d.
2*d**3*(d + 1)/7
Let g be 53/3 - (-24)/(-36). Suppose -3*u = -4*p + 7, -p + g = 3*u + p. Factor 6*w**4 + u*w**4 - 2*w**3 - 8*w**5 + w**4.
-2*w**3*(w - 1)*(4*w - 1)
Let p = -1742 + 1744. Suppose 0*q + 2/9*q**3 + 0*q**p + 0 = 0. What is q?
0
Let g(f) be the first derivative of -f**3/6 - 38*f**2 - 2888*f - 161. Factor g(b).
-(b + 76)**2/2
Suppose -12 = -3*i, -i = u - 0*i - 4. Let r be ((-2)/(-4))/((-2)/(-6)). Let -r*l**2 - 1/2*l + u = 0. What is l?
-1/3, 0
Let v = 9 + -11. Let o be (-4)/v + 2 - 2. Factor 1/5*u**o - 2/5*u + 1/5.
(u - 1)**2/5
Let d = -2239 - -2244. Let r(g) be the third derivative of 0*g**6 + 0*g**d + 0*g + 4*g**2 + 0*g**3 + 0*g**4 + 0 - 1/70*g**7. Determine w, given that r(w) = 0.
0
Let v(h) be the first derivative of 3/10*h**4 + 2/25*h**5 + 0*h + 1/5*h**2 + 17 + 2/5*h**3. Let v(j) = 0. What is j?
-1, 0
Let x(h) = h**3 + 15*h**2 - 16*h + 14. Let s be x(-16). Suppose s*l - 9*l = 20. Suppose 2/9*a**3 + 0 + 2/9*a**5 + 4/9*a**l + 0*a + 0*a**2 = 0. Calculate a.
-1, 0
Let u(r) = 10*r - 30. Let g be u(3). Let n(l) be the second derivative of 3/5*l**6 + 2*l**3 + 3*l + 0*l**2 + 1/14*l**7 + 39/20*l**5 + 3*l**4 + g. Factor n(y).
3*y*(y + 1)**2*(y + 2)**2
Let l be (-63)/(-27) - (0 - -1). Let v(g) be the first derivative of l*g**3 + 0*g - 3 + 2*g**2. Solve v(f) = 0.
-1, 0
Let o = 4 + -1. Factor 5*j**2 + 3*j**3 - 7*j**3 + 9*j**o.
5*j**2*(j + 1)
Let i(d) be the third derivative of 1/60*d**6 - 1/30*d**5 + 0*d**3 + 0 + 0*d**4 + 0*d - 33*d**2. Factor i(g).
2*g**2*(g - 1)
Let r be 0 - 2 - ((-27)/7 - -1). Let q(o) be the second derivative of -r*o**2 + 1/14*o**4 - 2*o + 0 - 1/3*o**3. Factor q(x).
2*(x - 3)*(3*x + 2)/7
Let x(k) be the third derivative of k**8/1344 + 5*k**7/168 + 167*k**6/480 + 119*k**5/240 - 7*k**4/4 - 6*k**3 - 74*k**2. Solve x(p) = 0 for p.
-12, -1, 1
Let x = -17 + 23. Suppose -8 = -10*u + x*u. Determine j, given that -j**u + 3*j**2 + j**2 + 6*j - 16 + 19 = 0.
-1
Let b(k) be the first derivative of -3/20*k**4 - 9/5*k + 3/5*k**3 - 6 + 3/10*k**2. Factor b(c).
-3*(c - 3)*(c - 1)*(c + 1)/5
Suppose 18818 - 194*a + 1/2*a**2 = 0. Calculate a.
194
Let p(s) be the second derivative of s**8/33600 - s**6/900 + s**4 - 42*s. Let r(h) be the third derivative of p(h). Suppose r(k) = 0. Calculate k.
-2, 0, 2
Let t(i) be the third derivative of 0*i - 1/27*i**4 - 11*i**2 + 0 - 1/540*i**5 - 8/27*i**3. Factor t(m).
-(m + 4)**2/9
Suppose -5*p - 349 = -384. Let j(g) be the third derivative of 0*g**4 + 1/105*g**6 + 0*g**3 + 1/735*g**p + 0*g - g**2 + 0 + 2/105*g**5. Factor j(t).
2*t**2*(t + 2)**2/7
Suppose -12*n + 78 = -666. Suppose n*k + 8 = 66*k. Solve 175/4*v**4 - 2*v + 17*v**k - 49/4*v**5 - 93/2*v**3 + 0 = 0.
0, 2/7, 1, 2
Let c(p) be the first derivative of 4/5*p**5 - 4/3*p**3 + 23 - 2*p**4 + 4*p**2 + 0*p. Factor c(b).
