ative of -4*o**3/3 - 25. Factor c(j).
-4*j**2
Let h(m) be the second derivative of m**5/90 + m**4/12 + 2*m**3/9 + 2*m**2 - 7*m. Let y(j) be the first derivative of h(j). Factor y(r).
2*(r + 1)*(r + 2)/3
Let o(d) be the first derivative of -2*d**3/15 - d**2/5 - 7. Determine r so that o(r) = 0.
-1, 0
Let j be 54/12 - (-6)/4. Suppose -3*b - 3*k = -j, 2*b = 7*b + 4*k - 12. Suppose 2/3*z**3 + 0 + 0*z - 2/3*z**b + 2/3*z**2 - 2/3*z**5 = 0. Calculate z.
-1, 0, 1
Let n(o) be the first derivative of -2/15*o**5 + 0*o**3 - 1/12*o**4 - 1/18*o**6 + 0*o**2 + 0*o - 7. Factor n(d).
-d**3*(d + 1)**2/3
Suppose l - 4*p = 13 + 5, 0 = -5*l + 5*p + 30. Let t be 128/336 - (-4)/14. Factor -4*b - t - 26/3*b**l - 8*b**3 - 8/3*b**4.
-2*(b + 1)**2*(2*b + 1)**2/3
Let j(q) = q**3 - 2*q**2 - 5*q + 6. Let v = 34 + -31. Let a be j(v). Solve a + 2/7*h**2 - 2/7*h = 0 for h.
0, 1
Let x(m) = m. Let q be x(3). Let i(f) be the second derivative of 4*f + 0 - f**2 - 1/24*f**4 - 1/3*f**q. Factor i(v).
-(v + 2)**2/2
Let x(d) be the first derivative of 0*d + 3/5*d**5 - 3/4*d**4 + 3/2*d**2 - d**3 - 3. Determine c, given that x(c) = 0.
-1, 0, 1
Let o be (1 - 0)/((-6)/(-30)). Let h = 7 - o. Suppose 2/3*i - i**h + 0 + 1/3*i**3 = 0. Calculate i.
0, 1, 2
Determine u so that 21*u**2 + 21/2 - 141/4*u + 15/4*u**3 = 0.
-7, 2/5, 1
Suppose -3*u + 6 = -5*s, 3*u = 4*s - 2*u - 3. Let f be 1/s*(-4 - -3). Factor 0*k + 2/3*k**4 + f*k**3 + 0 - 1/3*k**2.
k**2*(k + 1)*(2*k - 1)/3
Let a(f) = 8*f**3 + 4*f**2 + 6*f - 6. Let k(j) = -23*j**3 - 11*j**2 - 17*j + 17. Let o(z) = -17*a(z) - 6*k(z). Solve o(m) = 0.
0, 1
Let m(d) be the first derivative of 1/4*d**3 + 1/4*d**2 - 2*d + 1/8*d**4 - 1 + 1/40*d**5. Let i(x) be the first derivative of m(x). Factor i(n).
(n + 1)**3/2
Let t(w) = 3*w**2 + 2*w - 5. Let b be t(-4). Suppose -10*l - 5*v + b = -5*l, -3*l = -2*v + 4. Find g, given that -3*g + 4*g - g + g**l - 1 = 0.
-1, 1
Let y(l) = 2*l**2. Let s(c) = -c**2. Let m(f) = -9*s(f) - 4*y(f). Factor m(v).
v**2
Let r = -50 - -52. Factor -1/2*h + 0 + 3/4*h**r.
h*(3*h - 2)/4
Suppose -i + 2 = -3*i. Let y be i/(-2) + (-45)/(-18). Find g, given that -6*g + 3*g**2 + 0*g - y*g**3 + 6*g**3 = 0.
-2, 0, 1
Let o = 37213/5 + -7474. Let g = o - -161/5. Factor -2/5*d**3 + 0 + 0*d - g*d**2.
-2*d**2*(d + 2)/5
Suppose -3*l = 2*l - 5. Let r(n) = n. Let i(g) = -6*g**2 + 2. Let a(w) = l*i(w) - 4*r(w). What is t in a(t) = 0?
-1, 1/3
Let c = 65 - 65. Let h(f) be the second derivative of 0*f**3 + 0*f**4 + 3*f + 0*f**5 + c + 0*f**2 + 1/15*f**6. Factor h(u).
2*u**4
Let d(v) be the second derivative of -1/21*v**4 + 0*v**3 + 0*v**5 - 8*v + 0 + 1/105*v**6 + 1/7*v**2. What is z in d(z) = 0?
-1, 1
Factor -3*u**2 + 9*u**3 - 25*u**3 - 9 + 8*u**3 + 5*u**3 + 15*u.
-3*(u - 1)**2*(u + 3)
Find z, given that -1/4*z**2 + z - 3/4 = 0.
