*3 = 0.
-1, 0, 1
Suppose 14*p = 11*p + 6. Factor 0 - 1/3*z**p - 2/3*z.
-z*(z + 2)/3
Suppose -3*z + 10 = 2*z. Let b be ((-1)/2)/(z/(-12)). Find r, given that -b*r + r + 2*r**3 + 2 - 2*r**2 + 0 = 0.
-1, 1
Let u(t) be the third derivative of -t**8/672 - t**7/140 - t**6/120 + t**5/60 + t**4/16 + t**3/12 + 11*t**2. Determine n so that u(n) = 0.
-1, 1
Let a = -27 + 27. Let d(s) be the third derivative of a - 4/525*s**7 - 1/60*s**4 - 1/50*s**6 + 4*s**2 + 0*s - 2/75*s**5 + 0*s**3 - 1/840*s**8. Solve d(v) = 0.
-1, 0
Let o(c) be the third derivative of 0*c + 0*c**4 + 1/45*c**5 + 0*c**3 + 0 - 2*c**2 + 1/15*c**6 - 7/144*c**8 + 1/30*c**7. What is a in o(a) = 0?
-2/7, 0, 1
Let w(f) be the third derivative of f**8/1176 - f**7/245 + f**6/210 + f**5/105 - f**4/28 + f**3/21 + 7*f**2. Factor w(l).
2*(l - 1)**4*(l + 1)/7
Suppose -23*d + 50 = -42. Let 9/5*u**d + 9/5*u**5 - 13/5*u**2 + 4/5*u + 4/5 - 13/5*u**3 = 0. Calculate u.
-1, -2/3, 2/3, 1
Suppose -2*g + 4 = 3*t, -5*t + 0*t = g - 16. Let w be t/8 - (-3)/(-14). Suppose 20/7*l**5 - 2/7*l**2 - w*l**4 + 4/7 + 2*l - 34/7*l**3 = 0. Calculate l.
-1, -1/2, -2/5, 1
Suppose 3*k = 5*g - 8 + 23, 2*k - 10 = -g. Factor -4/5*t**5 - 6/5*t**4 + g*t**2 + 0 + 0*t - 2/5*t**3.
-2*t**3*(t + 1)*(2*t + 1)/5
Let i(x) be the third derivative of -x**8/3360 + x**7/420 - x**6/144 + x**5/120 - 2*x**3/3 - 5*x**2. Let t(g) be the first derivative of i(g). Factor t(f).
-f*(f - 2)*(f - 1)**2/2
Suppose 2/7*m**3 + 2/7*m**4 + 0*m**2 + 0*m + 0 = 0. What is m?
-1, 0
Let s be 6/(-3 - -4 - 2). Let r be (-2)/11 + s/(-33). Determine b so that 0*b + 2/3*b**2 + r = 0.
0
Let y be (-6)/2 - 27/(-3). Factor -3*u**2 + 0*u + y*u - 3 + 3.
-3*u*(u - 2)
Let x be 2*(4 - (-124)/(-32)). Factor x*v**2 + 0 + 1/4*v.
v*(v + 1)/4
Let b be 2 - 2 - -8 - (61 - 56). Determine u, given that 3*u + 1 - 3/4*u**4 + 5/4*u**5 - 17/4*u**b - 1/4*u**2 = 0.
-1, -2/5, 1, 2
Suppose -t + 3 = 4*q - 0, -q - 23 = 5*t. Let p(z) be the second derivative of -1/12*z**4 + 0*z**q + 1/6*z**3 + z + 0. Factor p(a).
-a*(a - 1)
Suppose w = f + 2*w - 4, 2*f - 3*w = 13. Suppose -f*i + 7*i = 0. Determine t so that -4/3*t**3 - t**4 + 0 + i*t - 1/3*t**2 = 0.
-1, -1/3, 0
Let o(c) be the second derivative of 1/15*c**6 + 0*c**2 - 1/2*c**4 - 2/3*c**3 + 0*c**5 + 0 - 5*c. Find z, given that o(z) = 0.
-1, 0, 2
Let z(j) = -j**3 + 6*j**2 - 4*j + 2. Let s(y) = -2*y**3 + 13*y**2 - 10*y + 5. Let o(h) = -2*s(h) + 5*z(h). Suppose o(p) = 0. What is p?
0, 4
Let l(w) = -2*w - 1. Let h be l(-2). Let c = h + -2. Factor c - 1 + 2*q**2.
2*q**2
Suppose -3*u + 5*w = -29, 3*u + w + 11 = -4*w. Let h be (-3)/(-9) + -5 + 5. What is d in -1/3*d**u + 1/3*d**5 + 1/3*d**2 + 0*d + 0 - h*d**4 = 0?
