t y be k(-4). Let q = 12 - y. Factor 1/2*j + j**2 + 2*j**q - 7/2*j**3 + 0.
j*(j - 1)**2*(4*j + 1)/2
Let c(f) be the first derivative of -2*f**3/27 + 4*f**2/9 + 8*f/3 - 34. Suppose c(d) = 0. Calculate d.
-2, 6
Let i(y) be the first derivative of 3/20*y**6 + 3 + 3/5*y**5 + 3*y**2 + 0*y**3 + 1/70*y**7 + y**4 + 0*y. Let f(o) be the second derivative of i(o). Factor f(w).
3*w*(w + 2)**3
Let m(s) be the third derivative of s**3 + 0*s - 1/18*s**4 + 0 - 12*s**2 - 1/270*s**6 + 1/45*s**5. Let u(h) be the first derivative of m(h). Factor u(k).
-4*(k - 1)**2/3
Let z be (-129)/15 + (0 - 4/10). Let w be (-5 + 5)/(1/(3/z)). Factor w + 1/2*y**2 + y**3 - 1/2*y**4 - y.
-y*(y - 2)*(y - 1)*(y + 1)/2
Factor 0 + 2/15*s**3 + 128/15*s - 32/15*s**2.
2*s*(s - 8)**2/15
Let z be (-4802)/147 + 2/(-6) + -1. Let a be z/(-6) + (-2 - 3). Solve -a + 4/9*x + 2/9*x**2 = 0 for x.
-3, 1
Let c(v) = v**2 - v - 12. Let i be c(5). Suppose 2*o - i = -2. Factor 0 - 2/11*r**o + 4/11*r - 2/11*r**2.
-2*r*(r - 1)*(r + 2)/11
Let h be 0 + (-3)/(-5 - -2) + 2. Factor 84*c**5 + 939*c**4 - 887*c**4 - 6*c**3 + 14*c**h.
4*c**3*(3*c + 1)*(7*c + 2)
Let n(l) be the first derivative of l**4/12 + 8*l**3/9 + 8*l**2/3 + 182. Solve n(o) = 0.
-4, 0
Let y(p) = 7*p**2 + 7*p + 36. Let a(m) = -30*m**2 - 30*m - 145. Let c(t) = 6*a(t) + 25*y(t). Factor c(h).
-5*(h - 2)*(h + 3)
Suppose 8*s - 7*s + 2 = 0. Let p be 24/(-15) - (s - 1) - 1. Let -p + y**2 - 3/5*y = 0. What is y?
-2/5, 1
Let j(c) be the first derivative of 0*c + 1/15*c**3 - 1/10*c**2 - 5. Solve j(f) = 0 for f.
0, 1
Determine l, given that 4*l**2 - 10*l**3 - 5*l**4 + 5*l + 9*l**2 - 15 + 5*l + 7*l**2 = 0.
-3, -1, 1
Let d(f) = 120*f**2 + 5979*f + 5994. Let o(q) = 9*q**2 + 460*q + 461. Let a(t) = -2*d(t) + 27*o(t). Let a(p) = 0. What is p?
-153, -1
Let o be 4/6 + 12/9. Suppose 0 + 162*k**o - 6*k**3 + 6*k + 4*k**4 - 9 - 7*k**4 - 150*k**2 = 0. What is k?
-3, -1, 1
Suppose -2*i - l + 6 = 0, -1 = -l - 3. Suppose -i*t + 3*o = -27, -2*o + 10 = 4. What is p in -3*p - 3*p**4 - t*p + 4*p**3 + 5*p**3 = 0?
-1, 0, 2
Let s(g) be the second derivative of 7*g**4/48 - 13*g**3/12 - g**2 + g. Factor s(v).
(v - 4)*(7*v + 2)/4
Suppose -35*r = -40*r. Let b(p) be the first derivative of -1/21*p**3 + 1 + 1/28*p**4 - 1/42*p**6 + r*p**2 + 0*p + 1/35*p**5. Determine a so that b(a) = 0.
-1, 0, 1
Let j = 20/1771 - -3482/5313. Factor 0 - 4*h**2 - j*h**3 + 0*h.
-2*h**2*(h + 6)/3
Find f such that -224*f**2 + 454*f**2 - 220*f**2 - 185 + 365*f = 0.
-37, 1/2
Let c(k) = -k + 11. Let v(z) = -3*z + 21. Let s(q) = -5*c(q) + 2*v(q). Let y be s(-13). Find w, given that 0 + 2/7*w - 2/7*w**3 + y*w**2 = 0.
-1, 0, 1
Suppose -32/7 + 20/7*l**3 + 80/7*l - 2/7*l**4 - 66/7*l**2 = 0. Calculate l.
1, 4
Let v(r) be the first derivative of r**6/2880 - r**5/240 + r**4/64 - 9*r**3 + 48. Let j(k) be the third derivative of v(k). Factor j(h).
