1/2*o**6 + 3/2*o**4 + 2*o**3 - 9/2*o**2 + 3*o - 15 - 9/5*o**5. Suppose n(c) = 0. Calculate c.
-1, 1
Factor -2/9*p**2 - 4/9*p - 2/9.
-2*(p + 1)**2/9
Let y(w) be the third derivative of w**5/12 + 25*w**4/24 + 10*w**3/3 - 100*w**2. Factor y(o).
5*(o + 1)*(o + 4)
Let h be (2/6)/((-1960)/180 + 11). Factor 3/10*p - 3/10*p**2 - 1/10 + 1/10*p**h.
(p - 1)**3/10
Let h be ((-13)/3)/((-3)/54). Suppose -h - 22 = -5*c. Factor -23*a**3 - 21*a**2 + 7*a**3 - 24*a - c*a**2 - 4 + 5*a**2.
-4*(a + 1)**2*(4*a + 1)
Suppose -22*o - 152 = -69*o + 9*o. Factor 0*z**2 + 0 - 4/7*z**5 + 8/7*z**3 + 0*z**o - 4/7*z.
-4*z*(z - 1)**2*(z + 1)**2/7
Solve -7*s**3 - 528*s**5 + 15*s**4 + 7*s**3 - 27*s**2 + 525*s**5 - 9*s**3 = 0 for s.
-1, 0, 3
Let u(q) be the first derivative of q**6/600 - q**4/10 - 5*q**3/3 - 1. Let s(y) be the third derivative of u(y). Let s(t) = 0. Calculate t.
-2, 2
Let a(f) = -15*f**4 + 30*f**3 + 134*f**2 - 88*f + 15. Let t(r) = -29*r**4 + 59*r**3 + 266*r**2 - 176*r + 30. Let v(l) = 11*a(l) - 6*t(l). Factor v(s).
(s - 5)*(s + 3)*(3*s - 1)**2
Let q(i) be the second derivative of -i**8/6720 + i**7/840 + i**6/120 - 19*i**3/3 + 3*i + 2. Let t(p) be the second derivative of q(p). Factor t(d).
-d**2*(d - 6)*(d + 2)/4
Let y(q) be the second derivative of -5*q**4/6 + 8*q**3/3 - 10*q**2 - 8*q. Let c(o) = -3*o**2 + 5*o - 7. Let m(v) = 14*c(v) - 5*y(v). Factor m(s).
2*(s - 1)*(4*s - 1)
Let n(o) be the first derivative of 1/20*o**5 + 1 + 0*o + 0*o**3 + 1/12*o**4 + 1/120*o**6 + 3/2*o**2. Let s(y) be the second derivative of n(y). Factor s(k).
k*(k + 1)*(k + 2)
Let b = -6227/6 - -1046. Let g = 26/3 - b. Find t, given that 1 - g*t - 1/2*t**2 = 0.
-2, 1
Suppose 5*o + 11 = w - 13, 4*w - 4*o = 16. Let q be (w - 3) + 8/1. Solve f**5 + 54*f**4 + 4*f**5 - 49*f**q = 0.
-1, 0
Suppose -21 - 4 = -5*b + n, -4*b + 14 = -2*n. Let g(w) be the second derivative of 0*w**2 + 0*w**3 - 1/4*w**4 - 1/10*w**b + 4*w + 0 + 3/10*w**5. Factor g(f).
-3*f**2*(f - 1)**2
Factor -27 + 3*l**2 - 11*l + 5*l - 18.
3*(l - 5)*(l + 3)
Let k = 4 + -2. Suppose w = 2*w - k. Factor c - 12*c + c - 5*c**w.
-5*c*(c + 2)
Let z = 46 + -44. Factor -z - 6 + t - t**2 - 10*t.
-(t + 1)*(t + 8)
Let w be (-13)/(-5) + (-8255)/3175. Suppose 0 = m + 2, 0*m + m + 12 = 5*p. What is t in 0*t**4 + 0 + 0*t + w*t**p + 1/7*t**5 - 1/7*t**3 = 0?
-1, 0, 1
Let s be ((-2)/(-14))/(21/12 + -2). Let z = s + 15/14. Suppose 0 - j + 3/2*j**2 - z*j**3 = 0. Calculate j.
0, 1, 2
Factor -1/9*k**3 - 1/9 + 1/9*k**2 + 1/9*k.
-(k - 1)**2*(k + 1)/9
Suppose 5*r - 2*f = -36, -3*f - 34 = 5*r + 12. Let s be 4/(((-12)/r)/3*13). Let 8/13*h**3 + 0 - s*h**4 + 0*h**2 + 2/13*h**5 + 0*h = 0. What is h?
0, 2
Suppose 0 + s**5 - 3/4*s**3 - 10*s**4 - 5/2*s + 31/4*s**2 = 0. What is s?
