- 1/3*u**3 + 1/3*u**4.
u**2*(u - 1)*(u + 1)**2/3
Let c = -90 + 92. Solve 116*q + 117*q - 6 + 3*q**c - 236*q = 0.
-1, 2
Suppose 6*y - 75 = -1023. Let j = -156 - y. Factor -3/2*u**j - 1/2 - 1/2*u**3 - 3/2*u.
-(u + 1)**3/2
Suppose 0 = -3*d + 12, -d = 2*n + 2*d - 20. Determine u, given that -3*u**3 + 8*u**4 + u**4 - 3*u**5 - 3*u**n = 0.
0, 1
Let o(j) = 16*j - 8. Let c be o(1). Suppose c - 44 = -12*m. Factor 0 - 1/4*u**m - 1/4*u - 1/2*u**2.
-u*(u + 1)**2/4
Let v(w) be the second derivative of -w**4/24 - 7*w**3/12 + 2*w**2 - 2*w + 3. Factor v(o).
-(o - 1)*(o + 8)/2
Let x(c) = 31*c + 2. Let i be x(-13). Let h = i + 2026/5. Let -9/5*q**2 + 0*q + 3/5*q**5 + 0 + h*q**3 - 3*q**4 = 0. Calculate q.
0, 1, 3
Suppose -174 + 40*z + 212 + 2*z**2 + 0*z**2 = 0. What is z?
-19, -1
Factor 4/13*h**2 - 18/13 - 6/13*h.
2*(h - 3)*(2*h + 3)/13
Let w be 2 - (13/((-260)/112) - -7). Determine t, given that w*t + 4/5 - 1/5*t**2 = 0.
-1, 4
Suppose 71*u - 34*u = 74. Factor 7/3*f + 0 - 1/3*f**u.
-f*(f - 7)/3
Let j(q) be the first derivative of 5*q**4/24 + 5*q**3/3 - 20*q**2/3 + 118. Factor j(c).
5*c*(c - 2)*(c + 8)/6
Let w be (-5)/10*-5 - 13/(-26). Let i(k) be the second derivative of 0 + 8*k + 0*k**w + 1/20*k**5 + 0*k**4 + 0*k**2. Factor i(m).
m**3
Suppose -4 + 140*t + 289*t**2 - 11*t**5 - 635*t**2 + t**5 + 112*t**4 - 12 + 142*t**3 - 22*t**5 = 0. What is t?
-2, 1/4, 1, 4
Let s be 288/(-162) - (-4)/18. Let t = s + 55/18. Factor 1 - 3/2*u**3 + t*u - 1/2*u**4 - 1/2*u**2.
-(u - 1)*(u + 1)**2*(u + 2)/2
Let m(z) be the second derivative of -80*z**7/7 - 2*z**6/3 + 7*z**5 - 145*z**4/48 + 5*z**3/12 - 2*z + 365. What is f in m(f) = 0?
-2/3, 0, 1/8, 1/4
Let i = -249/31 + 2801/341. Factor 2/11*p - i*p**4 + 2/11*p**2 - 2/11*p**3 + 0.
-2*p*(p - 1)*(p + 1)**2/11
Suppose -8*y + 15 = -25. Suppose 2*m - 3*m**2 - 2*m**y - 3*m**2 + 4*m**4 + 2*m**2 = 0. Calculate m.
-1, 0, 1
Let y = 16 + -6. Suppose -s + 15 = 5*v, 3*s - y - 5 = -5*v. Factor 3*h**3 + 2*h**5 - v*h**5 + 4*h**2 - 16 + 12*h**2 - 3*h**4 + h**3.
-(h - 2)*(h - 1)*(h + 2)**3
Let -52/3*p + 12 - p**2 = 0. What is p?
-18, 2/3
Let z(h) = -3*h**3 + 13*h**2 - 18*h - 4. Let t(v) = -15*v**3 + 64*v**2 - 90*v - 22. Let l(a) = 2*t(a) - 11*z(a). Factor l(x).
3*x*(x - 3)*(x - 2)
Let j(w) be the third derivative of -w**11/887040 + w**9/161280 + 7*w**5/60 - 4*w**2. Let b(d) be the third derivative of j(d). Let b(i) = 0. What is i?
-1, 0, 1
Let o(m) be the first derivative of 14 + 32/9*m - 8/9*m**2 + 5/9*m**4 - 4/45*m**5 - 8/9*m**3. Suppose o(h) = 0. Calculate h.
-1, 2
Factor -37/2*g**4 + 0 + 0*g - g**5 + 19/2*g**3 + 0*g**2.
-g**3*(g + 19)*(2*g - 1)/2
Let y(x) be the third derivative of x**6/120 + 2*x**5/15 + 2*x**4/3 - 99*x**2. Determine m so that y(m) = 0.