1, 3
Let h(a) be the first derivative of a**5/110 + a**4/66 - a**3/33 - a**2/11 - a - 2. Let b(u) be the first derivative of h(u). Factor b(i).
2*(i - 1)*(i + 1)**2/11
Let w(y) = 1 + 4*y - 6*y**4 - 1 + 2*y**2. Let b(v) = 7*v**4 - 2*v**2 - 5*v. Suppose 24 = -6*k - 6. Let x(o) = k*w(o) - 4*b(o). Factor x(d).
2*d**2*(d - 1)*(d + 1)
Solve -16/11*o**3 - 6/11*o**2 + 0 + 0*o - 6/11*o**4 + 4/11*o**5 = 0 for o.
-1, -1/2, 0, 3
Let n = 6/11 + -7/33. Suppose 0 - y**4 - 1/3*y**3 + y**2 + n*y = 0. What is y?
-1, -1/3, 0, 1
Let n be ((-10)/125)/((-12)/10). Let c(s) be the third derivative of -1/3*s**3 + s**2 + 0 + 0*s - n*s**5 + 1/30*s**6 - 7/24*s**4. Factor c(j).
(j - 2)*(2*j + 1)**2
Let z be (0/((-6)/(-1)))/(-2). Factor z + 1/3*q**2 + 1/3*q.
q*(q + 1)/3
Let h(f) be the second derivative of 1/60*f**4 + 0*f**3 + f + 0 + 0*f**2 + 1/100*f**5. Determine p so that h(p) = 0.
-1, 0
Let o be 455/143 - (-2)/(-11). Let x(g) be the third derivative of 0*g + 3*g**2 + 1/105*g**7 + 0*g**6 + 0*g**o + 0 - 1/30*g**5 + 0*g**4. Factor x(q).
2*q**2*(q - 1)*(q + 1)
Let d be (-2)/(-6)*0/(-1). Suppose d = s - 6 + 3. Suppose 1/3*z + 1/3*z**s + 0 - 2/3*z**2 = 0. Calculate z.
0, 1
Let r(v) be the second derivative of 0*v**5 - 1/147*v**7 + 1/21*v**3 - 3*v - 2/105*v**6 + 1/21*v**4 + 0 + 0*v**2. Suppose r(h) = 0. Calculate h.
-1, 0, 1
Suppose 0*a + 0*a**2 + 0 - 2/5*a**4 - 12/5*a**3 = 0. Calculate a.
-6, 0
Suppose -4*w**2 + 49/4*w**5 + 0 - 56*w**4 + 0*w + 29*w**3 = 0. Calculate w.
0, 2/7, 4
Let w(f) = f**4 - 3*f**3 - 4*f**2 + 5. Let b(c) = -4*c**3 - 4*c**2 + 4. Let k(t) = 5*b(t) - 4*w(t). Factor k(p).
-4*p**2*(p + 1)**2
Suppose 2*r - 3*r = 2, -4*o + r = -14. Let m(g) be the first derivative of -g - 28*g**o - 52*g**4 - 192/5*g**5 - 15/2*g**2 - 1. Factor m(f).
-(3*f + 1)*(4*f + 1)**3
Let f(p) be the third derivative of 0*p**4 - 1/75*p**5 + 1/75*p**7 + 0 + 1/60*p**6 + 0*p + 0*p**3 - 4*p**2. Factor f(y).
2*y**2*(y + 1)*(7*y - 2)/5
Solve 2/7*s**4 + 0*s**2 + 0*s + 0 + 0*s**3 = 0 for s.
0
Let j = -7853/4 + 1952. Let w = 23/2 + j. Solve -w + t - t**2 = 0.
1/2
Let -24*x**3 + 4*x**4 + 4*x**5 + 10*x**3 + 10*x**3 - 4*x**2 = 0. What is x?
-1, 0, 1
Let p(t) = -2*t**4 - 8*t**3 - 4*t**2 - t. Let w(b) = b**4 - b**2 - b. Let j(r) = r**2 - 3*r - 4. Let l be j(3). Let h(c) = l*p(c) + 12*w(c). Factor h(y).
4*y*(y + 1)**2*(5*y - 2)
Let s(u) be the first derivative of -3*u**2/2 - 3*u + 2. Let j be s(-2). Find w, given that 4*w**3 - 2 - 3*w**j + 5*w**3 - 6*w + 4*w**4 - 2*w**2 = 0.
-1, -1/2, 1
Let h(p) = 4*p**3 - 9*p**2 + p. Let z(v) = 12*v**3 - 26*v**2 + 3*v. Let n(y) = 11*h(y) - 4*z(y). Find u, given that n(u) = 0.
0, 1/4, 1
Factor 0 - 39/2*g**2 - 3/2*g**4 + 9*g + 10*g**3.
-g*(g - 3)**2*(3*g - 2)/2
Suppose c + c - 4*l = 20, 5*c + l - 17 = 0. Let y be 6/(-3) + 9/c. Solve -y - 1/4*a**2 + 1/2*a = 0 for a.