-1, 0, 1/2, 10
Let f(c) = -c**3 - 12*c**2 - 10*c - 1. Let b be f(-11). Let y be (9/(-6))/(9/b). Factor -4*h**2 - h**y + 3*h**2 + 2.
-2*(h - 1)*(h + 1)
Let f be -2 + -2*(-2)/4. Let l = f - -5. Find i, given that 4*i**4 + 6*i**3 + i**4 + i - 2*i**4 + i**5 + l*i**2 + i**4 = 0.
-1, 0
Let o(a) = -a**2 + 15*a - 81. Let f(x) = x**2 - 16*x + 81. Let z(g) = -6*f(g) - 4*o(g). Factor z(u).
-2*(u - 9)**2
Let i(j) be the second derivative of 1/12*j**4 + 19*j + j**3 + 5/2*j**2 + 0. Factor i(w).
(w + 1)*(w + 5)
Let z(h) be the first derivative of 2*h**5/5 - h**4/2 - 8*h**3/3 + 4*h**2 - 47. Suppose z(l) = 0. Calculate l.
-2, 0, 1, 2
Let w be 1/(-4)*-1 + 0 + 1. Let h = w + -37/36. Factor -h*z**3 + 4/9*z**2 + 0*z + 0 - 2/9*z**4.
-2*z**2*(z - 1)*(z + 2)/9
Let k = 7891/3 + -2629. Factor 0*d + 4/3*d**4 - 4/3*d**2 - k*d**3 + 4/3*d**5 + 0.
4*d**2*(d - 1)*(d + 1)**2/3
Let i(u) be the first derivative of -u**4/24 - u**3/6 - u**2/4 - u/6 - 228. Factor i(s).
-(s + 1)**3/6
Let r(a) be the first derivative of a**4/22 + 2*a**3/33 + 82. Factor r(q).
2*q**2*(q + 1)/11
Let i(w) be the first derivative of 5*w**3/3 + 5*w**2/2 - 10*w - 100. Solve i(p) = 0.
-2, 1
Let w(u) = 9*u - 157. Let a be w(18). Let b(k) be the third derivative of -2*k**2 + 0*k + 0*k**3 + 0 + 1/54*k**a + 1/54*k**4. Let b(h) = 0. What is h?
-2/5, 0
Factor -2/5*j**2 + 0*j - 2/5*j**5 + 2/5*j**3 + 2/5*j**4 + 0.
-2*j**2*(j - 1)**2*(j + 1)/5
Suppose -5*q - 2*i + 20 = i, i = 0. Suppose -2*t = q - 6. Let f(s) = 2*s**5 - 2*s**3 + 4. Let z(m) = -1. Let d(g) = t*f(g) + 4*z(g). Factor d(r).
2*r**3*(r - 1)*(r + 1)
Let i be ((-120)/33 - -2) + 98/49. Factor 8/11*u**2 + 14/11*u - i.
2*(u + 2)*(4*u - 1)/11
Let t(a) = -3*a**3 - 7*a**2 + 2*a + 32. Let x = -59 + 51. Let j(h) = -2*h**3 - 5*h**2 + h + 21. Let f(o) = x*j(o) + 5*t(o). Factor f(n).
(n - 1)*(n + 2)*(n + 4)
Let u be ((-40)/(-220))/2 + 86/22. Solve -40/13*a**u + 6/13*a**3 + 0 + 4/13*a**2 + 0*a - 42/13*a**5 = 0.
-1, -2/7, 0, 1/3
Let y(p) be the first derivative of -2*p**3/27 + 16*p**2/9 + 88*p/3 + 958. Factor y(l).
-2*(l - 22)*(l + 6)/9
Find j, given that 25*j - 43*j - 9*j - 34*j - 17*j - 2*j**2 = 0.
-39, 0
Suppose -8/3*j + 0 + 8/3*j**2 - 2/3*j**3 = 0. Calculate j.
0, 2
Let w(h) be the first derivative of -8/35*h**5 + 0*h**4 + 0*h**2 - 1/21*h**6 + 0*h + 18 + 0*h**3. Determine r, given that w(r) = 0.
-4, 0
Let d(r) be the third derivative of -1/420*r**5 + 1/14*r**3 + 11*r**2 + 0*r + 0 - 1/84*r**4. Factor d(v).
-(v - 1)*(v + 3)/7
Suppose 8 - 257/2*v**3 - 66*v + 169*v**2 + 21/4*v**4 + 49/4*v**5 = 0. What is v?
-4, 2/7, 1, 2
Suppose -3*n = 4*u - 12, -16*u + 11*u - 8 = -2*n. Let t(r) be the third derivative of -r**2 + u*r + 1/24*r**4 + 0*r**3 - 1/60*r**5 + 0. Solve t(f) = 0 for f.
