*n. Let r(y) be the second derivative of o(y). Factor r(t).
2*t**3*(t - 1)*(t + 3)/9
Suppose 0 = -0*n + 4*n - 12. Find d such that -4*d**4 + 5*d**4 + 0*d**3 - 4*d**n + 3*d**3 = 0.
0, 1
Let c(v) be the first derivative of v**4/2 - 2*v**3 + 8*v - 9. Determine m so that c(m) = 0.
-1, 2
Let q(p) = 3*p. Let h be q(-8). Let j be 18/h - 79/(-20). Factor j*s + 8/5 + 2*s**2 + 2/5*s**3.
2*(s + 1)*(s + 2)**2/5
Let g be 1/(-2) - 18*(-4)/16. Factor -2*t**3 - 1/5 - t - 1/5*t**5 - 2*t**2 - t**g.
-(t + 1)**5/5
Let i be 7*(30/14 + -3). Let l = 6 + i. Factor 0*d**2 + 0*d + 1/2*d**3 + l.
d**3/2
Let x be 1/(3/(-6)) - -4. Let r be -1 + 2/2 + x. Factor 8*w**r - w - w + 0*w.
2*w*(4*w - 1)
Let b be 13/12 + 6/(-8). Let z = -8 + 8. Suppose 0*n - b*n**2 + z = 0. Calculate n.
0
Let x(i) be the third derivative of i**8/1680 + i**7/525 + i**6/600 + 2*i**2. Determine y, given that x(y) = 0.
-1, 0
Let i(p) be the first derivative of p**7/1260 - p**5/180 - p**3/3 + 4. Let n(u) be the third derivative of i(u). Factor n(d).
2*d*(d - 1)*(d + 1)/3
Let c(q) = -q**3 + 9*q**2 + 12*q - 16. Let i be c(10). Let n(g) be the third derivative of -g**2 + 0*g**3 + 0 - 1/36*g**i + 0*g + 1/180*g**5. Factor n(t).
t*(t - 2)/3
Let h(u) be the first derivative of 2*u**6/3 - 4*u**5/5 - 6*u**4 + 14. Let h(i) = 0. Calculate i.
-2, 0, 3
Factor 11*b**3 - 24*b**3 - 15*b**2 - 125 + 14*b**3 + 75*b.
(b - 5)**3
Let d(p) = p**3 + 3*p**2 - 7*p - 1. Let y be d(-3). Let o = y - 79/4. Factor -1/2*q + 1/4*q**2 - o + 1/2*q**3.
(q - 1)*(q + 1)*(2*q + 1)/4
Suppose 4*t - 3*y = 8*t - 3, -2*y = t + 3. Let x(k) be the second derivative of -k + 0 + 9*k**2 + 2*k**t + 1/6*k**4. Determine l, given that x(l) = 0.
-3
Suppose 5*d = d. Let g(k) be the first derivative of d*k - 1/12*k**3 + 2 + 1/8*k**2. Factor g(y).
-y*(y - 1)/4
Suppose 0 = -2*o + 6 + 4. Suppose 2 - 11 = -3*x. Solve -x*f**2 + 2*f**3 + f**5 + o*f**2 - 3*f + 2*f**4 + 1 - 5*f**4 = 0 for f.
-1, 1
Let a(u) = u**4 - u**3 + u**2 + 1. Let g(d) = -4*d**2 - 2*d**2 - 4*d**4 - d - 3 + 0*d. Let j(c) = 3*a(c) + g(c). Let j(t) = 0. What is t?
-1, 0
Let o(t) = t**3 - 3*t**2 - 2*t + 2. Let k(j) = -2*j**3 + 3*j**2 + 2*j - 3. Let b(f) = 2*k(f) + 3*o(f). Factor b(z).
-z*(z + 1)*(z + 2)
Let t(x) = x**2 - 14*x - 9. Let h be t(15). Let i = h - 6. Solve 0 + i*r**2 - 2/5*r**3 + 2/5*r = 0 for r.
-1, 0, 1
Let k = 18 + -25. Let t be 64/28 + 2/k. Factor 7*l - 6*l**2 + 8*l**t - 2 - 4*l**2 - 3*l**3.
-(l - 1)*(l + 2)*(3*l - 1)
Factor -12*m**4 - 21*m + 2*m**3 - 6*m**3 + 5*m + 32*m**2.
-4*m*(m - 1)*(m + 2)*(3*m - 2)
Let s(f) be the third derivative of 1/18*f**3 + 1/90*f**6 + 0*f + 1/18*f**4 + 0 - 2*f**2 + 1/630*f**7 + 1/30*f**5. Factor s(l).
(l + 1)**4/3
Suppose 5*z = 2*b + 4 + 5, -z - 3 = -2*b. Suppose 5*p - 6*p + z*p**2 - 3*p - p**2 = 0. What is p?