1
Let d(k) = k**3 + 3*k**2 + 10*k + 16. Let c be d(-2). Factor 0 - 1/3*i**2 + 1/3*i**3 + c*i.
i**2*(i - 1)/3
Factor -8/3 - 6*m**3 - 20*m**2 + 46/3*m.
-2*(m + 4)*(3*m - 1)**2/3
Let i(g) be the first derivative of -g**5/10 - g**4/8 - 26. Let i(x) = 0. Calculate x.
-1, 0
Let y = 52/7 + -128/21. Let c(w) be the first derivative of 20/3*w**3 - 29/6*w**4 + 4 - 13/3*w**2 + y*w**5 + 4/3*w. Solve c(s) = 0 for s.
2/5, 1/2, 1
Let d be (36/32)/(6/8). Find u such that 0 - 3*u**4 - d*u**5 + 0*u + 0*u**2 - 3/2*u**3 = 0.
-1, 0
Let z(v) be the second derivative of -v**5/90 + v**4/18 + v**3/27 - v**2/3 + 15*v. Factor z(y).
-2*(y - 3)*(y - 1)*(y + 1)/9
Let m be (-128)/30*4/(-24)*9. Suppose m*a**3 + 2/5 + 48/5*a**2 + 18/5*a = 0. What is a?
-1, -1/4
Suppose 12 = 3*v - o, -22*v + 26*v = 4*o + 24. Factor 1/3*u**v + 0*u + 0 + 2/3*u**2.
u**2*(u + 2)/3
Factor -2*j**3 + 0*j**3 + 5*j**2 + j**5 + 0 + 1 + j - 7*j**2 + j**4.
(j - 1)**2*(j + 1)**3
Let m(z) = -z - 15. Let u be m(-17). Let o(c) be the first derivative of -2/3*c**3 - 2*c**4 + u*c + 4*c**2 + 2. Suppose o(j) = 0. Calculate j.
-1, -1/4, 1
Let i = 977/3 - 325. Let 0*h + 0*h**3 - i*h**4 + 0*h**2 + 0 = 0. Calculate h.
0
Let y(s) = s + 11. Suppose 5*n + i = 25 - 69, 4*i = 4*n + 40. Let f be y(n). Factor 0*r + 0 - 2/7*r**f.
-2*r**2/7
Let x = -17 - -24. Factor x*w**4 + 4*w**4 - 4*w**2 - 2*w**3 - 5*w**4.
2*w**2*(w - 1)*(3*w + 2)
Let a = 8/39 - -77/195. What is w in -3/5 + 3/5*w - 3/5*w**3 + a*w**2 = 0?
-1, 1
Let z(u) = u**3 + 5*u**2 - 8*u - 4. Let c be z(-6). Suppose 2*a**4 - 23*a + c*a**3 + 5*a - 2*a**2 + 8*a**2 + 2*a**3 = 0. What is a?
-3, 0, 1
Let w(x) be the third derivative of -x**6/40 - x**5/10 + 23*x**2. Factor w(i).
-3*i**2*(i + 2)
Suppose 3*l = -3*z - 2*z + 14, z + 3*l = -2. Factor -42*q**4 - z*q**2 + 22*q**4 + 8*q**3 + 16*q**4.
-4*q**2*(q - 1)**2
Let a be (7/49)/(36/14). Let x(k) be the second derivative of 0 - 1/20*k**5 - a*k**3 + 0*k**2 - 1/9*k**4 - k. Solve x(l) = 0 for l.
-1, -1/3, 0
Let r = 8 + -6. Factor l + 3*l**2 + l**2 - 3*l**r.
l*(l + 1)
Suppose -3*g - 1 = 4*d, -3*d - 5 = 2*d + 5*g. Suppose 4*y - 22 = d*v, -v + 0*v + 7 = 4*y. Determine f, given that 9/4*f**y - 3/4*f**2 - 3/2*f + 0 = 0.
-2/3, 0, 1
Let c(k) = k + 1. Let r be c(7). Suppose -2*f = -r - 2. Determine m so that f*m**2 - m - 25/4*m**3 + 0 = 0.
0, 2/5
Let i = 361/3 + -119. Let h = 0 - -1/3. Factor i*n**2 - 4/3*n**4 - h*n**3 + 0 + 1/3*n.
-n*(n - 1)*(n + 1)*(4*n + 1)/3
Solve -12*z**2 - 3*z**3 - 25*z + z + 15*z = 0 for z.
-3, -1, 0
Let x be (-106)/48*6/(-2). Let t = 223/24 - x. Let 8/3 - t*l + 2/3*l**2 = 0. Calculate l.
2
Suppose 24*b - 16*b = 11*b. Find t, given that 2/15*t**4 + b + 2/5*t**3 + 2/15*