/33 - 5*u**3/33 - u**2/11 - 11*u. Factor p(x).
-2*(x + 1)**5/11
Let i = 39 - 24. Let h = 33/2 - i. Find m such that -1/2*m**2 + h*m - 1 = 0.
1, 2
Let t be ((-36)/(-30))/(2/15). Let 16*g**2 + t*g**3 + 5*g - 5*g - 2*g - 2*g = 0. Calculate g.
-2, 0, 2/9
Let z(k) be the third derivative of k**8/21 + 6*k**7/35 + k**6/5 + k**5/15 + 36*k**2. Suppose z(l) = 0. What is l?
-1, -1/4, 0
Let d(l) be the first derivative of 0*l + 0*l**2 + 1/12*l**3 + 1/24*l**6 - 1/20*l**5 - 1/16*l**4 + 2. Factor d(k).
k**2*(k - 1)**2*(k + 1)/4
Let g(q) = q**3 - 18*q**2 - q + 19. Let l be g(18). Let p(v) be the first derivative of -l + 0*v - 1/15*v**3 + 1/10*v**2. Factor p(k).
-k*(k - 1)/5
Let l(p) be the third derivative of 0 + 1/9*p**3 + 1/45*p**5 - 8*p**2 - 1/360*p**6 + 0*p - 5/72*p**4. Factor l(q).
-(q - 2)*(q - 1)**2/3
Let h(c) be the second derivative of 0 - 7*c + 2/3*c**2 - 1/18*c**4 + 1/9*c**3. Factor h(y).
-2*(y - 2)*(y + 1)/3
Let n(w) be the second derivative of w**7/42 + 11*w**6/15 + 19*w**5/2 + 200*w**4/3 + 1625*w**3/6 + 625*w**2 - 44*w. Factor n(m).
(m + 2)*(m + 5)**4
Let l(r) be the third derivative of 0*r - 3*r**2 + 0 + 0*r**5 + 0*r**3 + 1/120*r**6 - 1/24*r**4. Suppose l(j) = 0. What is j?
-1, 0, 1
Let g(y) be the third derivative of -y**5/60 - y**4/6 - 2*y**3/3 + 23*y**2. Suppose g(a) = 0. What is a?
-2
Factor 8*l + 14 + 2*l**4 + 4*l**4 - 2*l**4 - 8*l**3 - 18.
4*(l - 1)**3*(l + 1)
Let z(r) be the third derivative of -r**7/35 - r**6/6 - 7*r**5/30 + r**4/3 + 4*r**3/3 + 6*r**2. Determine k so that z(k) = 0.
-2, -1, 2/3
Let q(r) be the third derivative of 5*r**8/336 - 5*r**6/12 + 5*r**5/3 - 25*r**4/8 + 10*r**3/3 + 31*r**2. Solve q(v) = 0 for v.
-4, 1
Let a = -143 + 17. Let h = a + 519/4. Factor 4*k**4 - h*k**2 + 0 + 1/2*k + 6*k**3.
k*(k + 2)*(4*k - 1)**2/4
Factor 8/5*z**2 + 0*z**3 - 4/5*z + 0 - 8/5*z**4 + 4/5*z**5.
4*z*(z - 1)**3*(z + 1)/5
Let m(i) = i**4 + i**3 - i**2 - i. Let p(t) = -7*t**4 - 4*t**3 + 4*t**2 + 4*t. Let g(q) = 4*m(q) + p(q). Solve g(c) = 0.
0
Let t(q) be the third derivative of -q**5/360 - q**4/144 + q**3/18 + 3*q**2. Solve t(w) = 0 for w.
-2, 1
Suppose -5*s + 6 = -2*j, 5*s - j = -0*j + 8. Let c = 4 - s. Factor 1/2*a**3 + 1/2*a**c - 1/2*a**4 - 1/2*a + 0.
-a*(a - 1)**2*(a + 1)/2
Let f be (-32)/15*3/(-4). Let r be (-10)/35 - (-60)/14. Solve 24/5*w + f + 2/5*w**r + 26/5*w**2 + 12/5*w**3 = 0.
-2, -1
Let j(u) = -u - 7. Let v be j(-8). Let x be (0 - (v + -1))/(-1). Suppose x - 1/3*d**4 - d**2 - 1/3*d - d**3 = 0. Calculate d.
-1, 0
Let w = 3289/9 + -365. Determine r, given that 14/9*r**3 - w*r**4 + 10/9*r - 2*r**2 - 2/9 = 0.
1/2, 1
Let o be (1/(-25))/(-3*1). Let y(i) be the second derivative of -2/5*i**2 + 1/10*i**5 - o*i**6 + 4*i + 7/15*i**3 - 3/10*i**4 + 0. Factor y(a).