-1, 0, 1
Suppose 0 = 2*b + 3*k, b - 3 = 3*k + 6. Factor 2*z + 6*z**b - 5*z**2 - 6*z + 3*z + 2*z**3 + 48*z**4.
z*(3*z - 1)*(4*z + 1)**2
Let x(f) = -9*f**5 + 48*f**4 - 98*f**3 + 88*f**2 - 41*f + 4. Let i(y) = -y**3 - y**2 - y - 1. Let r(h) = 2*i(h) - x(h). Factor r(j).
3*(j - 2)*(j - 1)**3*(3*j - 1)
Suppose -y + 23 = -5*q, 2*q = -4*y + 4*q + 20. Factor 2 - 3*f**3 - 5*f**2 + 2*f**2 + 3*f**4 + y*f - 2.
3*f*(f - 1)**2*(f + 1)
Let l(a) be the first derivative of 4 - 3*a**3 - 5/4*a**4 + 0*a + 7/6*a**6 + 9/5*a**5 - a**2. Factor l(t).
t*(t - 1)*(t + 1)**2*(7*t + 2)
Let q(z) be the first derivative of -z**4/6 + 4*z**3/3 - 4*z**2 + 2*z + 5. Let l(w) be the first derivative of q(w). Factor l(k).
-2*(k - 2)**2
Let t(s) be the second derivative of 3*s - 1/6*s**4 + 4/3*s**3 - 4*s**2 + 0. What is k in t(k) = 0?
2
Let d(i) be the second derivative of 3*i**5/140 + 3*i**4/28 - 3*i**3/7 - 12*i**2/7 + 11*i. Factor d(f).
3*(f - 2)*(f + 1)*(f + 4)/7
Let w = -22 - -14. Let q(v) = v**5 - 3*v**4 + 2*v**3 - v**2 + 1. Let j(z) = -3*z**5 + 9*z**4 - 6*z**3 + 2*z**2 + z - 3. Let i(t) = w*q(t) - 3*j(t). Factor i(p).
(p - 1)**4*(p + 1)
Let b(j) be the third derivative of j**7/105 + j**6/30 - j**5/6 - j**4/2 + 21*j**2. Determine a, given that b(a) = 0.
-3, -1, 0, 2
Let q be 4*(1/2 - -1). Let b(d) = -d**2 + 8*d + 4. Let f be b(q). Suppose 5*j**2 - 18*j**3 - 10 + 14 + f*j - 7*j**3 = 0. Calculate j.
-2/5, 1
Let o(c) be the second derivative of 3*c**5/140 - c**4/28 - c**3/7 - 6*c. Find z, given that o(z) = 0.
-1, 0, 2
Let l(k) be the third derivative of k**7/385 + 2*k**6/165 + k**5/330 - 2*k**4/33 - 4*k**3/33 + 10*k**2. Let l(p) = 0. What is p?
-2, -1, -2/3, 1
Let l be 9 + -12 - (-141)/58. Let x = -2/29 - l. Suppose 1/2*w**3 - 1/4*w - 1/4*w**5 - 1/4*w**4 - 1/4 + x*w**2 = 0. Calculate w.
-1, 1
Let n(t) be the third derivative of t**7/252 - t**6/60 + t**5/40 - t**4/72 + 12*t**2. Factor n(g).
g*(g - 1)**2*(5*g - 2)/6
Determine h so that -3/7*h**2 - 3/7*h + 0 = 0.
-1, 0
Let s = 222 + -220. Factor -1/3*u**4 - 4/3 - 13/3*u**2 + s*u**3 + 4*u.
-(u - 2)**2*(u - 1)**2/3
Let 0 - 14/5*i**5 + 6/5*i**3 + 17/5*i**4 - 2/5*i - 7/5*i**2 = 0. Calculate i.
-1/2, -2/7, 0, 1
Suppose 0*u - 7 = 2*t - 5*u, -t - 2*u = -10. Let k(d) be the third derivative of 3/2*d**3 + t*d**2 + 0*d - 1/20*d**5 - 1/4*d**4 + 0. Factor k(c).
-3*(c - 1)*(c + 3)
Let d(z) be the second derivative of -z**8/5880 - z**7/980 - z**6/420 - z**5/420 + z**3/3 - z. Let y(a) be the second derivative of d(a). Solve y(r) = 0 for r.
-1, 0
Let x be 5/14*594/55. Find p, given that 3/7*p**2 + x - 18/7*p = 0.
3
Let x(f) be the second derivative of f**5/300 + f**4/30 + 2*f**3/15 - 3*f**2/2 + 2*f. Let y(k) be the first derivative of x(k). Factor y(z).
(z + 2)**2/5
Let p(g) be the first derivative of 1/480*g**5 + 0*g**2 + 4 - 1/1440*g**6 + 0*g**4 + 0*g - 4/3*g**3. Let w(k) be the third derivative of p(k). Factor w(m).
