 + 1)/3
Let n = -62 - -249/4. Let l = -207/4 - -52. Factor n*k**2 + 0 + 0*k**3 - l*k**4 + 0*k.
-k**2*(k - 1)*(k + 1)/4
Let v be 1/(0 - 3/(-51)). Let y = -12 + v. Solve 139/3*z**3 - 97/3*z**2 + 32/3*z + 25/3*z**y - 95/3*z**4 - 4/3 = 0.
2/5, 1
Let n = -1/73 - -221/146. Let -1/2*o**3 + n*o**2 - 3/2*o + 1/2 = 0. What is o?
1
Let v(f) = -4*f**4 + 5*f**3 - 4*f**2 + f - 3. Let b(z) = 5*z**4 - 5*z**3 + 6*z**2 - 2*z + 2. Let g(t) = -5*b(t) - 6*v(t). Factor g(i).
-(i - 1)*(i + 2)**3
Let g be 1/2*(1 + (-3)/5). Let h(n) be the second derivative of -n + 0 - 2/3*n**3 + 1/2*n**4 + 1/2*n**2 - g*n**5 + 1/30*n**6. Find s, given that h(s) = 0.
1
Let w(k) be the second derivative of k**7/168 + k**6/40 + 3*k**5/80 + k**4/48 + 38*k. Factor w(d).
d**2*(d + 1)**3/4
Suppose 9*f - 13*f = -8. Let -2/5*j**f - 8/5 + 8/5*j = 0. What is j?
2
Suppose -5*j + 8 = -7. Suppose 0*f = f - 2*h + j, 0 = -3*f + 2*h + 7. Factor -1/2*y**4 + 1/2*y**f + 0*y**3 + 0 + 0*y**2 + 0*y.
y**4*(y - 1)/2
Let z(a) be the first derivative of a**3/24 - a/8 + 1. What is k in z(k) = 0?
-1, 1
Let z(f) = f**3 - f**2 + 2. Let q be z(0). Let l(v) be the second derivative of -4/9*v**2 - 4/27*v**3 - q*v - 1/54*v**4 + 0. Factor l(s).
-2*(s + 2)**2/9
Let i(f) be the first derivative of 1/5*f**2 + 4/5*f - 1 - 2/15*f**3. Factor i(w).
-2*(w - 2)*(w + 1)/5
Factor 27/7*q + 3/7*q**2 - 30/7.
3*(q - 1)*(q + 10)/7
Let q(z) = -z**2 + 2*z + 2. Let l be q(0). Suppose -l*a - 3*x = 6, 9 = -a - 4*x + x. Suppose 0*u + 2/5*u**a + 6/5*u**2 - 8/5 = 0. What is u?
-2, 1
Factor s**3 - 7*s**5 + 3*s**3 - s**3 + 4*s**2 - 4*s + 6*s**5 - 2*s**4.
-s*(s - 1)**2*(s + 2)**2
Let s(l) be the third derivative of 0 + 1/60*l**6 + 1/3*l**3 - 1/30*l**5 - 1/12*l**4 + 2*l**2 + 0*l. Factor s(j).
2*(j - 1)**2*(j + 1)
Let v(o) be the second derivative of 11*o**4/12 - o**3 - 17*o**2/2 + 5*o. Let s(u) = 16*u**2 - 9*u - 25. Let m(k) = -5*s(k) + 7*v(k). What is n in m(n) = 0?
-1, 2
Let d(n) be the second derivative of -1/6*n**4 - 2*n**2 + 0 - n**3 + 2*n. Let d(j) = 0. Calculate j.
-2, -1
Let d(v) be the first derivative of 4*v**5/5 - v**4/2 - 4*v**3 + 7*v**2 - 4*v + 2. Determine g, given that d(g) = 0.
-2, 1/2, 1
Suppose 25 = -2*q + 7*q. Let t = q - 3. Factor 2*c**4 + 0*c**3 - 4*c**3 + t*c**3.
2*c**3*(c - 1)
Let f(o) be the first derivative of 2*o**5/15 - o**4/12 - o**3/9 - 1. Factor f(t).
t**2*(t - 1)*(2*t + 1)/3
Let j(r) be the first derivative of r**6/75 + r**5/50 - r**4/30 - r**3/15 - 2*r - 1. Let f(n) be the first derivative of j(n). Suppose f(h) = 0. Calculate h.
-1, 0, 1
Suppose 0 = k - 4*t - 17, -5*k - t + 1 = -0. Let v(y) be the first derivative of 8/3*y - k - 14/9*y**3 + 4*y**2. Solve v(n) = 0 for n.
-2/7, 2
Let x be 12/2*(-8)/(-12). Suppose 0 = -d + 4*o - 2 + 1, x*o - 7 = -d. Determine w so that -4/7 - 2/7*w**2 + 2*w + 6/7*w**4 - 2*w**d = 0.