0, 2
Let c = -456 - -2741/6. Factor 0 - 5/6*r**2 - 1/3*r + c*r**4 + 1/3*r**3.
r*(r - 1)*(r + 1)*(5*r + 2)/6
Factor 4*x**4 - 3*x**4 + 3*x**5 + 6*x**2 - 3*x - x**4 - 6*x**4.
3*x*(x - 1)**3*(x + 1)
Let t = -5125 - -46171/9. Let w = -40/9 + t. Factor 1/3*i + 1/3*i**3 + w*i**2 + 0.
i*(i + 1)**2/3
Let d(r) be the third derivative of 0*r**3 - 1/30*r**6 - 1/12*r**4 + 0 - 7*r**2 + 1/56*r**8 + 4/105*r**7 + 0*r - 2/15*r**5. Find k, given that d(k) = 0.
-1, -1/3, 0, 1
Let n(a) be the first derivative of 1/18*a**4 - 6 + 4/9*a + 0*a**3 - 1/3*a**2. Factor n(v).
2*(v - 1)**2*(v + 2)/9
Suppose -4*b = -6*b + 24. Suppose 22 - b = 2*z. Factor -1 - 1/2*a**z - a**2 - 2*a**3 + 5/2*a + 2*a**4.
-(a - 2)*(a - 1)**3*(a + 1)/2
Factor 2/15 - 4/15*x + 2/15*x**2.
2*(x - 1)**2/15
Let m be ((12 - 3)/3)/1. Factor -g**2 + 3*g**3 - g**3 - 3*g**2 + 0*g**m.
2*g**2*(g - 2)
Let r be 6 - ((0 - -8) + -3 + -1). Let 8/11*s - 8/11 - 2/11*s**r = 0. What is s?
2
Let j(t) = -t + 9. Let g = 9 - 0. Let p be j(g). Factor p*u - 2/3*u**4 - 4/9*u**3 + 2/9*u**2 + 0.
-2*u**2*(u + 1)*(3*u - 1)/9
Let a = -207919/30 - -6930. Let w = 1/6 - a. Suppose w*x**2 + 0 + 0*x - 2/5*x**3 = 0. What is x?
0, 2
Let c(a) be the first derivative of a**6/14 + 12*a**5/35 - 33*a**4/28 + 6*a**3/7 - 15. Determine u so that c(u) = 0.
-6, 0, 1
Determine v so that 100*v**4 - 102*v**4 + 5*v**3 - 3*v**2 + 9*v**2 + v**5 - 2*v**5 = 0.
-3, -1, 0, 2
Suppose -2*b + 37 = -5*k, -5*k - 2 = 3*b + 5. Let x be 15/1 - (-4 - -3). Let -m**2 - b*m + x*m**2 + 8*m**4 - 14*m**4 - 9*m**4 + 6*m**3 = 0. Calculate m.
-1, 0, 2/5, 1
Let s be -4 + 4 + -2 + 4. Let g(z) be the second derivative of 1/22*z**4 + 1/110*z**5 + 0 + 1/11*z**3 + z + 1/11*z**s. Factor g(c).
2*(c + 1)**3/11
Let c = -12 + 12. Let g(s) be the second derivative of 1/30*s**6 + 2*s - 1/24*s**3 + 5/48*s**4 + 0*s**2 - 1/10*s**5 + c. Determine r, given that g(r) = 0.
0, 1/2, 1
Let v(k) be the third derivative of -k**6/72 - k**5/6 - 5*k**4/24 + 25*k**3/9 + 18*k**2. Find d, given that v(d) = 0.
-5, -2, 1
Let w(z) = 9*z**4 + 21*z**3 + 15*z**2 - 3. Let a(k) = -18*k**4 - 41*k**3 - 29*k**2 + 6. Let f(l) = 3*a(l) + 7*w(l). Factor f(g).
3*(g + 1)**3*(3*g - 1)
Let j(v) be the third derivative of -1/6*v**3 + 0*v - 1/240*v**5 + 2*v**2 + 0 + 1/24*v**4. Suppose j(t) = 0. What is t?
2
Let s(z) be the first derivative of z**5/20 - 5*z**4/16 + 3*z**3/4 - 7*z**2/8 + z/2 + 4. Factor s(r).
(r - 2)*(r - 1)**3/4
Let p(l) be the third derivative of -l**7/525 + l**6/100 - l**5/75 - 22*l**2. Determine m so that p(m) = 0.
0, 1, 2
Let l(v) be the first derivative of -7*v**5/80 - 5*v**4/32 + v**3/4 - 3*v**2/2 + 2. Let r(u) be the second derivative of l(u). Factor r(q).
