st derivative of -1/6*u**3 - 1 + 1/10*u**5 + 0*u - 1/4*u**2 + 1/8*u**4. Find f, given that t(f) = 0.
-1, 0, 1
Let r(o) be the first derivative of -1/6*o**3 - 1/4*o**2 + 3 + o. Find q such that r(q) = 0.
-2, 1
Let b(w) be the third derivative of -w**7/280 - 3*w**6/160 - w**5/40 + 25*w**2. Factor b(t).
-3*t**2*(t + 1)*(t + 2)/4
Suppose 4*r + 2 = -n + 10, n + 1 = -r. Let j(u) be the first derivative of u**2 - 1/3*u**r - u + 1. Factor j(z).
-(z - 1)**2
Factor 0*j**3 - 2/9*j**4 + 0 + 2/9*j**2 + 0*j.
-2*j**2*(j - 1)*(j + 1)/9
Let l = -61/3 + 21. Factor -2/3 - 8/3*z - 8/3*z**3 - 4*z**2 - l*z**4.
-2*(z + 1)**4/3
Let t(x) be the third derivative of 1/280*x**8 + 0*x**4 + 0*x**3 + 1/75*x**5 - 1/100*x**6 + 0*x + 4*x**2 - 2/525*x**7 + 0. Determine j so that t(j) = 0.
-1, 0, 2/3, 1
Let l be 2 + 2 + -6 + 6. Factor -3*f - 7*f**2 + 3*f - l + 11*f**2.
4*(f - 1)*(f + 1)
Let p be (-4)/14 + 592/14. Suppose 3*k**4 - 8 - 15*k**3 + p*k**5 - k**4 + 6*k**2 - 59*k**3 + 32*k = 0. Calculate k.
-1, 2/7, 2/3, 1
Let z = -9 - -12. Let q(y) be the second derivative of 0 - 2*y - 1/9*y**z - 2/3*y**2 + 1/18*y**4. Factor q(w).
2*(w - 2)*(w + 1)/3
Let r(t) = 7*t + 1. Let h be r(-1). Let k(b) = -b**4 - 10*b**3 - 9*b**2. Let u(l) = -2*l**4 - 10*l**3 - 8*l**2. Let j(g) = h*k(g) + 7*u(g). Factor j(c).
-2*c**2*(c + 1)*(4*c + 1)
Let v(w) = 3*w - 18. Let j = 29 - 23. Let z be v(j). Factor 0*d + 2/3*d**3 + 0*d**2 + z + 2/3*d**4.
2*d**3*(d + 1)/3
Let l(g) = -15*g**2 + 85*g - 125. Let f(x) = x**2 - 6*x + 9. Let v(s) = -55*f(s) - 4*l(s). Factor v(o).
5*(o - 1)**2
Let n be (-15)/(-100)*(-1308)/(-122). Let p = -1/122 + n. Suppose -6/5*z**2 + 8/5*z + p = 0. What is z?
-2/3, 2
Let f(q) be the first derivative of q**4/18 - 8*q**3/27 + 5*q**2/9 - 4*q/9 - 5. Factor f(d).
2*(d - 2)*(d - 1)**2/9
Suppose v = -2*v. Let f(s) be the second derivative of 25/6*s**4 - 10/3*s**3 + v + s**2 - s. Factor f(o).
2*(5*o - 1)**2
Let d(z) be the first derivative of 1/60*z**5 - 1/180*z**6 + 0*z - 2 + 0*z**2 - z**3 + 0*z**4. Let p(b) be the third derivative of d(b). Factor p(a).
-2*a*(a - 1)
Let p = 27 + -45. Let u be (p/15 - -1)*-21. Suppose -73/5*t**3 - 4/5 + 49/5*t**5 + 24/5*t + u*t**4 - 17/5*t**2 = 0. What is t?
-1, 2/7, 1
Let m(c) be the second derivative of c**5/50 + c**4/2 + 5*c**3 + 25*c**2 - 4*c. What is w in m(w) = 0?
-5
Let o(t) be the second derivative of 4*t**6/135 + 13*t**5/90 + 11*t**4/54 + 2*t**3/27 - 14*t. Let o(y) = 0. What is y?
-2, -1, -1/4, 0
Let y(u) be the third derivative of -1/210*u**5 + 0*u - 4/21*u**3 + 1/21*u**4 + 4*u**2 + 0. Determine r so that y(r) = 0.
2
Let s = 53 - 53. Factor 4/7*i**2 + 0*i - 2/7*i**3 + s.
-2*i**2*(i - 2)/7
Let l = 0 - -2. Let f(r) be the first derivative of -1/2*r**l - 2 + 1/4*r**4 - r + 1/3*r**3. Factor f(n).
(n - 1)*(n + 1)**2
Factor -35*l**2 - 6 + 0 + 6 - 10*l.