-2*(a - 2)*(a - 1)**3/5
Let o = 15 - 13. Let p(b) be the first derivative of -1/12*b**4 + 0*b**2 + 0*b + o - 1/9*b**3. Factor p(y).
-y**2*(y + 1)/3
Solve -229*h**4 + 214*h**4 - 6 + 5*h**5 + 6 = 0.
0, 3
Determine z, given that 4/5*z**3 - z**2 + 2/5*z + 0 - 1/5*z**4 = 0.
0, 1, 2
Suppose 4*x = 5*x - 3. Determine q so that -4*q**5 - q + 8*q**3 - x*q + 0*q**5 = 0.
-1, 0, 1
Let w = 54 + -51. Solve -d**w + 0 + 0*d**4 + 1/2*d + 1/2*d**5 + 0*d**2 = 0 for d.
-1, 0, 1
Let q be (((-48)/6)/32)/((-22)/32). What is j in -q + 6/11*j**2 + 10/11*j = 0?
-2, 1/3
Suppose 2 = 8*m - 7*m. Factor -2/11*k**4 + 8/11*k + 8/11*k**3 - 2/11 - 12/11*k**m.
-2*(k - 1)**4/11
Let p(m) be the first derivative of -m**4/2 - 2*m**3/3 + 5*m**2 - 6*m + 6. Suppose p(a) = 0. Calculate a.
-3, 1
Let j(l) = l**3 + 6*l**2 + 5*l + 4. Let z be j(-5). Let x = z + -2. Factor -3*k**4 - 4*k**x + 3*k**2 + 4*k**4.
k**2*(k - 1)*(k + 1)
Let k(h) = h - 14. Let o be k(14). Find t, given that o*t + 0 - 3/5*t**5 + 0*t**4 + 0*t**2 + 3/5*t**3 = 0.
-1, 0, 1
Let d(n) be the second derivative of -9*n + 1/105*n**6 + 0*n**3 + 0 - 1/70*n**5 + 0*n**2 - 1/21*n**4. Factor d(y).
2*y**2*(y - 2)*(y + 1)/7
Let l(h) be the third derivative of h**5/30 - 4*h**4/3 + 64*h**3/3 + 15*h**2. Determine f, given that l(f) = 0.
8
Let u(k) be the third derivative of -1/30*k**5 + 1/60*k**6 - 3*k**2 + 1/3*k**3 + 0*k + 0 - 1/12*k**4. Determine t, given that u(t) = 0.
-1, 1
Let r be 2/3 + 6/(-9). Let q(z) be the first derivative of 2*z - 3 + 3*z**2 + z - 4*z**3 + r*z + 5*z**3. Factor q(u).
3*(u + 1)**2
Let k be (-28)/(-6) - 2/(-6). Let w(a) = a**2 - 5*a + 4. Let s be w(4). What is o in -o**2 + 7*o + s + 0 - k*o = 0?
0, 2
Factor -25/6*t - 2/3*t**3 + 14/3*t**2 + 1.
-(t - 6)*(2*t - 1)**2/6
Factor -1/2*h**5 - 3*h**3 + 2*h**2 + 2*h**4 + 0 - 1/2*h.
-h*(h - 1)**4/2
Let l(y) be the third derivative of y**6/840 + y**5/210 + 2*y**2. Let l(f) = 0. Calculate f.
-2, 0
Let d(f) be the third derivative of f**8/2240 + f**7/280 + f**6/80 + f**5/40 + 5*f**4/24 - 4*f**2. Let c(n) be the second derivative of d(n). Factor c(b).
3*(b + 1)**3
Find d such that 0 + 0*d - 2/3*d**3 - 2/3*d**2 = 0.
-1, 0
Let c be (-4)/2*30/(-84). Let m = c - 8/21. Factor 0*g + m*g**2 - 1/3.
(g - 1)*(g + 1)/3
Suppose -k - 5 = w + 3*w, 4*w = 2*k - 14. Let 20 - 18*p + 8 + k*p**2 - 1 = 0. Calculate p.
3
Let w be (-16)/(-6) + (-42)/63. Suppose -1/5 + 0*v + 1/5*v**w = 0. Calculate v.
-1, 1
Let b(r) be the second derivative of r**7/13860 + r**6/990 + r**5/165 - r**4/6 - 3*r. Let c(l) be the third derivative of b(l). Factor c(o).
2*(o + 2)**2/11
Let v be -6*(-15)/220*(-12)/(-9). What is u in 4/11 + v*u + 2/11*u**2 = 0?
-2, -1
Determine m so that -6/7*m**2 - 4/7*m - 2/7*m**3 + 0 = 0.
-2, -1, 0
Let p(j) be the third derivative of j**8/1176 + j**7/147 + j**6/42 + j**5/21 + 5*j**4/84 + j**3/21 + 2*j**2. Factor p(f).
