 r(d) = 0.
-1, -2/5, 0, 2
Let n(p) be the first derivative of 1/35*p**6 + 5/42*p**4 - 1/21*p**3 - p - 1/10*p**5 + 0*p**2 + 4. Let i(g) be the first derivative of n(g). Factor i(u).
2*u*(u - 1)**2*(3*u - 1)/7
Let o(w) be the first derivative of w**6/180 - w**5/30 + w**4/12 + w**3 - 6. Let m(n) be the third derivative of o(n). Solve m(v) = 0 for v.
1
Let n be 16/4 + -1*2. Suppose 2*l = -n + 8. Factor 10*t**2 + 5*t**l + 12*t**5 - 13*t**5 - 15*t**3 + 5*t**4 - 5*t + 1.
-(t - 1)**5
Let c = -362/7 + 52. Factor -c*u**3 + 0 + 0*u - 4/7*u**2.
-2*u**2*(u + 2)/7
Let p(y) be the first derivative of -2/9*y - 4/9*y**3 - 2/45*y**5 + 2/9*y**4 + 4 + 4/9*y**2. What is i in p(i) = 0?
1
Let 2/9*o**5 - 4/9*o**4 + 0 + 4/9*o**2 + 0*o**3 - 2/9*o = 0. Calculate o.
-1, 0, 1
Let j(v) be the second derivative of -v**7/3780 + v**6/1080 + v**4/6 - 2*v. Let z(r) be the third derivative of j(r). Factor z(h).
-2*h*(h - 1)/3
Let f(w) = 14*w**2 - 3. Let y(d) = 5*d**2 - 1. Let a(o) = -4*f(o) + 11*y(o). Let u(k) = -4*k**2 + 4. Let n(l) = 10*a(l) - 2*u(l). Factor n(i).
-2*(i - 1)*(i + 1)
Let m = 10 + -10. Let y(g) be the second derivative of 7/24*g**3 - 1/20*g**5 + m - 1/12*g**4 - 1/4*g**2 + g. Determine o so that y(o) = 0.
-2, 1/2
Suppose 0 = 3*h - 4*t + 7, 3*t - 2 - 1 = 0. Let x be 3 - (1 + h)/(-1). Factor 1/2*z - 12*z**4 + x*z**2 + 1/2*z**3 + 8*z**5 + 0.
z*(z - 1)**2*(4*z + 1)**2/2
Let p = -110 + 113. Factor 2/3*c**2 - 2/3 - 5/3*c**p + 5/3*c.
-(c - 1)*(c + 1)*(5*c - 2)/3
What is c in -3*c - 781 + 3*c**2 + 781 = 0?
0, 1
Let l(b) be the second derivative of b**6/180 + b**5/90 - b**4/18 - 2*b**2 - 4*b. Let v(s) be the first derivative of l(s). Factor v(u).
2*u*(u - 1)*(u + 2)/3
Factor 7*s**4 + s**3 + 3*s**4 - 19*s**4 + 8*s**4.
-s**3*(s - 1)
Let i(v) be the third derivative of -v**8/588 + 4*v**7/735 - 2*v**5/105 + v**4/42 + 2*v**2. Let i(h) = 0. Calculate h.
-1, 0, 1
Solve 67*j**3 - 42*j**4 - 8*j**2 + 28*j**5 - 23*j**3 - 8*j**4 - 14*j**4 = 0.
0, 2/7, 1
Let j(a) be the first derivative of -a**6/12 + a**5/2 - 5*a**4/4 + 5*a**3/3 - 5*a**2/4 + a/2 - 48. Factor j(s).
-(s - 1)**5/2
Let x(u) be the third derivative of -u**5/160 - u**4/32 + 3*u**3/16 - 19*u**2. What is c in x(c) = 0?
-3, 1
Suppose 4*z = -r - 7, 0 = z - 5*r + 4 + 24. Let x(m) = 3*m**5 - 3*m**2 - 3*m. Let v(d) = -d**3 + d**2 + d. Let h(s) = z*v(s) - x(s). Factor h(b).
-3*b**3*(b - 1)*(b + 1)
Suppose -3*m + 48 = -5*m. Let r = 97/4 + m. Factor 0*n**3 + 0 - 1/2*n**2 - r*n**5 + 1/4*n + 1/2*n**4.
-n*(n - 1)**3*(n + 1)/4
Let j be -9*(0 - (-2)/(-6)). Let r(h) = h + 3*h**3 + h**3 - 3*h**j. Let l(v) = 20*v**3 - 14*v**2 + 14*v. Let i(k) = -l(k) + 10*r(k). Factor i(c).
-2*c*(c - 1)*(5*c - 2)
Let h(z) be the first derivative of z**4/10 - 8*z**3/15 + 4*z**2/5 + 22. Let h(i) = 0. Calculate i.
