e of 5*w**8/336 + 5*w**7/168 + w**6/96 - 31*w**2. Factor a(c).
5*c**3*(c + 1)*(4*c + 1)/4
Let q be -3 - (9/(-12))/(1/4). Factor 0*w**2 + q - 2/7*w**3 + 2/7*w.
-2*w*(w - 1)*(w + 1)/7
Suppose -4*d = 5*f + 1, f + 0*d + 5 = -2*d. Suppose -f*x + 8 = x. Factor 37/3*b**x + 10*b**3 + 3*b**4 + 20/3*b + 4/3.
(b + 1)**2*(3*b + 2)**2/3
Let b(y) = -2*y + 15. Let a be b(6). Suppose 0 + 4*f**4 + 16/3*f**2 + 0*f - 8*f**a - 2/3*f**5 = 0. Calculate f.
0, 2
Let f = -152/5 + 31. Factor -f*s - 3/5*s**2 + 0.
-3*s*(s + 1)/5
Let n(i) be the first derivative of i**3/12 - i**2/4 - 6. Factor n(v).
v*(v - 2)/4
Suppose r + 2*r = -2*n + 31, -3*n + 4*r = -4. Determine f so that -12*f**3 - 2*f - n*f**2 + 3*f**4 - 2*f**5 + 0*f**5 - 11*f**4 = 0.
-1, 0
Let l(p) be the first derivative of 5*p**3/9 + 25*p**2/6 + 20*p/3 + 5. Factor l(h).
5*(h + 1)*(h + 4)/3
Let d(i) = 3*i**2 + 1. Suppose -4 - 16 = 5*f, -5*b - 11 = 4*f. Let q be d(b). Factor 0*w**4 + 3*w**q - w**4.
2*w**4
Let c(t) be the third derivative of -t**7/140 + t**5/40 - 6*t**2. Factor c(r).
-3*r**2*(r - 1)*(r + 1)/2
Let q = -809/3 + 273. Factor -q*t**3 + 10/3*t**2 - 5/3*t - 1/3*t**5 + 5/3*t**4 + 1/3.
-(t - 1)**5/3
Let y be 86/6 + (-4)/(-6). Let p be 15/6*24/y. Solve 0*c**3 - 3/2*c**p + 0 + 3/4*c - 3/4*c**5 + 3/2*c**2 = 0 for c.
-1, 0, 1
Let a(u) be the second derivative of -3*u**5/50 - 7*u**4/30 + 12*u**3/5 - 4*u**2 + 19*u - 1. Factor a(s).
-2*(s - 2)*(s + 5)*(3*s - 2)/5
Let k(j) be the second derivative of -j**4/27 - 4*j**3/27 + 16*j**2/9 - 22*j. Factor k(x).
-4*(x - 2)*(x + 4)/9
Let n(v) be the first derivative of 0*v**2 + 2/9*v**3 - 1/2*v**4 + 2/5*v**5 - 1/9*v**6 + 4 + 0*v. Determine f so that n(f) = 0.
0, 1
Let t(v) be the second derivative of -1/50*v**6 - 1/5*v**3 + 0 + 0*v**4 + 4*v + 3/10*v**2 + 3/50*v**5. Suppose t(c) = 0. What is c?
-1, 1
Let l(a) be the second derivative of -1/3*a**2 + a + 1/18*a**4 - 1/30*a**5 + 0 + 1/9*a**3. Factor l(r).
-2*(r - 1)**2*(r + 1)/3
Let o(p) be the first derivative of p**3/21 + 3*p**2/14 + 2*p/7 + 6. Solve o(h) = 0.
-2, -1
What is r in 2/3*r**3 + 10/3*r - 8/3*r**2 - 4/3 = 0?
1, 2
What is c in 1/4*c - 1/4*c**2 + 1/4 - 1/4*c**3 = 0?
-1, 1
Suppose 10/9*h**3 + 0*h + 0 + 4/9*h**2 - 4/9*h**4 - 10/9*h**5 = 0. What is h?
-1, -2/5, 0, 1
Let x(h) be the first derivative of 9*h**4/4 - 2*h**3 - 9*h**2/2 + 6*h + 1. Find n, given that x(n) = 0.
-1, 2/3, 1
Let p = 899/2 + -463. Let y = -13 - p. Determine d, given that 4 + 6*d + y*d**3 + 3*d**2 = 0.
-2
Let b = -4941/5 - -989. Determine w so that 1/5*w**3 - 2/5 - b*w**2 + w = 0.
1, 2
Let c(v) be the first derivative of -v**6/15 + v**4/10 + 6. Factor c(h).
-2*h**3*(h - 1)*(h + 1)/5
Let f = 296/3 - 1462/15. Solve 6/5*n**2 + 0 + 2/5*n**4 + f*n**3 + 2/5*n = 0.
-1, 0
Factor -1/3*r**5 + 0 - r**3 + r**4 + 0*r + 1/3*r**2.