0, 1
Let b(m) be the first derivative of -m**4/38 + 6*m**3/19 - 27*m**2/19 + 54*m/19 + 99. Solve b(x) = 0 for x.
3
Let f(r) be the first derivative of -5/4*r**4 + 11 - 10*r + 5/2*r**2 + 10/3*r**3. Find o such that f(o) = 0.
-1, 1, 2
Let u(g) = -15*g**3 - 26*g**2 + 11*g + 4. Let f be 728/(-84)*6/(-4). Let j(x) = 30*x**3 + 53*x**2 - 23*x - 7. Let r(k) = f*u(k) + 6*j(k). Factor r(d).
-5*(d + 1)**2*(3*d - 2)
Solve 6/7*r**2 - 216/7*r + 1944/7 = 0.
18
Let n(f) = f**2 - 12*f + 37. Let k be n(8). Let q(v) be the first derivative of 0*v + 0*v**4 - 3/4*v**2 - 4 + 1/4*v**6 - 3/5*v**k + v**3. Factor q(b).
3*b*(b - 1)**3*(b + 1)/2
Let i(u) be the second derivative of -2*u**2 - 5/3*u**4 - 1/2*u**5 + 0*u**6 - 5/2*u**3 + 0 + 1/42*u**7 - 9*u. Find c such that i(c) = 0.
-1, 4
Solve -74/13*t + 0 - 2/13*t**3 - 76/13*t**2 = 0.
-37, -1, 0
Let l(z) be the first derivative of -z**6/27 - 8*z**5/45 + 7*z**4/18 + 68*z**3/27 - 4*z**2/3 - 16*z + 89. Suppose l(b) = 0. What is b?
-3, -2, 2
Let n(d) = 4*d**5 + 2*d**4 - d**2 - d + 2. Let l(y) = -y**5 + 2*y**4 - y**3 - y**2 + y - 2. Let v(b) = -l(b) - n(b). Determine i so that v(i) = 0.
-1, 0, 2/3
Determine t, given that 1/3*t + 5 - 1/3*t**3 - 5*t**2 = 0.
-15, -1, 1
Solve 0*s**3 - 9/2*s**2 + 8*s + 1/4*s**4 - 15/4 = 0.
-5, 1, 3
Let r(d) be the second derivative of 0*d**4 + 1/2*d**5 + 5*d - 3*d**2 + 0 + d**3. Let v(z) = -z**3 - z + 1. Let c(f) = -r(f) - 6*v(f). Factor c(w).
-4*w**3
Let h = 5420022/457 - 11860. Let v = 3638/4113 + h. Factor -v*l - 2/9*l**2 - 2/3.
-2*(l + 1)*(l + 3)/9
Let b(r) be the first derivative of -20*r**6/3 + 9*r**5 + 35*r**4/4 - 15*r**3 + 5*r**2/2 + 120. Suppose b(x) = 0. Calculate x.
-1, 0, 1/8, 1
Let n(o) = 3*o**3 - 15*o**2 - 3*o - 9. Let t(x) = x**3 - x**2 + x - 1. Let r(y) = n(y) - 6*t(y). Factor r(i).
-3*(i + 1)**3
Find r such that -20/21*r**2 + 12/7 - 40/21*r**3 + 2*r - 16/21*r**4 - 2/21*r**5 = 0.
-3, -2, -1, 1
Let l be 54/13 - ((-252)/52 + 5). Let m(g) be the second derivative of 0*g**2 + 1/9*g**3 - 1/36*g**l - 1/60*g**5 - 4*g + 0. Factor m(s).
-s*(s - 1)*(s + 2)/3
Let f(b) be the second derivative of b**4/4 + b**3/2 - 15*b**2/2 - 13*b. Let o(y) = -1. Let n(x) = f(x) - 15*o(x). Suppose n(z) = 0. Calculate z.
-1, 0
Let w(v) be the second derivative of -v**7/15 + 4*v**6/15 - 2*v**5/25 - 11*v**4/15 + 11*v**3/15 + 2*v**2/5 + 24*v - 2. Suppose w(t) = 0. What is t?
-1, -1/7, 1, 2
Suppose -150*a + 6 = -153*a. Let h be ((-3)/9)/(3/a). Factor h*d**2 + 0 - 2/9*d.
2*d*(d - 1)/9
Let q = -94 + 100. Let z(x) be the second derivative of -1/30*x**q + 1/6*x**4 - 1/2*x**2 - 6*x + 0*x**3 + 0*x**5 + 0. Find h, given that z(h) = 0.
-1, 1
Let t(j) = -j**3 + 5. Let q be t(0). Suppose -g + 0*g = -q. Solve -c + 6*c**3 + 10*c**5 - 2*c**5 - 8*c**4 - 5*c**g = 0 for c.
-1/3, 0, 1
Let o = 935/3 - 307. Solve -16/3*c + o*c**3 - 2/