-4, 0
Let j = -26306 - -131531/5. Factor 7/5*m + 0 + j*m**2.
m*(m + 7)/5
Suppose 10*b**3 + 35/2*b**2 + 0 - 5*b = 0. What is b?
-2, 0, 1/4
Let z(y) = -y**3 - 6*y**2 - 7*y + 5. Let u be z(-6). Suppose 119*l**2 - u*l**2 - 77*l + 103*l**2 + 40 - 113*l = 0. Calculate l.
2/7, 4/5
Let l(f) = -6*f**2 + 13*f**2 + 3*f + 0*f - 11 - 4*f**2. Let n(y) = 8*y**2 + 10*y - 32. Let v(m) = -14*l(m) + 5*n(m). Let v(g) = 0. What is g?
1, 3
Factor m**5 - 4817 - 31*m + 4897 - 10*m**4 + 20*m**3 - 65*m + m**4 + 16*m**2.
(m - 5)*(m - 2)**3*(m + 2)
Let a(v) be the first derivative of -192*v + 50 - 256/3*v**3 + 288*v**2 + 92/9*v**4 - 4/9*v**5. Let a(l) = 0. What is l?
2/5, 6
Let n = -8836 + 8839. Suppose 0*m**n - 2/15*m**4 - 4/15*m + 0 + 2/5*m**2 = 0. What is m?
-2, 0, 1
Let w(z) = -z**2 - 2. Let c(i) = 5*i**2 + 11. Let t(d) = 8*d + 10. Let h be t(-2). Let l(m) = h*c(m) - 33*w(m). Factor l(s).
3*s**2
Let g(o) be the second derivative of -1/18*o**3 + 1/36*o**4 + 0 + 0*o**2 + 3*o. Suppose g(a) = 0. What is a?
0, 1
Let a(l) be the third derivative of 0*l + 0 + 23*l**2 + 4/27*l**3 - 1/270*l**5 + 1/36*l**4. Factor a(s).
-2*(s - 4)*(s + 1)/9
Let z be 1/3 - 6/36*-6. Let a(o) be the first derivative of 2*o**2 - z*o**3 + 3 + 4*o - o**4. Factor a(y).
-4*(y - 1)*(y + 1)**2
Suppose -16 = 7*r - 15*r. Suppose 0 = -4*s - 4*y + 4, -5*s + 5*y = r*y - 13. Solve 1/2*i + 0*i**3 - i**4 + 0 - 1/2*i**5 + i**s = 0 for i.
-1, 0, 1
Suppose 5*l = -2*z - 1 - 2, 12 = -4*l - 4*z. Let h be l - 3/((-36)/(-8)). Factor 0*g + 2/3*g**2 + 0*g**3 - h - 1/3*g**4.
-(g - 1)**2*(g + 1)**2/3
Factor -14/5*g**2 - 2/5 + 2*g + 6/5*g**3.
2*(g - 1)**2*(3*g - 1)/5
Let o be (1 + 0)/(7 + 120/(-18)). Let j = 10 - -1. Factor 4*c**o - j*c + 0*c + 7*c.
4*c*(c - 1)*(c + 1)
Let k(d) be the second derivative of d**5/30 + 17*d**4/18 + 10*d**3/3 - 103*d - 1. Factor k(b).
2*b*(b + 2)*(b + 15)/3
Let p(t) be the first derivative of -t**5/20 - t**4/8 + 9*t**3/4 - 13*t**2/2 + 7*t + 197. Let p(y) = 0. What is y?
-7, 1, 2
Suppose 4*g - 20 = -3*i, 4*i = 3*g - 18 + 3. Find p such that 5*p**2 + g*p**2 + 17*p**3 + 2*p**2 - 20*p**3 = 0.
0, 4
Let t(z) = 11*z**2 - 29*z. Let w(p) = -5*p**2 + 15*p. Suppose -r - 4 = o, -2*r = r - 9. Let k(u) = o*w(u) - 3*t(u). Find y, given that k(y) = 0.
0, 9
Let s be (-2)/(-11) - 20/(-11). Let o(b) = -5*b**2 + 12*b + 13. Let l(q) = 5*q**2 - 13*q - 12. Let i(n) = s*l(n) + 3*o(n). Suppose i(d) = 0. What is d?
-1, 3
Suppose 5*r + 2*s = 3*s + 7, -2*r + 13 = 3*s. Let 6*z**4 + 50*z**3 - r*z**4 - 4*z**5 - 42*z**3 = 0. What is z?
-1, 0, 2
Suppose -30/11*x - 2/11*x**3 + 14/11*x**2 + 18/11 = 0. What is x?
1, 3
Let s = 1939 + -1936. Factor -1/3*w**4 + 2/3*w + 0 + 1/3*w**2 - 2/3*w**s.
-w*(w - 1)*(w + 1)*(w + 2)/3
Let c be ((-456)/95)/((-6)/(-40)). Let h be -3*(3 + (0 - c/(-10))). Find d, given that h*d + 3/5*d**2 - 6/5 = 0.