-5*l*(7*l + 2)
Suppose -9 = -h - 2*h. Factor -120*c**3 - 48*c**4 + 7*c - 24*c - 99*c**2 - h - 13*c.
-3*(c + 1)**2*(4*c + 1)**2
Let u(f) be the second derivative of -4*f**6/15 + f**5/5 + 2*f**4 - 14*f**3/3 + 4*f**2 - f - 2. Solve u(r) = 0 for r.
-2, 1/2, 1
Let a be (21/9)/(-7) - (-21)/36. Factor -a*r**4 - 1/4*r**3 + 1/4*r**2 + 1/4*r + 0.
-r*(r - 1)*(r + 1)**2/4
Let l(o) be the third derivative of o**5/15 - 2*o**4/3 + 8*o**3/3 + 9*o**2. Solve l(k) = 0.
2
Suppose -2*z = -3*g, z = -4*g + 4*z - 1. Factor a**2 + a - a**5 + 0*a**g + 2*a**4 - 6*a**2 + 3*a**2.
-a*(a - 1)**3*(a + 1)
Let g(s) be the first derivative of -2*s**3/27 - s**2/9 - 10. Solve g(f) = 0.
-1, 0
Suppose 0 = 4*j - 3 - 53. Let x = j - 12. Factor 1/2*b + 1/2*b**3 + 0 - b**x.
b*(b - 1)**2/2
Suppose -5*m - 4*z + z + 35 = 0, 8 = -3*m + 4*z. Let q(f) be the first derivative of -1/4*f**2 + 0*f + 1/3*f**3 - 1 - 1/8*f**m. Factor q(u).
-u*(u - 1)**2/2
Factor 72*k + 3*k**3 + 48*k**2 - 21*k**2 + 7 + 41.
3*(k + 1)*(k + 4)**2
Factor -8/5 - 2/5*r**2 - 8/5*r.
-2*(r + 2)**2/5
Let y(r) = -1. Let f(s) = -s**2 + 5*s - 1. Let j(m) = -f(m) - 3*y(m). Factor j(w).
(w - 4)*(w - 1)
Let -2/9*x**2 + 8/9*x - 2/3 = 0. What is x?
1, 3
Let q(l) be the first derivative of l**4 - 6*l**2 + 8*l + 1. Let q(n) = 0. Calculate n.
-2, 1
Let c be (-2 - 3 - -1) + 6. Suppose -10/3*f**c - 8/3 - 2/3*f**3 - 16/3*f = 0. What is f?
-2, -1
Let t(s) be the third derivative of s**7/840 - s**6/480 - 3*s**2. Find v such that t(v) = 0.
0, 1
Let j(w) be the second derivative of -1/3*w**4 + 1/21*w**7 + 0*w**3 + 1/2*w**5 + w - 4/15*w**6 + 0 + 0*w**2. Factor j(y).
2*y**2*(y - 2)*(y - 1)**2
Let w be 0 - (1 + -3)*1. Suppose f + 2*f**3 + 6 - 3*f**5 - w - 5*f**4 + 6*f**2 - 5 = 0. Calculate f.
-1, 1/3, 1
Let l = 44 - 44. Let r(w) be the first derivative of -8/9*w**3 + l*w + 1/6*w**4 - 3 + 4/3*w**2. Suppose r(j) = 0. What is j?
0, 2
Let -8/5 + 8/5*z**3 + 104/5*z**4 - 12*z**5 + 52/5*z - 96/5*z**2 = 0. What is z?
-1, 1/3, 2/5, 1
Let h(j) = -j + 14. Let t(n) = -3*n + 29. Let s(r) = 5*h(r) - 2*t(r). Let z be s(-8). Factor z - 6 - 4*d**2 + 9*d - 3*d**2.
-(d - 1)*(7*d - 2)
Factor 63*m + 32*m + 45*m**2 + 63 + 55*m + 62.
5*(3*m + 5)**2
Let k = 10/3 - 44/15. Factor -24/5*q - k*q**3 - 12/5*q**2 - 16/5.
-2*(q + 2)**3/5
Suppose 4*n = 3*a - 22, -2*a + 3*n = 3*a - 22. Factor 0*x**2 + x**2 + 8*x - a*x**2 - 3*x**2 + 12.
-4*(x - 3)*(x + 1)
Let s = -57 - -59. Determine t so that -4/7*t**s - 2/7*t + 4/7 + 2/7*t**3 = 0.
-1, 1, 2
Let t = -1/22 - -27/110. Let a(b) be the second derivative of t*b**3 - 2/5*b**2 - b - 1/30*b**4 + 0. Factor a(v).
-2*(v - 2)*(v - 1)/5
Let y be 25/5 - ((-18)/(-15) + 3). Factor y*z + 0 + 2/5*z**4 + 0*z**3 - 6/5*z**2.
