4 + 2*g**3/3 - 466. What is v in t(v) = 0?
-1, 0, 2
Suppose 5*f - 2*d = -0 + 3, -2 = -3*f + d. Let b(t) be the first derivative of 1/7*t**3 - 6/7*t - 3/14*t**2 - f. Factor b(r).
3*(r - 2)*(r + 1)/7
Let n(h) be the first derivative of 3/2*h + 3/10*h**5 - 22 - 1/12*h**6 + 1/4*h**4 - h**3 - 1/4*h**2. Solve n(y) = 0 for y.
-1, 1, 3
Let y(g) be the first derivative of g**3/9 + 4*g**2/3 - 20*g/3 - 103. Factor y(q).
(q - 2)*(q + 10)/3
Let z(g) be the second derivative of 0*g**2 + 1/2*g**3 - 3/20*g**5 + 24*g - 1/30*g**6 + 1/12*g**4 + 0. Factor z(y).
-y*(y - 1)*(y + 1)*(y + 3)
Let v(c) be the second derivative of 8/15*c**6 + 2/21*c**7 + 6/5*c**5 - 22*c + 2/3*c**3 + 0 + 0*c**2 + 4/3*c**4. Factor v(h).
4*h*(h + 1)**4
Let z(m) be the second derivative of -70/3*m**3 + 11/3*m**4 - 2*m - 1/5*m**5 + 2 + 50*m**2. Factor z(x).
-4*(x - 5)**2*(x - 1)
Let b(o) = o**3 - 9*o**2 + 8*o + 9. Let g be b(8). Suppose -g*x = 1 - 19. Factor 0*s**x + 0 + 2/9*s - 2/9*s**3.
-2*s*(s - 1)*(s + 1)/9
Let w = -1045 - -1046. Let q(t) be the first derivative of -1/3*t**2 - 2/9*t**3 - w + 0*t. Let q(f) = 0. Calculate f.
-1, 0
Let c(g) be the third derivative of g**6/96 - 11*g**5/80 + g**4/4 - 3*g**3 + 12*g**2. Let b(f) be the first derivative of c(f). Factor b(m).
3*(m - 4)*(5*m - 2)/4
Let s(z) be the second derivative of -4*z**7/105 + z**6/25 + 17*z**5/50 - 2*z**4/5 - 4*z**3/15 - 5*z + 10. Determine j, given that s(j) = 0.
-2, -1/4, 0, 1, 2
Let t = -1901 - -9508/5. Find i such that t - 1/5*i**2 + 2/5*i = 0.
-1, 3
Factor 0 - 1/2*w**4 - 3/2*w**3 + 0*w - 5/6*w**2 + 1/6*w**5.
w**2*(w - 5)*(w + 1)**2/6
Let s be 3 + -5 - (42/(-70))/((-45)/(-350)). Factor -s*f - 7/6*f**2 - 1/6*f**3 - 2.
-(f + 2)**2*(f + 3)/6
Suppose 0*g - 33/2*g**2 - 15*g**3 + 3/2*g**4 + 0 = 0. Calculate g.
-1, 0, 11
Let x = 29 - 26. Let d be (4 - x) + -2*11/34. Factor 4/17 - d*s + 2/17*s**2.
2*(s - 2)*(s - 1)/17
Let j(p) be the first derivative of 3*p**4/16 - 5*p**3/4 - 39*p**2/8 - 21*p/4 + 37. Let j(d) = 0. Calculate d.
-1, 7
Let b(c) be the third derivative of -1/3*c**3 + 5/72*c**4 + 1/90*c**5 - 1/360*c**6 + 11*c**2 + 0*c + 0. Determine l so that b(l) = 0.
-2, 1, 3
Let w = -6832 - -6834. Factor 2/11*y**w + 8/11 - 10/11*y.
2*(y - 4)*(y - 1)/11
Suppose 95*u + 52*u - 778 + 190 = 0. Factor 2/11*l**u - 8/11*l + 0 - 10/11*l**3 + 16/11*l**2.
2*l*(l - 2)**2*(l - 1)/11
Suppose -5*d + 2*c = 0, -4*d = -8*d + c. Let 53*n**5 + 132*n**4 + 8*n**3 - 80*n + 19*n**5 - 16 - 116*n**2 + d = 0. What is n?
-1, -2/3, -1/2, 1
Factor 72 - 114/25*i**4 - 1056/5*i - 2/25*i**5 - 1446/25*i**3 + 5042/25*i**2.
-2*(i - 1)**3*(i + 30)**2/25
Let q = -53 + 81. Let v be -1*(-100)/q + -3. Suppose -4/7*k - v*k**2 - 1/7 = 0. Calculate k.
-1/2
Let i = 6 + -10. Let l(s) = s**2 + 5*s + 6. Let o be l(i). Factor 14*x + 6*x**o - 4*x**2 - 12*x.
2*x*(x + 1)
Let d be (8*1/1)/2. Let u be -1 + (-294)/(-234) - (-1)/13. Solve -y**2 - 1/3*y**d - u*y**5 + 5/3*y**3 + 0*y + 0 = 0 for y.