-1, 1/3, 1, 2
Let o(k) = 2*k**2 + 13*k + 6. Let v be o(-6). Let j(a) be the third derivative of v*a + a**2 + 0*a**4 - 1/30*a**5 + 0 - 1/60*a**6 + 0*a**3. Solve j(y) = 0.
-1, 0
Let n be 4/(-6) - 28/(-15). Let h(c) = -22*c - 86. Let r be h(-4). Determine v, given that 3/5 + 0*v**3 + 0*v - n*v**r + 3/5*v**4 = 0.
-1, 1
Let k be 2/3 - (-16)/(-24). Let r(w) be the second derivative of 0*w**2 + 1/63*w**7 - 1/18*w**4 + k - w - 1/30*w**5 + 0*w**3 + 1/45*w**6. Factor r(q).
2*q**2*(q - 1)*(q + 1)**2/3
Let y(g) be the first derivative of -g**4/36 + g**2/6 + 3*g - 2. Let z(s) be the first derivative of y(s). Factor z(p).
-(p - 1)*(p + 1)/3
Let j(r) = 2*r**3 - 2*r**3 - 6 + 6*r**2 + 6*r**3 - 2*r - 4*r. Let w(s) = s**3 + s**2 - s - 1. Let c(x) = -j(x) + 3*w(x). Factor c(z).
-3*(z - 1)*(z + 1)**2
Let j(k) be the second derivative of -k**5/30 + k**4/18 + k**3/9 - k**2/3 + 3*k. Solve j(z) = 0.
-1, 1
Let n = 3 - -4. Find u, given that 7 + u**3 - n + 3*u - 2*u**3 + 2 = 0.
-1, 2
Let q(i) be the third derivative of i**6/420 + i**5/70 + i**4/28 + i**3/21 - 2*i**2. Factor q(z).
2*(z + 1)**3/7
Suppose 5*d - 5*u = -10, -30 = -5*d + 3*u - 6*u. Factor -1/3*f + 2*f**d + f**5 + 0*f**2 + 0 + 8/3*f**4.
f*(f + 1)**3*(3*f - 1)/3
Suppose 4*c = -4*j + 8, -52 = -4*c + 3*j - 23. Suppose -c*z - 3*w = -5*w, 3*z - w - 1 = 0. What is h in -12 - 2*h**2 - 3*h - h**z - 9*h = 0?
-2
Let i(f) be the first derivative of f**4/18 - 4*f**3/27 + 64. Factor i(p).
2*p**2*(p - 2)/9
Let x = 10 + -10. Let h(c) be the third derivative of 0*c**5 + c**2 - 1/12*c**4 + 0*c**7 + x*c**3 + 0*c + 0 + 1/30*c**6 - 1/168*c**8. Factor h(n).
-2*n*(n - 1)**2*(n + 1)**2
Let a(o) be the second derivative of -o**4/42 + 2*o**3/21 + 3*o**2/7 + 23*o - 1. Factor a(y).
-2*(y - 3)*(y + 1)/7
Let c(i) = -14*i + 1. Let y be c(-1). Let k be 36/y + (-2)/5. Factor 5*s**2 + k + 9*s + 0 - s - s.
(s + 1)*(5*s + 2)
Determine f, given that 2/5*f + 0 + 1/5*f**2 - 36/5*f**3 = 0.
-2/9, 0, 1/4
Let l be (-2)/108*(-21)/14. Let o(i) be the second derivative of -2*i + 0 + 1/6*i**2 - l*i**4 + 0*i**3. Let o(v) = 0. Calculate v.
-1, 1
Let y(a) be the second derivative of 19/12*a**6 - 25/84*a**7 + 0 - 139/40*a**5 + a**2 + 97/24*a**4 - 8/3*a**3 + a. Factor y(n).
-(n - 1)**3*(5*n - 2)**2/2
Factor 5 - 5 + 4*p**4 - 4*p**2 + 4*p**3 - 4*p**5.
-4*p**2*(p - 1)**2*(p + 1)
Let y = -3/4 - -19/20. Let i(n) be the second derivative of 2*n + 0 + 1/75*n**6 + 2/25*n**5 + 4/15*n**3 + y*n**2 + 1/5*n**4. Determine z, given that i(z) = 0.
-1
Suppose -4*i = -0*i - i. Factor 0 + 0*o**2 - 1/3*o**3 + 1/3*o**5 + 0*o + i*o**4.
o**3*(o - 1)*(o + 1)/3
Let g(m) be the second derivative of -m**7/21 - 2*m - 1. Suppose g(d) = 0. What is d?
0
Solve -242/17*y**2 - 72/17 - 10/17*y**4 + 264/17*y + 84/17*y**3 = 0.
