 Let w be f(3). Suppose -w = -s + 4*g, 3*g = 5*s - 1 - 2. Factor -1 + 1/4*d**3 + s*d + 3/4*d**2.
(d - 1)*(d + 2)**2/4
Let 6/7*c - 6/7*c**2 - 2/7 + 2/7*c**3 = 0. Calculate c.
1
Factor 0*v + 0 + 0*v**2 + 4/5*v**4 + 12/5*v**3.
4*v**3*(v + 3)/5
Find m, given that -17*m**4 + 14*m**3 + 7*m**4 + 2*m**2 - 4*m**2 - 6*m + 4*m**2 = 0.
-3/5, 0, 1
Suppose -2*c - 72 = 184. Let d = 642/5 + c. Factor -8/5 - d*b**2 + 8/5*b.
-2*(b - 2)**2/5
Let n(q) be the third derivative of -1/1008*q**8 + 0*q**3 + 0*q**4 + 0*q + q**2 + 0 - 1/360*q**6 + 1/315*q**7 + 0*q**5. Factor n(v).
-v**3*(v - 1)**2/3
Let v(a) be the third derivative of a**6/160 - a**5/20 + 3*a**4/32 + 15*a**2. Find q such that v(q) = 0.
0, 1, 3
Let p(v) be the third derivative of v**6/30 - v**4/6 + 9*v**2. Factor p(w).
4*w*(w - 1)*(w + 1)
Suppose q - i + 5*i = -66, 246 = -4*q + 2*i. Let p = -184/3 - q. Determine d, given that -2/3*d - p*d**2 + 0 = 0.
-1, 0
Solve 6*t**2 + 2/5 - 13/5*t - 32/5*t**3 - 3/5*t**5 + 16/5*t**4 = 0.
1/3, 1, 2
Let t(z) = 5*z**3 + z**2 - z - 1. Let d(l) = 9*l**3 + l**2 - l - 2. Let h(x) = -4*d(x) + 7*t(x). Factor h(s).
-(s - 1)**3
Let q(x) be the first derivative of 5*x**4/4 + 20*x**3/3 + 10*x**2 + 34. Factor q(t).
5*t*(t + 2)**2
Let k be (2/36)/((-20)/(-6)). Let o(p) be the third derivative of -1/30*p**5 - 2*p**2 + 0*p + 0 - 1/12*p**4 + k*p**6 + 1/3*p**3. Factor o(g).
2*(g - 1)**2*(g + 1)
Let d(c) be the first derivative of -10*c**3/21 - 18*c**2/7 + 16*c/7 - 11. Factor d(f).
-2*(f + 4)*(5*f - 2)/7
Let d be 3/4 + (-590)/40. Let z be (4/14)/((-6)/d). Factor -4/3*a + 0 + 2*a**2 - z*a**3.
-2*a*(a - 2)*(a - 1)/3
Let g(u) be the third derivative of 0*u**6 + 0*u**4 + 0 - 1/630*u**7 + 0*u + 0*u**3 - u**2 + 1/180*u**5. Find w such that g(w) = 0.
-1, 0, 1
Let a(i) = i**5 + i**4 - i**3 - i. Let x(c) = 8*c**5 + 6*c**4 - 26*c**3 + 40*c**2 - 36*c + 8. Let r(t) = 12*a(t) - 2*x(t). Let r(g) = 0. What is g?
-4, 1
Let q(u) = 1 + 9*u - 1 - 4*u**2 - 5 - 4. Let i(h) = -2*h**2 + 5*h - 5. Let x(y) = 7*i(y) - 3*q(y). Solve x(b) = 0.
2
Let n be 516/108 + 2/9. Suppose 0 = -5*d - 14 - 1, n*w + d = -3. Factor 0 + w*m - 3/5*m**2 - 3/5*m**3.
-3*m**2*(m + 1)/5
Factor -4/11*j**3 + 2/11*j**5 + 2/11 + 2/11*j + 2/11*j**4 - 4/11*j**2.
2*(j - 1)**2*(j + 1)**3/11
Let f(s) be the first derivative of -11*s**3/5 + 27*s**2/10 + 6*s/5 + 32. Factor f(d).
-3*(d - 1)*(11*d + 2)/5
Suppose 4*o + d - 22 = 34, 2*d - 28 = -2*o. Let h = o + -40/3. Factor -4/9 - 2/9*b**3 + 0*b**2 + h*b.
-2*(b - 1)**2*(b + 2)/9
Let d(k) = -k**5 - k**4 + k**3 + k - 1. Let h(f) = 5*f**5 - 4*f**4 + f**3 - 2*f + 2. Let u(x) = -2*d(x) - h(x). Suppose u(z) = 0. What is z?
0, 1
Find j, given that -24/5*j - 32/5 + 3/2*j**2 - 1/10*j**3 = 0.