4*b*(b - 2)*(b - 1)*(b + 1)
Suppose -d - 15 = -3*n + 2*d, -5*n + 15 = -3*d. Suppose 0 = 2*k - 2*v - 4, n = -3*v - 4 + 7. Factor -1/4*r**k - 2 - 3*r - 3/2*r**2.
-(r + 2)**3/4
Let r(l) be the first derivative of -36/25*l**5 + 0*l + 2/5*l**3 - 3 - 9/20*l**4 - 7/10*l**6 + 0*l**2. Determine z so that r(z) = 0.
-1, 0, 2/7
Let d(h) be the first derivative of 2*h**6/21 + 4*h**5/5 + 15*h**4/7 + 52*h**3/21 + 8*h**2/7 + 94. Factor d(x).
4*x*(x + 1)**3*(x + 4)/7
Let d(a) = -8*a**2 - 201*a. Let x(w) = -12*w**2 - 200*w. Let u(p) = 4*d(p) - 3*x(p). Find t such that u(t) = 0.
0, 51
Let z(f) = f**2 + 11*f - 9. Let h(y) = 5*y**2 + 43*y - 36. Let u(a) = -2*h(a) + 9*z(a). Let t be u(12). Solve -23/5*n + 4/5 - 28/5*n**t + 44/5*n**2 = 0.
1/2, 4/7
Suppose 5*f + 10 = 0, -2*w - 13 = -3*f + 1. Let m be 24/(-36)*6/w. Determine k, given that m*k**2 - 2/5*k + 0 = 0.
0, 1
Let v(n) be the second derivative of -n**4/42 + 16*n**3/21 - 15*n**2/7 + 24*n. Factor v(i).
-2*(i - 15)*(i - 1)/7
Let u(i) = 2*i**2 - 17*i - 171. Let f be u(-6). Suppose -3*m**2 - 3/2 + 4*m + 0*m**f + 1/2*m**4 = 0. What is m?
-3, 1
Let r(o) be the second derivative of -4/135*o**6 + 15*o + 0*o**2 + 0 + 1/54*o**4 + 0*o**3 + 1/30*o**5. What is q in r(q) = 0?
-1/4, 0, 1
Let y(o) be the second derivative of -9/2*o**2 + 0 + 1/4*o**4 - o**3 + 19*o. Factor y(a).
3*(a - 3)*(a + 1)
Factor -8*t**2 - 2*t + 47*t + 3*t**2 - 10*t + 150.
-5*(t - 10)*(t + 3)
Let a(c) = 2*c - 6. Let q be a(5). Let x be 2 - (-4)/(q + 0). Suppose -32/5*y**4 + 0*y - 4/5*y**2 - 22/5*y**x + 0 - 14/5*y**5 = 0. What is y?
-1, -2/7, 0
Let j(c) be the first derivative of 9*c**6/11 - 174*c**5/55 - 171*c**4/22 + 298*c**3/11 + 36*c**2 - 216*c/11 - 62. Let j(r) = 0. What is r?
-2, -1, 2/9, 3
Let d(t) be the third derivative of -t**6/48 - t**5/8 + 5*t**4/8 + 10*t**3/3 - 7*t**2. Let d(j) = 0. What is j?
-4, -1, 2
Let n = -6995/2 - -3508. Factor -45/2*h**2 - 27/2*h - n*h**3 - 3/2*h**4 + 0.
-3*h*(h + 1)*(h + 3)**2/2
Let r(b) = -4*b**2 + 8*b + 12. Let g(l) = -2*l**2 + 2*l + 4. Let h(c) = -8*g(c) + 3*r(c). What is j in h(j) = 0?
-1
Let q(g) be the third derivative of 0 + 7/6*g**3 + 0*g + 1/24*g**5 + 5/12*g**4 + 5*g**2 - 1/72*g**6. Let n(m) be the first derivative of q(m). Factor n(t).
-5*(t - 2)*(t + 1)
Let w = 39 - 34. Let p = 9 - w. Determine l so that 0 - 1/3*l**p - 2/3*l + 1/3*l**2 - 1/3*l**5 + l**3 = 0.
-2, -1, 0, 1
Suppose 255/4*n**3 + 5/4*n**4 + 495/4*n**2 + 0 + 245/4*n = 0. Calculate n.
-49, -1, 0
Let h(u) be the second derivative of -u**4/4 - 13*u**3 - 75*u**2/2 + 19*u - 1. Factor h(j).
-3*(j + 1)*(j + 25)
Suppose -5*x + 163*t - 14 = 160*t, 24 = 4*x + 2*t. Suppose -5*g + 0 - 5/2*g**x = 0. Calculate g.
-2, 0
Solve 94*a**2 - 160*a + 12 + 40*a**3 + 26*a**2 - 278 - 5*a**4 - 134 = 0 for a.