2/5, 2, 3
Let v(o) = o**3 - o**2 + 1. Let z(k) = 8*k**3 - 14*k**2 - 2*k + 10. Let u(y) = -10*v(y) + z(y). Let u(r) = 0. Calculate r.
-1, 0
Let t be (7/(-5))/(1/(-2)). Let g(w) = -18*w - 648. Let n be g(-36). Factor 4/5*p + n - t*p**2.
-2*p*(7*p - 2)/5
Let q = -1266/5 - -254. Factor -q + 0*s + 1/5*s**2.
(s - 2)*(s + 2)/5
Factor -6*l**2 + 11*l**2 + 21*l**2 + 12*l + 4*l**3.
2*l*(l + 6)*(2*l + 1)
Let n(z) = 27*z**4 - 20*z**3 + 3*z**2 + 2*z - 2. Let t(c) = 27*c**4 - 21*c**3 + 3*c**2 + 3*c - 3. Let r(h) = -3*n(h) + 2*t(h). Find d, given that r(d) = 0.
0, 1/3
Let y(t) = t**2 - 6*t + 10. Let c be y(4). Let k(l) be the second derivative of -1/8*l**4 - l + 1/8*l**5 - 5/12*l**3 + 1/15*l**6 - 1/4*l**c + 0. Factor k(g).
(g - 1)*(g + 1)**2*(4*g + 1)/2
Let g(n) be the first derivative of -1/22*n**4 - 2 - 2/11*n - 3/11*n**2 - 2/11*n**3. Determine q, given that g(q) = 0.
-1
Let w(d) be the first derivative of -2*d**6/9 - 22*d**5/15 - 23*d**4/6 - 46*d**3/9 - 11*d**2/3 - 4*d/3 - 5. Find s such that w(s) = 0.
-2, -1, -1/2
Let n(o) = -o**2 + 6*o + 9. Let d be n(7). Suppose 0 = -d*w - w. Factor w*b**2 - 8*b**3 + 20*b**4 - 10*b**3 + 4*b**2.
2*b**2*(2*b - 1)*(5*b - 2)
Suppose 0 = 54*j - 55*j. Let u(d) be the second derivative of j*d**2 - 1/50*d**5 + 0*d**4 + 1/15*d**3 - 3*d + 0. Factor u(k).
-2*k*(k - 1)*(k + 1)/5
Let w(l) = -l**2 + 4*l + 2. Let u be w(4). Factor -4*k**3 - 14*k**5 + 0*k**4 + 5*k**4 + 6*k**5 - u*k**2 + 9*k**4.
-2*k**2*(k - 1)**2*(4*k + 1)
Suppose -5*m + 4*a = 9, 3*m = 5*a + 1 - 9. Let y be -1*(m*2)/1. Let -2*j**y - j**4 + j**3 + j**2 - 3*j**3 = 0. What is j?
-1, 0
Factor 23/3*r**4 + 0 + 4/3*r**5 + 14*r**3 + 20/3*r**2 - 8/3*r.
r*(r + 2)**3*(4*r - 1)/3
Let j(p) be the second derivative of -p**5/5 - 4*p**4/3 - 10*p**3/3 - 4*p**2 + p. Let j(x) = 0. What is x?
-2, -1
Suppose t + 4 = 2*k, 0*t + 4*k - 2 = 5*t. Factor -1/4*x**3 + 1/2 - 3/4*x**t + 1/4*x**4 + 1/4*x.
(x - 2)*(x - 1)*(x + 1)**2/4
Suppose 3*r = -8*r + 22. Let g(z) be the third derivative of 1/66*z**5 - 1/660*z**6 + 4/33*z**3 - 4*z**r + 0 + 0*z - 2/33*z**4. Suppose g(v) = 0. What is v?
1, 2
Let w(d) = 35*d**4 - 94*d**3 + 84*d**2 - 29*d + 4. Let a(y) = -35*y**4 + 94*y**3 - 83*y**2 + 28*y - 4. Let k(v) = 3*a(v) + 4*w(v). Suppose k(t) = 0. What is t?
2/7, 2/5, 1
Suppose 2*w = w + 3*n + 9, 4*n = -5*w - 12. Let m(p) be the first derivative of -2/5*p**5 + 0*p - 1/2*p**4 + w*p**2 + 0*p**3 + 1. Let m(o) = 0. What is o?
-1, 0
Let t(z) be the second derivative of -z**7/630 + z**5/90 - z**3/18 + z**2 + 4*z. Let k(x) be the first derivative of t(x). Factor k(o).
-(o - 1)**2*(o + 1)**2/3
Factor -1/2*i**3 + 0 + i - 1/2*i**2.
-i*(i - 1)*(i + 2)/2
Suppose 0 = -2*r + 5*t - t + 4, 0 = 5*t. Determine c so t