-1, 8
Let r(j) be the second derivative of 1/48*j**4 + 0*j**5 + 0*j**2 + 0 - 1/120*j**6 + 3*j + 0*j**3. Factor r(a).
-a**2*(a - 1)*(a + 1)/4
Let s be (-2)/11 - (-35)/11. Factor -2 + 2*g + 0*g**4 + 2*g - 2*g**s + 2*g**4 - 2*g**3.
2*(g - 1)**3*(g + 1)
Let y(h) be the first derivative of -h**4/3 + 40*h**3/9 - 50*h**2/3 + 1. Solve y(z) = 0 for z.
0, 5
Let t(z) = -z + 6. Let y be t(10). Let q be 10*y/16*-2. Suppose -1/4*n**2 + 1/4*n**q - 1/4*n**3 + 0*n + 0 + 1/4*n**4 = 0. What is n?
-1, 0, 1
Let r(f) = -f**2 + 6*f - 2. Let b be r(5). Factor d + 11*d**3 - 9*d**2 + 3*d**5 - 11*d**4 + d + 4*d**b.
d*(d - 1)**3*(3*d - 2)
Suppose o**3 - o - 1/3*o**2 + 0 + 1/3*o**4 = 0. Calculate o.
-3, -1, 0, 1
Let l(j) be the second derivative of -j**4/30 - j**3/5 - 2*j**2/5 + 7*j. Factor l(n).
-2*(n + 1)*(n + 2)/5
Suppose 96 - 3/2*z**3 - 72*z + 18*z**2 = 0. Calculate z.
4
Factor 0 - 4/7*b**2 - 4/7*b.
-4*b*(b + 1)/7
Suppose -4*l + 1 = -7. Let t(h) be the first derivative of 4/7*h - 3/7*h**2 + l + 2/21*h**3. Solve t(o) = 0.
1, 2
Let f(i) be the second derivative of -9*i**5/4 + 35*i**3/6 + 5*i**2 - 14*i. Solve f(t) = 0 for t.
-2/3, -1/3, 1
Let u(a) be the first derivative of a**4/54 + 8*a**3/27 + 16*a**2/9 - 6*a + 1. Let q(x) be the first derivative of u(x). Factor q(j).
2*(j + 4)**2/9
Let s be -6 - -8 - -7 - 6. Determine b, given that 1/3*b + 1/2*b**2 + 0 + 1/6*b**s = 0.
-2, -1, 0
Factor -l**4 - 3*l**3 + 3*l + l**2 + 0*l**2 + 2*l**4 - 2.
(l - 2)*(l - 1)**2*(l + 1)
Let t be (4 - (1 - -1))*1. Factor -3*p**2 - 3 + 3*p + 4 - t + p**3.
(p - 1)**3
Suppose -8 - 8*i**2 + 19*i - i**2 + i**2 + 15*i = 0. Calculate i.
1/4, 4
Let n(k) be the third derivative of -1/12*k**4 + 3*k**2 + 0 - 1/105*k**7 + 0*k - 1/10*k**5 - 1/20*k**6 + 0*k**3. Factor n(g).
-2*g*(g + 1)**3
Let k(t) be the second derivative of 0*t**3 + 0 - 1/14*t**7 + 0*t**2 - 2*t - 1/12*t**4 + 1/6*t**6 - 1/20*t**5. Factor k(z).
-z**2*(z - 1)**2*(3*z + 1)
Let p = 72 - 863/12. Let g(h) be the second derivative of 0 - 1/3*h**3 + 0*h**2 - 2*h - p*h**4 + 1/20*h**5. Factor g(f).
f*(f - 2)*(f + 1)
Factor 50/3 + 2/3*p**2 + 20/3*p.
2*(p + 5)**2/3
Let p(o) be the first derivative of -1 - 1/10*o**2 - 1/15*o**6 - 9/20*o**4 + 0*o + 7/25*o**5 + 1/3*o**3. Factor p(c).
-c*(c - 1)**3*(2*c - 1)/5
Let a(h) be the second derivative of -h**5/15 - 12*h. Determine o so that a(o) = 0.
0
Let f(g) = g**2 + 15*g + 38. Let j be f(-12). Factor -16 - 12*i - 1/4*i**3 - 3*i**j.
-(i + 4)**3/4
Suppose 5*t - 18 = -3. Let x be 3/(t/2)*2. Factor 1 + d**2 - 5 + x + 2 - 3*d.
(d - 2)*(d - 1)
Suppose 3 + 13 = 4*t. Suppose -3*v - 2 = -t*v. Solve -v*z**4 + z**3 + 5*z**3 - 6*z - 3 + 5*z**4 = 0 for z.
-1, 1
Let a be (-82)/(-10) + (-7)/(-140)*-4. Find v such that -a*v**3 + 18*v**4 + 8*v - 8/9 - 154/9*v**2 = 0.