(h - 3)*(h - 1)/8
Let w be ((-95)/(-76) - 18) + 17. Let w*t**2 - 3/4*t + 0 = 0. What is t?
0, 3
Let v be ((-24)/462)/(124/(-868)). Factor -6/11*h - v - 2/11*h**2.
-2*(h + 1)*(h + 2)/11
Let n(v) = -v**4 - 53*v**3 - 89*v**2 + 45*v + 90. Let m(a) = a**4 + 108*a**3 + 179*a**2 - 90*a - 180. Let j(r) = 4*m(r) + 9*n(r). Determine f so that j(f) = 0.
-6, -3, -1, 1
Let o(g) = -3*g**5 + 9*g**4 + 3*g**3 - 21*g**2 - 3*g + 9. Let h(m) = m**3 + m**2. Let f(k) = 3*h(k) + o(k). Suppose f(z) = 0. Calculate z.
-1, 1, 3
Let j(x) be the third derivative of x**6/240 + 13*x**5/12 + 4225*x**4/48 - 228*x**2 - 1. Factor j(c).
c*(c + 65)**2/2
Let i(s) = s**3 + 4*s**2 - 7. Let n be i(-3). Let j be n/(-6) - 9/((-81)/6). Suppose -j*c**2 - 2/3 - c = 0. What is c?
-2, -1
Let a = -23 + 28. Factor -4*i**4 + 9*i**4 - 10*i**2 + 8*i - 5*i**5 - 3*i + a*i**4.
-5*i*(i - 1)**3*(i + 1)
Factor -2/5*i**4 + 2/5*i + 0 + 2/5*i**2 - 2/5*i**3.
-2*i*(i - 1)*(i + 1)**2/5
Let f(s) be the third derivative of s**5/12 + 5*s**4/2 - 70*s**3/3 - s**2 + 40. Determine n, given that f(n) = 0.
-14, 2
Let j be (16/6)/(2/6). Suppose j = 2*a + 2*a. Solve -49*o + o**2 + o**a + 45*o + 0*o**2 = 0.
0, 2
Let o = -345/8 + 46579/1080. Let y(t) be the third derivative of 14*t**2 - 4/27*t**3 + 0*t - o*t**5 - 5/108*t**4 + 0. Factor y(z).
-2*(z + 1)*(z + 4)/9
Let -22/3*m + 1/6*m**2 - 15/2 = 0. What is m?
-1, 45
Suppose 3*u + 12 = 5*u. Let h be 2*9/u + 1. Suppose t**3 + t**5 + 4*t**3 + 2*t**4 - h*t**3 = 0. Calculate t.
-1, 0
Let a(x) be the third derivative of -2*x**2 + 0*x**5 - 2/27*x**3 + 0 - 1/540*x**6 + 1/36*x**4 + 0*x. Solve a(m) = 0.
-2, 1
Let j be (-4 + 0)*(-3)/(-40)*-4. Let n be (9 - 2) + (-164)/41. Suppose -6/5 - 3/5*k**n + 3/5*k + j*k**2 = 0. What is k?
-1, 1, 2
Let i(j) be the second derivative of -1/3*j**3 - 3/4*j**2 - 6*j - 1/24*j**4 + 5. Factor i(t).
-(t + 1)*(t + 3)/2
Solve -209*n**3 + 13*n**2 - 6*n + 217*n**3 - 2*n**5 + 4 - 17*n**2 = 0 for n.
-2, -1, 1
Let m(q) be the first derivative of -q**6/48 + q**4/16 - q**2/16 + 42. Factor m(i).
-i*(i - 1)**2*(i + 1)**2/8
Determine t so that 3*t - 18*t + 36*t**2 - t = 0.
0, 4/9
Let k(g) be the second derivative of -9*g + 1/8*g**4 + 0 - 1/2*g**3 + 0*g**2. Determine h so that k(h) = 0.
0, 2
Let m(n) = -8*n**4 + 2*n**3 - 6*n**2 + 6*n + 6. Suppose 4*o = 8 - 0. Let x(s) = s**o - 1 + s**4 - 4*s + 3*s + 0*s. Let d(l) = m(l) + 6*x(l). Factor d(z).
-2*z**3*(z - 1)
Let y(a) = 6*a**2 - 2*a. Suppose -4*u + 32 = 3*p, 0 = 2*p - 7*p + 3*u + 5. Let d(j) = -5*j**2 + 2*j. Let x(i) = p*y(i) + 5*d(i). Factor x(k).
-k*(k - 2)
Let m(z) be the second derivative of -z**6/195 - z**5/13 - 6*z**4/13 - 56*z**3/39 - 32*z**2/13 + 61*z. Determine f so that m(f) = 0.