2*z*(z - 1)**2*(z + 2)/5
Let b(n) be the third derivative of -n**7/280 + n**6/160 + n**5/40 + 21*n**2. Factor b(i).
-3*i**2*(i - 2)*(i + 1)/4
Factor -5/2*c + 1/2*c**2 + 2.
(c - 4)*(c - 1)/2
Let d(r) be the third derivative of 0*r + 0 + 0*r**3 - 1/150*r**5 + 3*r**2 - 1/75*r**6 + 0*r**4. Let d(h) = 0. What is h?
-1/4, 0
Let j(k) be the third derivative of -k**6/120 + k**5/20 - k**4/12 - 8*k**2. Solve j(m) = 0 for m.
0, 1, 2
Let c(b) = -b**3 - 3*b**2 + b + 6. Let y be c(-3). Let x(f) be the first derivative of y + 3/5*f**2 - 3/10*f**4 - 2/3*f**3 + 8/25*f**5 + 2/5*f. Solve x(k) = 0.
-1, -1/4, 1
Factor 4/3*z**2 + 0 + 0*z + 1/3*z**3.
z**2*(z + 4)/3
Let r(j) be the first derivative of -j**4/28 + j**2/14 + 10. Factor r(h).
-h*(h - 1)*(h + 1)/7
Let b(m) be the first derivative of 5*m**3/12 + 55*m**2/4 + 605*m/4 - 37. Factor b(w).
5*(w + 11)**2/4
Let 8*x - 11 - 2 - 3 - 2*x**2 + x**2 = 0. What is x?
4
Let o = 1099/2493 - -1/277. Factor -2/9*i**2 + o + 2/9*i.
-2*(i - 2)*(i + 1)/9
Suppose 3*b + 15 = 0, 2*x - 5*b = -20 + 45. Let d(t) be the third derivative of -1/30*t**5 + 1/8*t**4 + x*t + 0 + t**2 + 1/3*t**3. Factor d(q).
-(q - 2)*(2*q + 1)
Factor 4*y**4 - 4*y**3 + 5*y**5 - y**5 + 4*y**4 - 8*y**2.
4*y**2*(y - 1)*(y + 1)*(y + 2)
Let o = -12 + 12. Let v be 0/(-2 + o - -5). Factor -1/2*d**2 + 0*d + v.
-d**2/2
Suppose -5*b = -20, 4*l - 16 = 26*b - 30*b. Factor 0 + l*t + 0*t**2 + 0*t**3 + 1/6*t**4 - 1/6*t**5.
-t**4*(t - 1)/6
Let v(c) be the third derivative of c**5/140 - 5*c**4/56 + 2*c**3/7 - 19*c**2. Determine y so that v(y) = 0.
1, 4
Determine w, given that -5/2*w + 5/4*w**2 + 5/4 = 0.
1
Let f(c) be the second derivative of 3*c**5/20 + c**4/4 + 8*c. Determine b so that f(b) = 0.
-1, 0
Let x(r) be the third derivative of -r**7/1575 + r**6/225 - r**5/225 - r**4/45 + r**3/15 + 43*r**2. Determine d, given that x(d) = 0.
-1, 1, 3
Let f be (-2)/9 + (-14)/18. Let k be f/(-10) + 10/25. Factor -1/2*t + k*t**3 + 0 + 2*t**2 - 2*t**4.
-t*(t - 1)*(t + 1)*(4*t - 1)/2
Find i such that 0 + 0*i + 0*i**4 - 1/3*i**2 + 1/2*i**3 - 1/6*i**5 = 0.
-2, 0, 1
Let u(f) be the third derivative of -f**8/840 + f**6/180 + f**3/3 + f**2. Let w(g) be the first derivative of u(g). Suppose w(l) = 0. Calculate l.
-1, 0, 1
Suppose -4*o + 2*k + 2*k = -4, -o - 3 = -3*k. Let y = -4 + 6. Factor o*j - 2*j**y + 0*j**3 + j**3 - 2*j.
j*(j - 1)**2
Suppose 2 = -l - 1, 8 = -2*m - 4*l. What is y in 2*y - 4*y**2 - 5*y + m*y = 0?
-1/4, 0
Let p(c) be the second derivative of c**5/45 + 2*c**4/27 - 2*c**3/27 - 4*c**2/9 + 28*c. Factor p(d).
4*(d - 1)*(d + 1)*(d + 2)/9
Let v(d) be the second derivative of 3*d**5/10 + 7*d**4/6 - 4*d**2 + 2*d. Find r, given that v(r) = 0.
-2, -1, 2/3
Suppose -2*f + 16 = 4*q - 2*q, 3*q + 48 = 5*f. Factor 0*s**2 + f*s**2 - 7*s**2.
2