-m*(m - 1)/4
Suppose -5*o = 1 - 16. Suppose -2*g + 1 = -o. Factor -1/3*p - 1/3 + 1/3*p**3 + 1/3*p**g.
(p - 1)*(p + 1)**2/3
Let h(b) be the second derivative of -b**4/21 + 4*b**3/7 - 18*b**2/7 - 12*b. Factor h(q).
-4*(q - 3)**2/7
Let o(l) be the second derivative of l**2 + 0 + 1/42*l**4 - l - 1/21*l**3 - 1/210*l**5. Let d(p) be the first derivative of o(p). Solve d(v) = 0.
1
Let f = -5833/13 + 449. Let t = f + 14/39. Factor 8/3*i + 8/3 + t*i**2.
2*(i + 2)**2/3
Let o = -1 - -1. Suppose o = 4*q + q. Let 1/4*v**2 + q - 1/4*v = 0. What is v?
0, 1
Let q(b) be the first derivative of -b**6/9 + 2*b**5/15 + b**4/6 - 2*b**3/9 - 20. Factor q(v).
-2*v**2*(v - 1)**2*(v + 1)/3
Let l = 251 - 249. Factor -146/3*h**3 - 2/3 - 86/3*h**l - 22/3*h - 112/3*h**4 - 32/3*h**5.
-2*(h + 1)**3*(4*h + 1)**2/3
Suppose -5 = 5*n, -2*u - 45*n + 41*n + 4 = 0. Determine l so that 1/7*l**3 - 1/7*l - 3/7*l**2 + 1/7*l**u + 2/7 = 0.
-2, -1, 1
Suppose a - 2*a - 7 = -3*o, -2*a = 4*o - 6. Let p(c) be the third derivative of 1/9*c**3 + 0*c - o*c**2 + 1/180*c**5 + 0 + 1/24*c**4. Solve p(x) = 0.
-2, -1
Let s(y) = -4*y**2 + 3*y + 4. Let a be s(3). Let m = -23 - a. Suppose m*n**3 + 0 + 0*n + 1/2*n**4 - 1/2*n**2 = 0. What is n?
-1, 0, 1
Let h(i) = -40*i**5 + 41*i**3 - i**2. Let d(p) = -8*p**5 + 8*p**3. Let u(s) = -22*d(s) + 4*h(s). Find a such that u(a) = 0.
-1/2, 0, 1
Let t(n) = n**3 + 5*n**2 + 3*n - 4. Let p be t(-4). Determine v, given that 1/4*v**2 + p*v + 0 = 0.
0
Suppose 5*y = t + 3*t - 53, 0 = 4*t - 3*y - 43. Factor -n**3 + 7 - t - n**2.
-n**2*(n + 1)
Suppose 4*d + 12 = -12. Let b be -6*((-4)/d - 1). Solve p - 2*p**b - 3*p + 4*p - 3*p - p**3 = 0.
-1, 0
Let d(a) be the first derivative of -55*a**4 - 172*a**3/3 + 32*a**2 + 16*a + 6. Solve d(x) = 0.
-1, -2/11, 2/5
Let f(r) be the second derivative of -r**4/54 + r**3/27 + 2*r**2/9 + 8*r. Factor f(j).
-2*(j - 2)*(j + 1)/9
Let v = 2/21 + -1/35. Let m(k) be the second derivative of 1/6*k**4 + 2*k + v*k**6 + 0*k**3 + 1/5*k**5 + 0 + 0*k**2. Suppose m(w) = 0. Calculate w.
-1, 0
Suppose 0 = -2*n + d + 20, 0*n = 5*n - 3*d - 49. Factor -2*i**4 + 11*i + 2*i**2 - n*i.
-2*i**2*(i - 1)*(i + 1)
Let c(w) = w**2 - 8*w + 2. Let m be c(8). Solve t - 3*t + 0*t + 2*t**m = 0 for t.
0, 1
Let t(g) be the third derivative of -g**6/30 + g**5/3 - 4*g**4/3 + 8*g**3/3 - 24*g**2. Determine c, given that t(c) = 0.
1, 2
Let z(r) be the second derivative of r**4/96 - r**3/16 + r**2/8 + 15*r. Find o, given that z(o) = 0.
1, 2
Suppose 0*k = -k + 2. Let u be 1 - (k + -3 - 1). Let 0*c**u + 4/3*c**2 - 2/3*c**4 - 2/3 + 0*c = 0. Calculate c.
-1, 1
Let k = 7 - 5. Factor -2*h + h**3 - k*h - 2*h**2 + 5*h.
h*(h - 1)**2
Let d(l) = -20*l**3 + 12*l**2 + 24*l. Let m(t) = -7