-2, 2, 10
Let a(n) be the first derivative of 0*n**2 + 3 - n**3 + 0*n - 1/220*n**5 + 1/66*n**4 + 1/1980*n**6. Let m(r) be the third derivative of a(r). Factor m(u).
2*(u - 2)*(u - 1)/11
Let n = -294 - -294. Let x(z) be the first derivative of n*z + 6 + 1/10*z**4 + 0*z**2 + 2/15*z**3. What is b in x(b) = 0?
-1, 0
Let c = 9 - 6. Suppose 6 = -c*y, 5*s + 0*s - 3*y - 31 = 0. Factor -3*j**3 - 5*j**3 + 0*j**s - 2*j**5 - 8*j**4.
-2*j**3*(j + 2)**2
Let x(r) = -44*r + 2337. Let c be x(53). Solve -2/19*a**3 - 2/19*a**4 + 0 + 2/19*a**c + 2/19*a**2 + 0*a = 0 for a.
-1, 0, 1
Suppose 5*v = 4*v + 3. Suppose 0 = h - v*h. Let -1/2*p + h - 1/2*p**2 = 0. What is p?
-1, 0
Factor 80*b**3 + 86*b**2 - 60*b**2 - 80*b - 377 + 5*b**4 + 57 + 289*b**2.
5*(b - 1)*(b + 1)*(b + 8)**2
Let c(x) be the first derivative of -x**5/120 + 7*x**4/72 - 11*x**3/36 + 5*x**2/12 - 3*x - 6. Let j(m) be the first derivative of c(m). Let j(u) = 0. What is u?
1, 5
Solve -103/2*j + 15 - 7/2*j**2 = 0.
-15, 2/7
Let t(g) be the second derivative of -5*g**4/18 - 5*g**3/18 + 53*g. Suppose t(f) = 0. What is f?
-1/2, 0
Let r be (6/7)/2 + (-30)/(-28). Let h(d) = -10*d - 78. Let f be h(-8). Suppose 6*m - r - 15/2*m**f + 3*m**3 = 0. What is m?
1/2, 1
Let q(m) = 3*m**4 - 12*m**3 - 18*m**2 - 20*m - 9. Let l(r) = -r**4 + r**3 + r + 1. Let k(s) = -4*l(s) - q(s). What is c in k(c) = 0?
-5, -1
Let t be (7/5*1)/((-49)/(-14)). Determine c so that -10 - 4*c - t*c**2 = 0.
-5
Let h be 2 - ((2 - 1) + -1). Suppose -50 = -9*w + 112. Factor -w*o + 12*o**2 + h*o**3 - 5*o**3 + 0*o**3 + o**3.
-2*o*(o - 3)**2
Let m = 4304 - 4304. Determine v so that -2/13*v**2 + m - 8/13*v = 0.
-4, 0
Let i be ((-66)/(-9))/(1/3). Suppose 5*y = 4*m + 37, 0 = -3*y + 5*y - 4*m - i. Factor -72*u**3 - 16*u**2 - 24*u**5 + 3*u**4 + 44*u**y + 30*u**5 - 63*u**4.
2*u**2*(u - 2)*(5*u + 2)**2
Let f(r) be the first derivative of r**4/4 - 13*r**3 + 507*r**2/2 + 11*r + 30. Let c(m) be the first derivative of f(m). Determine h so that c(h) = 0.
13
Let d(x) = x**3 - 5*x**2 - 3*x. Let i(c) be the second derivative of 3*c**5/20 - 3*c**4/4 - 7*c**3/6 - 8*c. Let f(p) = 7*d(p) - 3*i(p). Factor f(g).
-2*g**2*(g + 4)
Let g be 35/(-28)*-4 + 69. Suppose 0 = -g*l + 75*l. Factor l*a**3 + 1/3*a**2 + 0 + 0*a - 1/3*a**4.
-a**2*(a - 1)*(a + 1)/3
Suppose -7*g = 16 + 26. Let t(v) = -9*v**2 - 3*v. Let r(s) = s**2 + s. Let d(p) = g*r(p) - t(p). Find j such that d(j) = 0.
0, 1
Factor 202*r**4 - r**2 + r**2 - 5*r**3 - 192*r**4 - 5*r**5.
-5*r**3*(r - 1)**2
Let d = 2/16753 + 16739/117271. Find o such that -1/7*o**5 - 1/7*o + 2/7*o**3 - 1/7*o**4 + 2/7*o**2 - d = 0.
-1, 1
Suppose 2*m - 114 = -122. Let l be 3/4 - -1*m/16. Factor 0 - 3/4*b**2 + l*b + 1/4*b**3.
b*(b - 2)*(b - 1)/4
Let d(w) = w**2 