-3*(q + 1)*(7*q - 2)/4
Let h(y) = y. Suppose 0 = 4*a, 6 = -0*m + m + 4*a. Let j be h(m). Factor -10*c + 12*c**4 + j*c**4 - 42*c**3 + 2*c + 32*c**2.
2*c*(c - 1)*(3*c - 2)**2
Let q(y) be the first derivative of 8*y**5/45 - 7*y**4/18 - 4*y**3/27 + 15. Determine d so that q(d) = 0.
-1/4, 0, 2
Suppose l + 3 = 2*l. Factor 10*g**3 + l*g**2 - 11*g**3 - g**2 - g.
-g*(g - 1)**2
Suppose f - 4*f = 0. Let g(j) be the third derivative of -j**2 + 0 + 1/135*j**5 + 0*j**3 + 1/108*j**4 + f*j. Suppose g(r) = 0. Calculate r.
-1/2, 0
Let d(k) = -k + 5. Let u be d(4). Suppose 0 = -i + 2, u = q - 2*i. Suppose -2*f**5 + q*f**2 + 0*f**4 - 12*f**3 + 0*f**5 + 8*f**4 - 2*f + 3*f**2 = 0. What is f?
0, 1
Let c(k) be the third derivative of -k**6/45 - k**5/15 - k**4/12 + k**3/3 - 2*k**2. Let u(d) be the first derivative of c(d). Factor u(p).
-2*(2*p + 1)**2
Suppose 0 = -5*t - 29 + 84. Factor 13*d**2 + t*d**2 - 26*d**2 + d**3 + d.
d*(d - 1)**2
Let k be 1/3 + 5/3. Factor 0 - 2/3*c**k + 0*c + 2/9*c**3.
2*c**2*(c - 3)/9
Let z(u) be the first derivative of u**4 + 20*u**3/3 + 16*u**2 + 16*u + 2. Suppose z(d) = 0. Calculate d.
-2, -1
Let w be 21392/(-30) - (-14)/35. Let i = w - -719. Suppose -8/3*o + 1/3 + i*o**2 - 4*o**3 = 0. What is o?
1/4, 1/3, 1
Factor 7/4*u**4 - 7*u**2 + 2*u + 0 - 1/2*u**3.
u*(u - 2)*(u + 2)*(7*u - 2)/4
Factor -64*r**3 - 215*r + 207*r - 20*r**2 + 28*r**4 + 64*r**2.
4*r*(r - 1)**2*(7*r - 2)
Let l(f) be the third derivative of 2*f**2 + 0 + 0*f**3 + 1/60*f**6 + 1/210*f**7 + 0*f**4 + 1/60*f**5 + 0*f. Suppose l(v) = 0. What is v?
-1, 0
Factor 10/11*o**3 - 2/11*o**4 - 18/11*o**2 + 14/11*o - 4/11.
-2*(o - 2)*(o - 1)**3/11
Determine v so that 2/9*v**3 + 2*v**2 + 4/9*v + 0 - 8/3*v**4 = 0.
-2/3, -1/4, 0, 1
Let p = 4 + 7. Suppose -p = -3*t - 2. Let 0 - 2*d**2 - t - 2*d + 7 = 0. What is d?
-2, 1
Let d = 309 + -309. Factor 1/4*f**3 + 0 + d*f**2 + 0*f.
f**3/4
Let y(w) be the third derivative of -w**5/30 + w**4/12 - 4*w**3/3 + 2*w**2. Let p(m) = -2*m**2 + m - 9. Let z(n) = 4*p(n) - 5*y(n). Factor z(c).
2*(c - 2)*(c - 1)
Suppose -45 = 5*u - 15. Let b(c) = -2*c**4 - c**3 + 3*c**2 - 2*c - 4. Let n(l) = 3*l**4 + l**3 - 5*l**2 + 4*l + 7. Let f(g) = u*n(g) - 10*b(g). Factor f(i).
2*(i - 1)*(i + 1)**3
Let p(w) be the third derivative of -w**6/200 + w**5/20 - 7*w**4/40 + 3*w**3/10 + 4*w**2. Let p(q) = 0. What is q?
1, 3
Let i(m) be the third derivative of -m**5/510 - m**4/17 - 12*m**3/17 + 61*m**2. Factor i(f).
-2*(f + 6)**2/17
Let l(n) = n**3 + 4*n**2 + 2*n - 1. Let u be l(-2). Find r such that -3*r**2 - 11*r**4 - r**2 - u*r**4 - 18*r**3 = 0.
-1, -2/7, 0
Let n be -2*3/(-6) + 4. Suppose n*o + 0*o = 10. Suppose 10/7*p**o + 2*p**3 + 0 - 4/7*p = 0. Calculate p.
-1, 0, 2/7
Let n(x) be the second derivative of -2/33*x**3 + 0 - 1/66*x**4 - 1/11*x**2 + 4*x. Let n(a) = 0. What is a?
-1
Let h = 1