d**4/12 - 5*d**3/3 + 53*d. Solve x(z) = 0 for z.
0, 2
Suppose 0 = 103*u - 97*u. Let v(x) be the third derivative of -1/24*x**4 + 1/180*x**5 + u*x + 1/9*x**3 + 0 + 2*x**2. Factor v(q).
(q - 2)*(q - 1)/3
Let z(g) = -3*g**3 - g**2 + 1. Let m be z(-1). Let c(l) be the first derivative of 6*l**2 + 38*l - 12 - 18*l + m*l**3 - 17*l. Factor c(o).
3*(o + 1)*(3*o + 1)
Let r be -1*18/14 - (-34 - -31). Determine h so that -4/7 - 12/7*h**2 + 4/7*h**3 + r*h = 0.
1
Let d(c) be the third derivative of 1/150*c**5 + 0 + 0*c - 21*c**2 - 1/10*c**4 + 3/5*c**3. Let d(r) = 0. What is r?
3
Let w(r) = -2*r**3 - 6*r**2 + 27*r - 27. Let p(n) = 7*n**3 + 25*n**2 - 108*n + 108. Let b(v) = -6*p(v) - 22*w(v). Factor b(x).
2*(x - 3)**3
Let y be 30/(-4)*(-48)/20. Let t be 24*2/y*6/4. Factor -1/4*o**5 + 0 - 5/4*o**2 + 1/2*o + 1/4*o**t + 3/4*o**3.
-o*(o - 1)**3*(o + 2)/4
Let n(d) be the second derivative of d**7/42 - d**6/3 + 29*d**5/20 - 5*d**4/3 - 2*d - 45. What is r in n(r) = 0?
0, 1, 4, 5
Let p(v) = v**3 - 12*v**2 + 2*v + 4. Let r be p(0). Solve 0 + 2/3*s - 2/9*s**5 + 4/3*s**3 + 16/9*s**2 + 0*s**r = 0.
-1, 0, 3
Let c = -92 + 144. Factor -28 - 12 + 0*y - 24*y**2 - 4*y**3 + 16*y**2 + c*y.
-4*(y - 2)*(y - 1)*(y + 5)
Suppose 145 + 339 + 185*f**2 - 900*f - 10*f**3 - 79 = 0. What is f?
1/2, 9
Let g(m) be the first derivative of 361*m**3/7 + 342*m**2/7 + 108*m/7 - 239. Determine v so that g(v) = 0.
-6/19
Let o(x) be the second derivative of x**7/1120 - x**6/120 + x**5/40 + 17*x**3/6 + 17*x. Let h(z) be the second derivative of o(z). Factor h(l).
3*l*(l - 2)**2/4
Factor 0 - 73/3*v - 1/3*v**3 - 74/3*v**2.
-v*(v + 1)*(v + 73)/3
Solve 9*l - 20*l**3 + 5*l**5 + 6*l + 33 - 23 - 10*l**2 = 0 for l.
-1, 1, 2
Let k(u) = 5*u**2 - 3*u. Let p(h) = -56*h**2 + 32*h. Let x be ((-544)/(-24))/((-2)/(-6)). Let o(n) = x*k(n) + 6*p(n). Factor o(q).
4*q*(q - 3)
Factor 4/5*c**3 + 0*c**2 - 8/5 - 12/5*c.
4*(c - 2)*(c + 1)**2/5
Let b(k) be the third derivative of -k**5/40 - 3*k**4/4 - 8*k**3 - 9*k**2 - 18. Factor b(i).
-3*(i + 4)*(i + 8)/2
Let u(c) = -c**3 + 6*c**2 - 5*c + 18. Let r be u(4). Factor -18*t**2 - 25*t**3 + 3*t - 12*t**2 + r + 22*t**3.
-3*(t - 1)*(t + 1)*(t + 10)
Let h = 65 - 25. Suppose 2*w - 112 + h = 0. What is u in 8*u**3 + 54 + w*u**2 + 2/3*u**4 + 72*u = 0?
-3
Let w(a) = 5*a + 4. Let z be w(-6). Let y = -20 - z. Factor 6*q**3 + q + y*q**2 - 5*q**3 - 6*q**2 + 2*q**2.
q*(q + 1)**2
Let i(s) be the first derivative of -19 - 2/21*s**3 + 12/7*s - 5/7*s**2. Factor i(u).
-2*(u - 1)*(u + 6)/7
Let h be (167 - 12)/((-1134)/(-8)). Let n = h + 4/81. Factor n*t - 8/7 + 2/7*t**4 + 6/7*t**2 - 8/7*t**3.
2*(t - 2)**2*(t - 1)*(t + 1)/7
Let f(r) be the first derivative of 4/7*r - 3/7*r**2 - 2/35*r**5 - 24 - 2/21*r**3 + 3/14*r**4. What is p in f(p) = 0?