-r**2*(r - 1)**3/3
Let t(i) = i**3 - i**2. Let s(w) = -w**3 - 15*w**2 - 8*w. Let c(k) = -s(k) + 3*t(k). Factor c(d).
4*d*(d + 1)*(d + 2)
Let y(j) be the third derivative of -6*j**2 + 0 - 1/5*j**5 - 3/40*j**6 + 1/112*j**8 + 1/35*j**7 + 0*j**3 + 1/2*j**4 + 0*j. Solve y(c) = 0.
-2, 0, 1
Suppose 32 = 4*u - 4*a, -4*u + 0*a + 2*a = -24. Let d(h) = h**4 + h**3 + h. Let j(m) = 5*m**4 + 2*m**3 + m**2 + 4*m. Let w(c) = u*d(c) - j(c). Factor w(z).
-z**2*(z - 1)**2
Let y(s) be the second derivative of 0 - 1/8*s**3 - 4*s - 1/16*s**4 + 0*s**2. Factor y(q).
-3*q*(q + 1)/4
Let h(p) be the first derivative of 2*p**3/3 + 10*p**2 + 68. Determine f so that h(f) = 0.
-10, 0
Let d(j) be the third derivative of 0*j + 0*j**3 + 1/180*j**5 + 0 - 5*j**2 + 0*j**4 - 1/120*j**6. Factor d(k).
-k**2*(3*k - 1)/3
Suppose 0 = -2*t - 5 + 11. Factor -7*l**2 + 12*l**2 + t*l - 8*l**2 - 3*l**3 + 3.
-3*(l - 1)*(l + 1)**2
Suppose -2 = k - 3, -4*a = -5*k - 19. What is v in -9*v**3 + a*v**2 + 2 - 9*v - 30*v**2 + 4 = 0?
-2, -1, 1/3
Factor -1/5*d**3 + 1/5*d**4 + 1/5*d - 1/5*d**2 + 0.
d*(d - 1)**2*(d + 1)/5
Let g(d) be the second derivative of d**4/16 - d**3/4 - 9*d**2/8 - 17*d. Factor g(p).
3*(p - 3)*(p + 1)/4
Factor -20*t - 6 - 3*t**3 + 9*t**2 - 3 - 14*t + 37*t.
-3*(t - 3)*(t - 1)*(t + 1)
Let v(i) be the first derivative of -49*i**4/4 + 7*i**3 + 12*i**2 + 4*i - 7. Factor v(s).
-(s - 1)*(7*s + 2)**2
Let y(p) be the third derivative of p**7/1680 + p**6/192 + p**5/60 + p**4/48 + 8*p**2. Find b such that y(b) = 0.
-2, -1, 0
Suppose -6*o - 10 = -11*o. Suppose 7*j**2 - 2*j**3 + 12*j + 6*j**o - j**2 + 5*j**3 = 0. Calculate j.
-2, 0
Let l(k) = 2*k**2 - 1 - k**3 - k + 4*k - 5 + 3. Let f be l(2). Solve -2/3 + 5/3*s**4 + 7/3*s - s**2 - 7/3*s**f = 0 for s.
-1, 2/5, 1
Let t(v) be the second derivative of v**6/40 + v**5/16 - v**4/24 + 5*v. Suppose t(j) = 0. What is j?
-2, 0, 1/3
Let z = 21 + 3. Let t be (-4)/6 + z/9. Factor 2/11*u + 2/11*u**t - 4/11.
2*(u - 1)*(u + 2)/11
Let i(c) = -c**3 + 6*c**2 + 2. Let z be i(6). Solve 6 + z*k**3 + 23*k + k**3 - 8*k + 12*k**2 = 0.
-2, -1
Let w(j) be the first derivative of -1/21*j**6 - 4/35*j**5 + 0*j**3 + 0*j**2 - 1/14*j**4 + 0*j - 3. Find u, given that w(u) = 0.
-1, 0
Factor -1 + 3/4*f + 1/4*f**2.
(f - 1)*(f + 4)/4
Let g be (-13)/(-3)*21/28 - 3. Factor s**3 + 3/2*s + 9/4*s**2 + g.
(s + 1)**2*(4*s + 1)/4
Let j(x) be the first derivative of x**5/40 - 3*x**4/32 - x**3/8 + 7*x**2/16 + 3*x/4 - 7. Find g such that j(g) = 0.
-1, 2, 3
Let u(s) be the second derivative of s**6/30 + 2*s**5/5 + 2*s**4 + 16*s**3/3 + 8*s**2 + 5*s. Factor u(b).
(b + 2)**4
What is o in 15*o - 9*o**2 - 11*o**3 - 13*o**3 - 16*o**4 + 32*o**2 + 2 = 0?
-2, -1/4, 1
Let c(j) be the third derivative of j**6/72 - j**5/18 + 5*j**4/72 - 9*j**2. Factor c(d).