2*(f + 1)**5/7
Let u(f) be the third derivative of -3*f**2 + 0 + 0*f + 1/3*f**3 + 1/5*f**5 + 3/8*f**4 + 1/24*f**6. Factor u(i).
(i + 1)**2*(5*i + 2)
Let d(n) be the first derivative of 2*n**3/9 - n**2/3 - 1. Factor d(u).
2*u*(u - 1)/3
Let q = 1198061/694824 - -5/53448. Let k = 1/39 + q. Factor 1/2 + 5/4*n - k*n**2.
-(n - 1)*(7*n + 2)/4
Let j(c) be the third derivative of c**5/330 + c**4/33 + 4*c**3/33 + 3*c**2. Let j(b) = 0. What is b?
-2
Suppose 3*f - 4*c - 29 = 0, -2*f + c + 2 = -9. Let j = -1 + f. Determine g, given that 4*g - 2*g**j - 35*g**3 + g**2 - 3*g**2 + 0*g = 0.
-2/5, 0, 2/7
Solve -1/4 + 1/2*y - 1/4*y**2 = 0 for y.
1
Suppose 0 = 5*k + 3*w - 25, 2*k + 3*k - 15 = -w. Factor -5 - 2*y**3 + 6*y**2 + 1 - k*y**4 + 4*y + 3*y - 5*y.
-2*(y - 1)**2*(y + 1)*(y + 2)
Let g(u) be the third derivative of 0 - 1/6*u**4 + 2/3*u**3 + 0*u + u**2 + 1/60*u**5. Determine r so that g(r) = 0.
2
Factor -19 - 13 + 44*v - 8 - 4*v**2.
-4*(v - 10)*(v - 1)
Let v be (-27)/(-6) - (-6 - -4). Let g = v + -6. Factor -1/2*x**2 + 0*x + g.
-(x - 1)*(x + 1)/2
Suppose -2*p - 14 = -4*q, -4*p - 1 - 3 = 0. Solve -c**2 + 2*c**4 + 2*c**5 - c**2 - 2*c**q + 0*c**4 + 0*c**2 = 0 for c.
-1, 0, 1
Let r be ((-12)/18)/(1/(-3)). Let x = -5 - -7. Factor x*u + 2 + u**r - 1 - 1.
u*(u + 2)
Let x = 4 + -6. Let c be (-14*(-2)/(-2))/x. Solve 1 - c*b**5 - 15*b - 40*b**2 - 30*b**4 - 4 + 1 - 50*b**3 = 0 for b.
-1, -2/7
Let w(k) be the second derivative of -k**5/3 + 23*k**4/36 - k**3/18 - k**2/3 - 26*k. Let w(q) = 0. Calculate q.
-1/4, 2/5, 1
Suppose -d - 6 = -8. Factor 126*r**d - 39 + 113*r**3 - 15*r**3 + 30*r + 41.
2*(r + 1)*(7*r + 1)**2
Let d be 2/9 + (-7810)/99. Let g = d + 80. What is n in 0 + 2/3*n + 2/3*n**3 - g*n**2 = 0?
0, 1
Suppose -3*c - 3*k - 2 = 4, -c + 3*k + 14 = 0. Factor 3/7 + 6/7*y**c - 1/7*y**4 + 8/7*y + 0*y**3.
-(y - 3)*(y + 1)**3/7
Let t(w) be the second derivative of -w**10/45360 - w**9/22680 + w**8/10080 + w**7/3780 - 2*w**4/3 + 4*w. Let r(v) be the third derivative of t(v). Factor r(d).
-2*d**2*(d - 1)*(d + 1)**2/3
Let v(a) be the second derivative of -a**7/210 - a**6/150 + 3*a**5/100 + a**4/12 + a**3/15 + 29*a. What is l in v(l) = 0?
-1, 0, 2
Let j = -8 - -11. Suppose r**2 + 5*r**5 - r**5 - r**3 - j*r**5 - r**4 = 0. What is r?
-1, 0, 1
Let n(w) be the second derivative of w + 0 + 1/24*w**3 + 1/24*w**4 - 1/80*w**5 - 1/4*w**2. Find p such that n(p) = 0.
-1, 1, 2
Let h be ((-3)/36)/(4/20)*-4. Factor 10/3*p**2 + 1/3 + 5/3*p + 1/3*p**5 + 10/3*p**3 + h*p**4.
(p + 1)**5/3
Let a(z) be the first derivative of z**3/5 - 3*z**2 + 15*z + 7. Solve a(q) = 0.
5
Factor -408*s - 16 - 1261*s**3 - 1113*s**2 - 8565*s**3 + 110*s**2 - 2465*s**2.
-2*(17*s + 2)**3
Let c(w