-1, 1, 2
Suppose -3*u + 0*d = -4*d + 8, d = 2*u + 2. Let x = 3 + u. Determine o, given that -2 + 15*o - 5*o**2 - 5 + 0*o**2 - x = 0.
1, 2
Let v(g) = -g**2 - 10*g + 2. Let n be v(-10). Suppose -12 = -n*z - 0. Determine t, given that z*t**2 + 4 + 4 - 2 - 8*t - 4 = 0.
1/3, 1
Let l be ((-2)/(-14))/((-37)/(-148)). Let j = -467/7 - -69. Let 8/7*u**3 - l - j*u**4 + 2/7*u + 20/7*u**2 - 10/7*u**5 = 0. What is u?
-1, 2/5, 1
Let w(v) be the third derivative of -5/6*v**3 + 0 - 6*v**2 - 5/24*v**4 + 1/24*v**6 + 0*v + 1/12*v**5. Factor w(q).
5*(q - 1)*(q + 1)**2
Let m = -2384/217 + 345/31. Factor -1/7*s - m*s**2 + 6/7.
-(s - 2)*(s + 3)/7
Let l(h) be the second derivative of h**7/8820 + h**6/630 + h**5/105 - 7*h**4/3 + 9*h. Let i(m) be the third derivative of l(m). Let i(v) = 0. What is v?
-2
Let z(o) be the third derivative of 0*o - 1/48*o**4 - 1/120*o**5 + 1/2*o**3 + 0 + 20*o**2. Determine q so that z(q) = 0.
-3, 2
Factor -171/8*d**2 + 27*d - 15/2 + 15/8*d**3.
3*(d - 10)*(d - 1)*(5*d - 2)/8
Let h(w) = 3*w - 2. Let m be h(4). Suppose 2*j - m = -3*j. Factor 3/2*l**j + 1/2*l**3 + 3/2*l + 1/2.
(l + 1)**3/2
Let l be ((-51)/153)/(2/(8/(-10))). Let o(k) be the third derivative of l*k**3 + 1/40*k**4 + 0 + 14*k**2 - 1/300*k**5 + 0*k. Let o(i) = 0. Calculate i.
-1, 4
Let b(a) be the third derivative of a**6/1380 - 4*a**5/5 + 368*a**4 - 270848*a**3/3 + 149*a**2. What is s in b(s) = 0?
184
Let m be (-4)/(-6)*45/60. Let n = 115/222 + -2/111. Suppose n*c**3 + 0 - m*c**2 + 0*c = 0. What is c?
0, 1
Let b be 6/(-15) - 1/27*(-1596)/70. Factor 0 + 0*u - b*u**2.
-4*u**2/9
Let j(n) be the second derivative of -n**5/25 + 19*n**4/30 - 22*n**3/15 - 16*n**2/5 - 8*n + 28. Determine d so that j(d) = 0.
-1/2, 2, 8
Let i = 4974 + -44764/9. Determine o, given that -2/9*o**2 + 0*o - i*o**4 + 0 + 4/9*o**3 = 0.
0, 1
Suppose k + 2 + 0 = 0. Let i be (4*k/(-24))/((-2)/(-9)). Factor 0*f + 0 - 1/2*f**5 - 1/2*f**2 - i*f**3 - 3/2*f**4.
-f**2*(f + 1)**3/2
Suppose 5*a = 173 + 37. Let x = a + -40. Suppose -2/3 - 7/3*d**x - 3*d = 0. Calculate d.
-1, -2/7
Let j(g) be the second derivative of 5*g**4/12 - 10*g**3 - 27*g. Suppose j(z) = 0. Calculate z.
0, 12
Let p(q) = 3*q**2 + 62*q + 146. Let g be p(-18). Find y, given that -5/3*y + y**g + 2/3 = 0.
2/3, 1
Let a = 173 + -173. Let q(g) be the second derivative of 1/48*g**4 + 4*g + a*g**3 + 0 + 0*g**5 + 0*g**2 - 1/120*g**6. Factor q(u).
-u**2*(u - 1)*(u + 1)/4
Let y = 6725/11 + -611. Factor -2/11*c**3 - 4/11*c**2 + 2/11*c + y.
-2*(c - 1)*(c + 1)*(c + 2)/11
Let j(r) = r + 10. Suppose -5*t = -d - 15, 6 - 16 = -5*t. Let w be j(d). Factor z**3 - z**w - z**2 + z**4 + 2 - 4 + 2.
-z**2*(z - 1)**2*(z + 1)
Factor -5*h**2 + 35*h + 10*h**2 - 18 + 48 + 0*h**2.
5*(h + 1)*(h + 6)
Let q = 10/67 - -47/134. Let h(c) be the second derivative of -1/60*c**6 + q*c**2 - 2*c + 0 + 1/40*c**5 + 1/8*c**4 - 5/12*c**3. Solve h(f) = 0.