0, 2
Let s(y) be the first derivative of 48*y**4 - 80*y**3 - 261*y**2/2 - 54*y + 57. Factor s(q).
3*(q - 2)*(8*q + 3)**2
Let p(w) be the third derivative of -1/378*w**8 + 0*w + 1/135*w**5 - 4/945*w**7 + 3*w**2 + 1/180*w**6 - 1/108*w**4 + 0 + 0*w**3. Factor p(r).
-2*r*(r + 1)**2*(2*r - 1)**2/9
Suppose 7*i - 30 = -8*i. Solve r - 1/3*r**i - 2/3 = 0.
1, 2
Let y be (-4)/(-8) - (-2)/(-4). Suppose 0 = 2*d + b - 9, -b + 11 = 3*d - y. Factor -1 + 2*o - 4*o**d + 0 + 4*o**2 - o**2.
-(o - 1)**2
Factor 10*q**2 - 11*q**2 - q**3 - 2*q + 4*q.
-q*(q - 1)*(q + 2)
Suppose -172*c = -178*c + 18. Suppose 27/5*z + 1/5*z**c - 27/5 - 9/5*z**2 = 0. Calculate z.
3
Let l(i) = i**5 - 3*i**4 - 5*i**3 + 3*i**2 - 4. Let q(t) = 3*t**5 - 8*t**4 - 14*t**3 + 8*t**2 - 11. Let p(x) = 11*l(x) - 4*q(x). Solve p(h) = 0 for h.
-1, 0, 1
Let k(s) be the second derivative of 0*s**2 - 1/3*s**3 + 1/10*s**6 + 0 - 1/4*s**4 + 1/20*s**5 + 1/42*s**7 + 2*s. Let k(m) = 0. What is m?
-2, -1, 0, 1
Let w = 29 - 17. Let p = -5 + w. Factor -2*a**4 + 2*a**2 - p*a + 7*a.
-2*a**2*(a - 1)*(a + 1)
Let q = -17 - -69/4. Factor -1/2*s**2 - q*s**3 + 0 + 0*s.
-s**2*(s + 2)/4
Let z(g) be the third derivative of -4*g**2 + 1/21*g**4 + 4/21*g**3 + 0 + 1/210*g**5 + 0*g. What is j in z(j) = 0?
-2
Let s(t) = 2*t**2 + 4*t + 7. Let r(l) = -l**2 - 2*l - 4. Let x(z) = 5*z - 1. Let f be x(2). Suppose 4*a = a + f. Let q(k) = a*s(k) + 5*r(k). Factor q(w).
(w + 1)**2
Let i(p) be the third derivative of 1/50*p**5 + 0*p + 0 - 1/40*p**4 + 5*p**2 - 1/200*p**6 + 0*p**3. Factor i(u).
-3*u*(u - 1)**2/5
Let t = 90 + -628/7. Factor -t*x**3 + 2/7*x**2 + 2/7*x - 2/7.
-2*(x - 1)**2*(x + 1)/7
Let s be (((-8)/20)/2)/(-1). Let p(r) be the second derivative of -1/2*r**2 - s*r**5 - r + 0 + 2/3*r**3 + 1/12*r**4. Find y, given that p(y) = 0.
-1, 1/4, 1
Let m(y) = 7195*y**4 - 4108*y**3 + 344*y - 56. Let u(t) = -4797*t**4 + 2739*t**3 - 229*t + 37. Let c(x) = 5*m(x) + 8*u(x). Factor c(h).
-(7*h - 2)**3*(7*h + 2)
Let g(k) = -3*k - 9. Let h be g(-7). Suppose -h = -c - 2*c. Factor -c*v + 0 + 4*v - 3*v**2 + 3.
-3*(v - 1)*(v + 1)
Factor 0 - 5*m + 10*m**2 + 2*m**3 - 2 + 3*m**3 - 8.
5*(m - 1)*(m + 1)*(m + 2)
Factor 39/4*k**2 + 27 + 3/4*k**3 + 30*k.
3*(k + 2)**2*(k + 9)/4
Let h(f) be the first derivative of f**4/12 - f**2/6 - 1. Factor h(k).
k*(k - 1)*(k + 1)/3
Let y(b) = b**3 + 7*b**2 + 5*b - 4. Let k be y(-6). Let 66*i**3 - 23*i**4 - 24*i + 34*i**k + 3*i**4 - 8 + 4*i**4 - 10*i**4 - 42*i**5 = 0. What is i?
-1, -2/7, 2/3, 1
Find j, given that -2/19*j**4 + 8/19*j - 8/19 - 4/19*j**3 + 6/19*j**2 = 0.
-2, 1
Suppose -2*t + 3*d = -13, -3*d + 4*d = -3. Factor -2/9*c**t - 8/9*c**4 + 0*c - 10/9*c**3 + 0.