-1, 2/9, 1
Let u(o) be the first derivative of -1/2*o**6 + 0*o**5 + 0*o + 3/2*o**4 - 3/2*o**2 - 4 + 0*o**3. Suppose u(q) = 0. What is q?
-1, 0, 1
Let l = -4/58403 + 3096199/12264630. Let v = l - -1/30. Suppose -4/7*z**2 + 0*z**3 + 2/7*z**4 + v + 0*z = 0. Calculate z.
-1, 1
Suppose -8/9 + 40/9*i - 50/9*i**2 = 0. What is i?
2/5
Let d(l) be the third derivative of 0*l**5 + 0 - 1/126*l**8 + 1/63*l**7 + 0*l - 1/180*l**6 + 0*l**3 - l**2 + 0*l**4. Solve d(x) = 0 for x.
0, 1/4, 1
Let v(p) be the first derivative of 5*p**3/3 + 5*p**2 + 7. Solve v(m) = 0.
-2, 0
Let b(i) be the second derivative of -i**5/50 + i**4/15 + 4*i**3/15 - 8*i**2/5 + 2*i. Determine x so that b(x) = 0.
-2, 2
Let l(i) be the first derivative of -3 + 0*i - 4/3*i**3 - 2*i**2. Factor l(a).
-4*a*(a + 1)
Let c be 17/(-3) + 6 - (-3)/(-9). Solve 1/4*z**3 - 1/2*z**2 + 1/4*z + c = 0.
0, 1
Suppose -2*p + 24 = -5*s, -p - 3*s - 4 = 3*p. Solve 2*r**2 + 5*r - 5*r**2 - p*r = 0 for r.
0, 1
Let o be (-4)/(-2*(3 - (-10)/(-4))). Suppose 0*l**2 + 0*l - 3/4*l**3 + 3/4*l**o + 0 = 0. What is l?
0, 1
Let n = 17445694610/6471281721 - 2/15745211. Let b = n - 4/137. Solve -6*q**4 + 2/3 - 5/3*q**5 - b*q**2 - 22/3*q**3 + q = 0.
-1, 2/5
Let b(l) = l**2 - 5*l + 2. Let g be b(5). Let f(v) be the first derivative of 0*v - 1 - 1/20*v**4 - 1/10*v**g - 2/15*v**3. Determine u so that f(u) = 0.
-1, 0
Let i be 5*-1*112/(-70). Let r(o) be the second derivative of 0 - i*o**2 + 1/10*o**5 + 4*o**3 - o**4 - o. Factor r(l).
2*(l - 2)**3
Let y be (-2)/3 + (-112)/(-42). Let n(f) be the first derivative of y - 1/7*f**2 + 2/7*f**3 + 0*f. Factor n(b).
2*b*(3*b - 1)/7
Factor 4*r**2 + 26 - 12 - 9*r - 12.
(r - 2)*(4*r - 1)
Let t be ((-4)/(-6))/(1/3). Factor 2*c**4 - 3*c**5 + c**4 + 2*c**5 - t*c**5.
-3*c**4*(c - 1)
Let d(u) = -4*u**5 + 17*u**3 + 8*u**2 - 5*u. Let h(p) = 2*p**5 - 8*p**3 - 4*p**2 + 2*p. Let l(a) = -2*d(a) - 5*h(a). Let l(c) = 0. Calculate c.
-1, 0, 2
Let m(n) be the first derivative of -2*n**5/85 + n**4/17 - 15. Factor m(r).
-2*r**3*(r - 2)/17
Let w(q) be the third derivative of -1/525*q**7 + 0*q - 1/60*q**4 + 0*q**3 + 0 - 1/100*q**6 + 2*q**2 - 1/50*q**5. Factor w(u).
-2*u*(u + 1)**3/5
Suppose 4 = 2*n - 4*k, 8 = -n - 3*k - 5. Let o be n/(-2) - (-32)/(-18). Factor -2/9*b**2 + 0 + 0*b + o*b**3.
2*b**2*(b - 1)/9
Let w = -4/13 + 25/39. Factor -l + l**2 + 1/3 - w*l**3.
-(l - 1)**3/3
Suppose -2*v = 4, 9 = w - 3*v - 4. Factor -65*f - 8*f**3 + 5*f**2 + w*f**4 + 64*f - 3*f**4.
f*(f - 1)*(2*f - 1)**2
Let v(u) be the first derivative of u**3 - 6*u**2 + 12*u - 13. Factor v(x).
3*(x - 2)**2
Suppose -a**2 + 0 - 1/2*a - 1/2*a**3 = 0. What is a?
-1, 0
Let c(k) = k**2 - 6*k + 4. Let y be c(4). Let b be y*(-1)/(-2)*-2. Let -4/5*u**3 + 2/5*u + 2/5*u**5 - 4/5*u**2 + 2/5 + 2/5*u**b = 0. Calculate u.
-1, 1
Let z(m) = -2*m**3 + 2*m**2 + 3*