-2, 1
Let o be (-7)/105*-39 - 6/10. Factor 10*u**2 - 5*u - 13 + o + 0 + 6.
5*(u - 1)*(2*u + 1)
Let w = 1 + 3. Suppose -3*f + m = -1, f + 0*f - w*m = -18. Suppose 4*h**2 + 72*h - 66*h - h**f = 0. What is h?
-2, 0
Find z, given that 1/2*z**3 - 3*z**2 - 15/2*z - 4 = 0.
-1, 8
Let m be (-22)/6 - (-2265)/90. Suppose -1 - 12*r**3 - m*r**2 - 21/2*r = 0. Calculate r.
-1, -2/3, -1/8
Let t(q) be the first derivative of 32/3*q**3 + 14 - 2/3*q**6 - 8/5*q**5 + 8*q + 2*q**4 + 14*q**2. Find g, given that t(g) = 0.
-1, 2
Let c(j) be the first derivative of -j**5/5 - 5*j**4/2 - 12*j**3 - 28*j**2 - 32*j - 457. Factor c(u).
-(u + 2)**3*(u + 4)
Let f(i) = 823*i**2 - 262*i + 20. Let d(p) = 822*p**2 - 263*p + 20. Let v(s) = -2*d(s) + 3*f(s). Find r, given that v(r) = 0.
2/15, 2/11
Let h(p) be the second derivative of p**5/40 - 11*p**4/24 - p**3/12 + 11*p**2/4 - 22*p - 5. Suppose h(f) = 0. Calculate f.
-1, 1, 11
Factor -25/2*r - 5/2*r**2 + 0.
-5*r*(r + 5)/2
Let c(k) be the third derivative of 1/48*k**4 - 7*k**2 + 1/105*k**7 + 0*k - 1/30*k**5 + 0*k**3 - 1/240*k**6 + 0. Solve c(t) = 0 for t.
-1, 0, 1/4, 1
Let p(t) = -3*t**2 - 13*t - 32. Let v(h) = -h + 1. Let b = 25 - 22. Suppose -b*o - 16 = 2*z - 0, -4 = 2*o. Let f(q) = z*v(q) - p(q). Factor f(d).
3*(d + 3)**2
Determine d, given that 12*d**3 + 24*d**2 - 46*d**2 + 22*d**2 - 1 - 48*d + 22*d**2 - 55 - 2*d**4 = 0.
-2, -1, 2, 7
Suppose 4*l - 49 = -1. Let u = 18 - l. Solve -u*g + 11 - 3*g - g**2 + 4*g**2 - 5 = 0.
1, 2
Let p = -29/8 + 263/72. Let b(k) be the first derivative of 0*k**2 - 1 + 1/30*k**5 - 1/18*k**3 - 1/24*k**4 + p*k**6 + 0*k. Factor b(q).
q**2*(q - 1)*(q + 1)**2/6
Factor 6/7*n**2 - 300/7 - 30/7*n.
6*(n - 10)*(n + 5)/7
Let k(o) = -3*o**3 + 9*o**2 - 125*o + 127. Let z(g) = -2*g**3 + 7*g**2 - 83*g + 85. Let d(u) = -5*k(u) + 8*z(u). Factor d(l).
-(l - 5)*(l - 3)**2
Let r be (180/28 - 6)*(-154)/(-132). Factor 0 + 0*z**3 + r*z**2 - 9/8*z**4 + 0*z.
-z**2*(3*z - 2)*(3*z + 2)/8
Let s(v) = 8*v + 11*v - 18*v + 1 + 1 - v**2. Let f be s(-1). Solve f + 16/7*u**2 - 4/7*u - 3/7*u**3 - 16/7*u**4 + u**5 = 0.
-1, 0, 2/7, 1, 2
Factor -3/2*q + 3/4*q**2 + 0.
3*q*(q - 2)/4
Let t(h) = 6*h**3 - h**2 + h - 1. Suppose 5 = 4*q + 1. Let n be t(q). Factor -n*j - 3*j - 44*j**2 + 12*j**2 - 14*j**3.
-2*j*(j + 2)*(7*j + 2)
Let 14792/11 + 344/11*h + 2/11*h**2 = 0. Calculate h.
-86
Let m(r) = -r + 13. Let q = 23 - 12. Let j be m(q). What is h in 2/3*h**j + 0 - 2/3*h = 0?
0, 1
Let q(p) = -p + 1. Let i be q(10). Let d = i + 11. Factor -11*a - 4*a**2 - 3*a**3 + 11*a - d*a**2.
-3*a**2*(a + 2)
Suppose 0 = 2*q + 2*i - 12, -5*q + 31 = i + 5. Suppose 7 = q*n - 3. Factor -4/3 - 2