5*d*(d - 1)**2/3
Let d(k) be the first derivative of k**6 - 16/9*k**3 - 16/5*k**5 - 3 + 1/3*k**2 + 0*k + 11/3*k**4. Determine m, given that d(m) = 0.
0, 1/3, 1
Factor 0 + 0*h - 3/7*h**3 - 9/7*h**2.
-3*h**2*(h + 3)/7
Let d(b) be the second derivative of b**5/25 + 2*b**4/15 - 2*b**3/15 - 4*b**2/5 + 24*b. Determine t so that d(t) = 0.
-2, -1, 1
Let h(v) be the second derivative of -4*v**5 - 13*v**4 + 6*v + 8*v**2 + 8/3*v**3 + 0 + 40/3*v**6. Factor h(r).
4*(2*r - 1)**2*(5*r + 2)**2
Let i(w) be the third derivative of -3*w**8/224 + 11*w**7/140 - 23*w**6/120 + w**5/4 - 3*w**4/16 + w**3/12 - 3*w**2. Factor i(m).
-(m - 1)**3*(3*m - 1)**2/2
Let n(j) be the second derivative of -j**4/6 - 10*j**3/3 - 25*j**2 + 68*j. Factor n(c).
-2*(c + 5)**2
Let m(a) be the second derivative of 0 + 1/36*a**4 - 1/6*a**3 + 5*a + 1/3*a**2. Factor m(n).
(n - 2)*(n - 1)/3
Let 0*d**3 + 0 - 1/5*d**2 + 1/5*d**4 + 0*d = 0. Calculate d.
-1, 0, 1
Determine x so that -2/5*x**3 + 0 + 1/5*x**4 - 3/5*x**2 + 0*x = 0.
-1, 0, 3
Let l(z) = -5 + 0 + z**2 - 2*z**2 + 2*z**2 - 6*z. Let a be l(7). Solve 2/5 - 4/5*t + 2/5*t**a = 0.
1
Suppose 4*z + 5*j = 12, 2*z + 4*j + 4 = 10. Let n(k) = k + 1. Let h be n(z). Let 4*f**3 - 3*f**3 - 3*f**3 - 3*f**4 + 2*f**h = 0. Calculate f.
-2, 0
Let p(h) be the second derivative of 75*h**7/14 - 127*h**6/6 - 7*h**5 + 80*h**4 + 80*h**3/3 - 40*h**2 - 34*h. What is r in p(r) = 0?
-1, -2/5, 2/9, 2
Let j = 2158/7 + -308. Factor -4/7 + 2/7*d**3 - j*d + 4/7*d**2.
2*(d - 1)*(d + 1)*(d + 2)/7
Let a(t) be the second derivative of 0*t**2 + 1/15*t**3 + 4*t + 1/30*t**4 - 1/75*t**6 + 0 - 1/50*t**5. Determine k so that a(k) = 0.
-1, 0, 1
Let c = -30 + 26. Let i be -3*(-21)/(-18) - c. Factor -h + 1/2 + i*h**2.
(h - 1)**2/2
Factor -64*u**3 + 0 - 6 + 61*u**3 + 8*u + u.
-3*(u - 1)**2*(u + 2)
Let -2*j**3 + j - 6*j**2 + 4*j**2 + 2 + j = 0. Calculate j.
-1, 1
Suppose 7*v - 9*v = 52. Let n = v - -28. Factor 3/5*z**4 + 0 + 3/5*z**n + 6/5*z**3 + 0*z.
3*z**2*(z + 1)**2/5
Let x(a) = -a + 3. Let t be x(3). Let f(h) = h + 4. Let n be f(t). Factor -2*i + 2*i**5 + n*i + 3*i**3 - i**3 - 6*i**3.
2*i*(i - 1)**2*(i + 1)**2
Let d = -6 + 3. Let p be d/(-1) - 20/(-12). Suppose -p*j - 4/3 - 2*j**2 = 0. Calculate j.
-2, -1/3
Let q(l) = l**5 - l**4 - l**2 + l + 1. Let o(m) = 6*m**5 - 24*m**4 + 45*m**3 - 30*m**2 + 3*m + 3. Let k(f) = -o(f) + 3*q(f). Factor k(z).
-3*z**2*(z - 3)**2*(z - 1)
Let a be (-94)/235 + (-116)/(-90). Factor 2/9*r**4 - a*r - 8/9 + 2/3*r**2 + 8/9*r**3.
2*(r - 1)*(r + 1)*(r + 2)**2/9
Factor -2/9*o**3 - 196/9 - 14/3*o + 8/3*o**2.
-2*(o - 7)**2*(o + 2)/9
Determine i so that -12/17*i**2 + 2/17*i**3 - 8/17 + 18/17*i = 0.
1, 4
Let u = 27 + -27. Suppose 6*z - 10*z = u. Let 8*s**4 + 0*s - 11