-3, 0, 1
Let g = 184 - 27599/150. Let u(r) be the third derivative of -1/30*r**4 + 0*r - 1/15*r**3 - g*r**5 - 3*r**2 + 0. Factor u(s).
-2*(s + 1)**2/5
Let p = 207 + -8693/42. Let i(s) be the third derivative of -1/42*s**5 - p*s**4 + 0 - 1/105*s**6 + 0*s - 2*s**2 + 0*s**3 - 1/735*s**7. Factor i(l).
-2*l*(l + 1)**2*(l + 2)/7
Let -3175 + 8*s**2 + 118*s - 4107 + 1207 - 11*s**2 + 152*s = 0. What is s?
45
Let r be (-12)/(-48)*((-33)/(-18) + (-9)/18). Factor 1/3*l - r*l**2 + 4.
-(l - 4)*(l + 3)/3
Suppose 5*p - 2*p + 5*f = 26, 5*f = 5*p + 10. Factor 25*t - 10*t**2 + 29*t**2 + 30 - 14*t**p.
5*(t + 2)*(t + 3)
Let o be 1474/616 - (-5)/20*-5. Factor 0 - o*y**3 - 4/7*y**2 + 4/7*y.
-4*y*(y + 1)*(2*y - 1)/7
Let x = 3/55 - -159/110. Let s(p) be the first derivative of p**3 + x*p**2 - 1 - 6*p. What is u in s(u) = 0?
-2, 1
Let 2*s + 2/11*s**3 + 0 + 24/11*s**2 = 0. What is s?
-11, -1, 0
Let a be 6/((-4)/(-56)*-3). Let h be 1/4 - 1/a. Let 0*m**2 + h*m + 0 - 2/7*m**3 = 0. Calculate m.
-1, 0, 1
Let t = -1914 - -13414/7. Factor -4/7*i**5 - 12/7*i**4 + 0 + t*i**2 + 0*i**3 + 0*i.
-4*i**2*(i - 1)*(i + 2)**2/7
Determine x so that 276*x**3 + 16*x**2 - 517*x**3 + 4*x**4 - 48*x + 269*x**3 = 0.
-6, -2, 0, 1
Let k be (120/54)/(-10) + (-2)/(-9). Let w(c) be the second derivative of k - 5*c - 1/4*c**2 + 1/48*c**4 - 1/24*c**3. Factor w(f).
(f - 2)*(f + 1)/4
Let o(x) = 3*x**2 + x - 6. Let d(w) = -17*w**2 - 6*w + 36. Suppose -72 = -2*g + q + q, 4*g - 153 = q. Let m(h) = g*o(h) + 6*d(h). Factor m(p).
3*(p - 1)*(5*p + 6)
Let c(g) be the third derivative of -g**6/320 - g**5/20 + 9*g**4/64 - 48*g**2 + 3. Let c(i) = 0. What is i?
-9, 0, 1
Let q(f) be the third derivative of -f**7/1260 + f**6/120 + 167*f**5/360 - 11*f**4/3 - 1936*f**3/9 + 477*f**2. Factor q(d).
-(d - 11)**2*(d + 8)**2/6
Suppose -159*z = -146*z. Let k(j) be the second derivative of -1/20*j**5 + 0*j**2 + z*j**3 + 1/12*j**4 + 3*j + 0. Factor k(a).
-a**2*(a - 1)
Let q be (-23)/10 - (4 - 9). Let x(r) be the first derivative of 4 + 1/6*r**3 + 0*r + 9/8*r**4 + 0*r**2 + 9/4*r**6 + q*r**5. Factor x(h).
h**2*(3*h + 1)**3/2
Let f(v) be the second derivative of v**6/1440 - v**5/240 - v**4/32 + 8*v**3/3 + 17*v. Let w(y) be the second derivative of f(y). Solve w(d) = 0 for d.
-1, 3
Suppose -24 = 4*b - 10*b. Let m(w) = w - 1. Let v be m(4). Let -l**3 - 2*l**b + 9*l**v - 2*l**2 - 4*l**3 = 0. Calculate l.
0, 1
Suppose -4*u + 102*g - 101*g = -16, -5*g - 4 = -u. Factor 3/2*x**5 + 9*x**u + 3 + 24*x**2 + 27/2*x + 21*x**3.
3*(x + 1)**4*(x + 2)/2
Let d(v) be the third derivative of 2*v**5/15 + 7*v**4/2 + 20*v**3/3 - 8*v**2. Factor d(z).
4*(z + 10)*(2*z + 1)
Let r = -1081/21 - -1032397/20055. Let t = 939/7640 + r. Suppose 1/8*s**2 - 1/8*s**4 + 0 - 1/8*s + t*s**3 = 0. What is s?
-1, 0, 1
Let u(h) = h**3 - 23*h**2 + 40*h + 45. Let a be u(21). Let m(o) be the first derivative of -7/6*o**a + o + 5/4*o**2 - 3. Factor m(p).
-(p - 1)*(7*p + 2)/2
Let d = -6/8869 + 15210/8869. Fin