-4, -2
Let b(q) = -8*q + 27. Let f be (-8)/(-40) + 14/5. Let y be b(f). Factor 1/7*l**y - 1/7 + 1/7*l**2 - 1/7*l.
(l - 1)*(l + 1)**2/7
Let i(c) = 0*c**2 + 8*c**2 - 14*c - 2*c**3 - 4*c**2. Let q(w) = w**2 - w. Let n(j) = i(j) - 10*q(j). Factor n(r).
-2*r*(r + 1)*(r + 2)
Let s(g) be the third derivative of -g**8/1344 + g**6/120 + g**5/120 - g**4/32 - g**3/12 + 3*g**2 + 15. Let s(h) = 0. Calculate h.
-1, 1, 2
Let d(k) be the first derivative of k**5/60 + k**4/72 - k**3/9 - 14*k**2 - 13. Let p(c) be the second derivative of d(c). Factor p(w).
(w + 1)*(3*w - 2)/3
Let i(z) be the third derivative of z**6/30 - 7*z**5/3 - 76*z**4/3 - 104*z**3 - 733*z**2. Factor i(b).
4*(b - 39)*(b + 2)**2
Factor -27/2 + 1/2*l**4 + 18*l - 3*l**2 - 2*l**3.
(l - 3)**2*(l - 1)*(l + 3)/2
Let 25881*t**3 + 3*t**2 + 3*t**5 - 21*t**2 - 24*t**4 - 25842*t**3 = 0. Calculate t.
0, 1, 6
Factor -12*s**2 + 100*s - 4*s**2 + 20*s**2 - 32*s + 32*s.
4*s*(s + 25)
Suppose 6*i = 14 + 28. Factor 9*x**2 + 3*x**4 + i*x**3 - 21*x**3 - x**3 + 3*x**5.
3*x**2*(x - 1)**2*(x + 3)
Find x such that 14*x - 126*x**2 - 3 - 11 + 258*x**2 - 2 - 130*x**2 = 0.
-8, 1
Let o(b) be the third derivative of b**5/60 - 37*b**4/12 + 1369*b**3/6 + 93*b**2. Factor o(l).
(l - 37)**2
Factor -2*x + 20*x + x**2 - 54 + 0*x**2 + 5*x**2 - 2*x**3.
-2*(x - 3)**2*(x + 3)
Let x(p) = -4*p**3 + 8. Let h(j) = j**3 - j**2 - j - 1. Let r(v) = 3*h(v) + x(v). Let y(u) be the first derivative of r(u). Factor y(b).
-3*(b + 1)**2
Let h(j) = -193*j - 1737. Let d be h(-9). Factor -3*s**2 - 3*s**3 - 3/4*s**4 + 0*s + d.
-3*s**2*(s + 2)**2/4
Let 1/5*u**4 + 5*u + 0 + 7*u**2 + 11/5*u**3 = 0. Calculate u.
-5, -1, 0
Factor 75/2*x**3 + 0 - 6*x + 0*x**2.
3*x*(5*x - 2)*(5*x + 2)/2
Determine c so that -4*c**2 - 144/7 - 120/7*c - 2/7*c**3 = 0.
-6, -2
Let j be (-88)/(-24) + (-4)/6. Factor w**2 + w**4 + w**5 + 0*w**j - w**3 - 2*w**2.
w**2*(w - 1)*(w + 1)**2
Let c(h) = -6*h - 9. Let i be c(-2). Solve w**5 - w**2 - 2*w**2 - 3*w**i + 2*w**5 + 3*w**4 = 0 for w.
-1, 0, 1
Let 8192/7 + 0*r**3 + 0*r - 256/7*r**2 + 2/7*r**4 = 0. Calculate r.
-8, 8
Let k(t) be the third derivative of t**7/105 - 2*t**6/15 + t**5/2 + t**2 + 6*t. Suppose k(h) = 0. Calculate h.
0, 3, 5
Suppose -3*g - 27*p + 31*p - 12 = 0, -9 = g - 3*p. Solve 8/7*a - 2/7*a**5 + 8/7*a**2 - 6/7*a**3 - 8/7*a**4 + g = 0.
-2, -1, 0, 1
Let f(u) = u**3 + 3*u**2 + 7*u - 3. Let w(g) = -3*g**2 - 6*g + 3. Suppose 3*j - 4 + 16 = 0. Let y(z) = j*w(z) - 3*f(z). Let y(i) = 0. Calculate i.
-1, 1
Let o(k) be the first derivative of k**3/27 - 22*k**2/9 + 484*k/9 - 187. Solve o(y) = 0 for y.
22
Let c be 32/(-18)*279/(-310). Factor 4/5*z**2 + 2/5*z**3 + c - 14/5*z.
2*(z - 1)**2*(z + 4)/5
Let y(b) be the third derivative of -2/15*b**3 + 0