-2, 1
Let i = 8687 - 17373/2. Suppose -i*v**3 - 21/2*v + 9 + 4*v**2 = 0. Calculate v.
2, 3
Let j be (-2 - 80)/(20/(-6) - -4). Let k = -364/3 - j. Let k*q**2 - 1/3*q**3 - q - 3 = 0. Calculate q.
-1, 3
Let l(h) = h**3 - 2*h**2 - 9*h + 18. Let g be l(3). Let z(i) be the second derivative of -6*i + g + 1/2*i**3 - 1/12*i**4 + 0*i**2. Find q, given that z(q) = 0.
0, 3
Factor -296/5 - 156/5*c - 4/5*c**2.
-4*(c + 2)*(c + 37)/5
Let l(t) = -5*t**3 - 99*t**2 + 2505*t - 2401. Let m(c) = 14*c**3 + 297*c**2 - 7514*c + 7203. Let p(k) = -17*l(k) - 6*m(k). Solve p(w) = 0.
1, 49
Let d(i) be the second derivative of i**6/120 - i**5/80 - i**4/3 - 5*i**3/6 - 6*i + 18. Solve d(o) = 0.
-2, 0, 5
Let a(q) be the first derivative of -q**5/30 + 2*q**3/9 - 227. Determine p so that a(p) = 0.
-2, 0, 2
Let m be 3 + (-11)/(-6 + -5). What is z in 0 + 0*z**2 + 0*z + 1/3*z**3 + 0*z**m - 1/3*z**5 = 0?
-1, 0, 1
Let i be (126/(-105))/(6/(-15)). Let z(o) be the second derivative of i*o**3 + 0 + 1/4*o**4 + 27/2*o**2 - 2*o. Factor z(c).
3*(c + 3)**2
Suppose 13 = w + 25. Let c(t) = -t**2 - 13*t - 12. Let p be c(w). Solve -7*q + p + 6*q**3 + q - 3 + 3*q**4 = 0.
-1, 1
Let t(u) be the second derivative of -1/3*u**4 + 0 - 1/10*u**5 + 0*u**2 - 17*u - 1/3*u**3. Factor t(j).
-2*j*(j + 1)**2
Let y(x) = x**2 - 8*x - 18. Let u be y(10). Factor 11*a**u - 2*a + 5*a**3 - 4 - 3*a + 4*a**2 - 11.
5*(a - 1)*(a + 1)*(a + 3)
Factor 24*p**2 + 25*p**2 - 208*p + 2704 - 66*p**2 + 21*p**2.
4*(p - 26)**2
Factor 60 + 18 - 17*r**2 - 192*r - 3*r**2 + 2 + 0*r**2.
-4*(r + 10)*(5*r - 2)
Suppose -i + j - 5*j + 6 = 0, -3*i - 2*j + 8 = 0. Factor m**4 - 36*m - m**i + m**3 + 20*m + 15*m.
m*(m - 1)*(m + 1)**2
Let s(c) be the third derivative of -5*c**5/12 - 55*c**4/24 - 5*c**3/3 - 483*c**2. Factor s(i).
-5*(i + 2)*(5*i + 1)
Factor -512 + 11*d**5 - 200*d**2 - 82*d + 484*d + 10*d**4 - 10*d**5 + 238*d - 20*d**3.
(d - 2)**3*(d + 8)**2
Suppose -4*s - 19 - 1 = -4*v, 0 = -s + 3*v - 15. Let l be -2*1 - (-7 - -2). Factor 6*b**2 + 0*b + s*b**l - 12 - 3/4*b**4.
-3*(b - 2)**2*(b + 2)**2/4
Let o be 2/4 - 28/120. Let w(b) be the first derivative of 4/25*b**5 + 0*b + 0*b**4 + 1/5*b**2 - 1/15*b**6 + 3 - o*b**3. Solve w(a) = 0.
-1, 0, 1
Let b(c) be the third derivative of c**5/12 + 35*c**4/2 + 1470*c**3 + 100*c**2. Solve b(v) = 0 for v.
-42
Let n be (2 - 1)/(-81)*(-249)/166. Let y(h) be the third derivative of -1/270*h**6 - 5*h**2 + 0 + 0*h**3 + 0*h + 0*h**5 + n*h**4. Determine s so that y(s) = 0.
-1, 0, 1
Let d be 2/(-7)*20 + (-8)/28. Let u be ((-3)/2)/(-1*(-3)/d). Suppose 0*b**2 + 0 + 1/4*b + 0*b**4 + 1/4*b**5 - 1/2*b**u = 0. Calculate b.
-1, 0, 1
Let l be (64/12)/((-2)/(-33)). Factor -3*y**4 + 7*y**4 - 1143*y**3 - 96*y + l*y**2 + 1111*y**3 + 36.
4*