-2*c**2*(c + 1)*(4*c + 1)/9
Let l(a) be the first derivative of -2*a**3/15 + 12*a**2/5 - 72*a/5 - 25. Factor l(g).
-2*(g - 6)**2/5
Let i(p) be the third derivative of p**6/360 - p**5/120 - p**4/12 - 2*p**3/3 + 2*p**2. Let o(s) be the first derivative of i(s). Solve o(q) = 0 for q.
-1, 2
Suppose 0*h + 0*h**3 - 27/4*h**5 + 0*h**2 + 0 + 3/2*h**4 = 0. What is h?
0, 2/9
Let z = -1 - -4. Suppose -3*d + 10 = -m, 2*d = m + z*m. Factor 3*y**2 - 3*y**4 + m*y**3 + 12*y**5 - 4*y**4 - 2*y**2 - 8*y**5.
y**2*(y - 1)**2*(4*y + 1)
Let f(h) be the first derivative of -3*h**5/5 + 3*h**4 - 5*h**3 + 3*h**2 + 46. Factor f(a).
-3*a*(a - 2)*(a - 1)**2
Let d(i) be the third derivative of 1/600*i**6 + 2/15*i**3 + 7*i**2 + 0 + 1/15*i**4 + 0*i + 1/60*i**5. Factor d(c).
(c + 1)*(c + 2)**2/5
Let h be 1 - (-2)/(5 + -3). Suppose -4*c + 24 = -4*g, 2*c + g = -h*g - 8. Determine i, given that 0 + 1/2*i - 5/4*i**c = 0.
0, 2/5
Let k(y) be the second derivative of -y**5/120 + y**4/24 - y**3/18 + 7*y. Let k(w) = 0. What is w?
0, 1, 2
Suppose 0 = -5*j - 8 - 12. Let u(d) = 8*d**2 + 3*d - 11. Let b(t) = 3*t**2 + t - 4. Let k(c) = j*u(c) + 11*b(c). Find s such that k(s) = 0.
0, 1
Let y(c) be the second derivative of -c**5/30 + c**3/3 + 2*c**2/3 - 8*c. Suppose y(p) = 0. Calculate p.
-1, 2
Let f(a) be the third derivative of -a**2 + 0 - 1/8*a**4 - 3/20*a**5 + 0*a**3 + 0*a. Determine r so that f(r) = 0.
-1/3, 0
What is t in -5*t**3 - t**4 + 2*t - 2 - 7*t - 9*t**2 - 2*t = 0?
-2, -1
Let h(c) = 5*c**5 + 21*c**4 - 2*c**3 - 13*c**2 + 11*c. Let d(i) = -i**5 - i**4 + i**2 - i. Let y(r) = 22*d(r) + 2*h(r). Let y(m) = 0. What is m?
-1/3, 0, 1
Let f(y) be the second derivative of -y**5/90 - y**4/36 - y**2/2 + 4*y. Let n(o) be the first derivative of f(o). Find z, given that n(z) = 0.
-1, 0
Let p be (-16)/12*(-2)/20. Let g(n) be the first derivative of 0*n - 2/27*n**3 - p*n**5 + 0*n**2 - 2/9*n**4 + 1. Factor g(u).
-2*u**2*(u + 1)*(3*u + 1)/9
Let t(p) be the second derivative of p**10/10080 + p**9/3024 + p**8/6720 - p**7/2520 - 5*p**4/12 - p. Let m(n) be the third derivative of t(n). Factor m(q).
q**2*(q + 1)**2*(3*q - 1)
Suppose -5*s = -3*g - 20, 2*g + s = 3 + 1. Factor -1/4*r - 1/2*r**3 + g + 3/4*r**2.
-r*(r - 1)*(2*r - 1)/4
Let r(l) be the second derivative of l**5/20 - l**3/6 - 4*l. Let v be r(1). Solve 0 + 0*i**2 + 2/5*i**5 - 2/5*i**3 + v*i + 0*i**4 = 0 for i.
-1, 0, 1
Determine k so that 1 - 5 + 4*k**2 - 4*k + 0 + 4*k**3 = 0.
-1, 1
Let o(i) be the first derivative of 3/10*i**5 + 3/2*i**2 - 3/4*i**4 - 1/2*i**3 - 7 + 0*i. Factor o(s).
3*s*(s - 2)*(s - 1)*(s + 1)/2
Let y(k) be the second derivative of 1/4*k**3 + 0*k**2 + 2*k + 0 + 1/8*k**4. Suppose y(q) = 0. Calculate q.
-1, 0
Suppose -2 = s - 6. Let v be (6/s)/(8/16). Factor 6*a**3 - 2*a**2 - 11*a**3 + 0*a**v.
-a**2*(5*a + 2)
Suppose 5*b = -b + 30. Let y(v) be the secon