 0, 1
Let b(f) be the second derivative of -f**7/840 - f**6/240 + f**5/240 + f**4/48 - 5*f**2/2 + f. Let o(v) be the first derivative of b(v). Factor o(s).
-s*(s - 1)*(s + 1)*(s + 2)/4
Let c(a) = -9*a**3 + 6*a**2 + 4*a + 4. Let t(y) = 19*y**3 - 13*y**2 - 9*y - 9. Let k(s) = -9*c(s) - 4*t(s). Determine f so that k(f) = 0.
0, 2/5
Let 0*v**4 - 7*v**2 - 3*v**2 + 13*v**2 - 2*v + 4*v**3 - 4*v**4 - 1 = 0. Calculate v.
-1/2, 1
Solve -h**2 - 4 + 5*h**2 - 4*h**4 + 4*h**2 + 0*h**4 = 0.
-1, 1
Factor -27/4*a + 0 + 3/4*a**4 - 3/4*a**2 + 27/4*a**3.
3*a*(a - 1)*(a + 1)*(a + 9)/4
Let d = -6 + 7. Let t be d/3 + 1/(-21). Solve -t*b - 16/7*b**5 + 6/7*b**3 + 0 + 8/7*b**2 - 20/7*b**4 = 0.
-1, 0, 1/4, 1/2
Let i be 5/40 + (-65)/(-120). Let -i*s**2 + 0 - 4/3*s = 0. Calculate s.
-2, 0
Let b(u) = 2*u**2 + 13*u - 7. Let r be b(-7). Let n(h) be the first derivative of r*h**2 + 1/9*h**4 + 0*h + 2/27*h**3 - 2 + 2/45*h**5. Factor n(l).
2*l**2*(l + 1)**2/9
Let w = -271/35 + 57/7. Factor 0*i**3 + 0 + 0*i + 0*i**2 - 3/5*i**5 - w*i**4.
-i**4*(3*i + 2)/5
Let z be (-14 + 20)/(4/2). Suppose -k - z*k = 0. Factor 0*i**4 + 0 - 2/7*i**5 + k*i**2 + 2/7*i**3 + 0*i.
-2*i**3*(i - 1)*(i + 1)/7
Let n be 0 - -2 - (7 - 1). Let k = 1 - n. Factor -k*v**3 - 2 - 5*v**5 + 7*v**4 - 32*v**2 - 13*v - 29*v**4 - 33*v**3.
-(v + 1)**4*(5*v + 2)
Let s = -89 + 89. Factor 1/6*p**2 + s + 1/3*p.
p*(p + 2)/6
Suppose o = -4, -2*b - b + 26 = -5*o. Let 1/4*h**3 + 1 + 2*h + 5/4*h**b = 0. What is h?
-2, -1
Let z(f) be the third derivative of f**5/60 + 5*f**4/12 - 4*f**3/3 - f**2. Let q be z(-11). Factor 0*k + 0 - k**q - 1/3*k**5 - 1/3*k**2 - k**4.
-k**2*(k + 1)**3/3
Let h(v) be the first derivative of -1 + 0*v**2 - 1/6*v**3 + 0*v + 1/24*v**6 - 1/16*v**4 + 1/10*v**5. Determine l, given that h(l) = 0.
-2, -1, 0, 1
Let i(n) be the first derivative of n**6/9 + 4*n**5/15 + n**4/6 + 6. Solve i(q) = 0.
-1, 0
Let p(x) be the third derivative of -x**5/180 + x**3/18 - 5*x**2. Factor p(n).
-(n - 1)*(n + 1)/3
Let w(c) = -c**4 - c**3 + c**2 + 1. Let t(x) = 3*x**4 + 4*x**3 - 2*x**2 - 5. Let q(h) = -t(h) - 4*w(h). Let l(f) be the first derivative of q(f). Factor l(v).
4*v*(v - 1)*(v + 1)
Let o(i) be the second derivative of -i**6/55 + 3*i**4/11 - 8*i**3/11 + 9*i**2/11 + 4*i. Let o(k) = 0. What is k?
-3, 1
Let n(a) be the first derivative of -a**3/12 - a**2/4 - a/4 + 9. Determine c, given that n(c) = 0.
-1
Let p(f) be the first derivative of f**4/40 - f**3/15 - f**2/20 + f/5 - 7. Factor p(v).
(v - 2)*(v - 1)*(v + 1)/10
Let n(u) be the second derivative of -25*u**4/9 + 10*u**3/9 - u**2/6 + 9*u. Suppose n(m) = 0. What is m?
1/10
Let u(d) be the second derivative of -d**6/60 - d**5/40 + d**4/24 + d**3/12 + 2*d. Factor u(k).
-k*(k - 1)*(k + 1)**2/2
Let g(q) be the first derivative of -q**4/42 - 10*q**3/63 - q**2/3 - 2*q/7 + 51. Factor g(k).
-2*(k + 1)**2*(k + 3)/21
Let m(d) be the third derivative of d**8/2352 - 4*d**7/735 + 11*d**6/420 - d**5/15 + 17*d**4/168 - 2*d**3/21 + 5*d**2. Factor m(n).
(n - 4)*(n - 1)**4/7
Let c be (-3)/(-2) - (-17)/34. Let a(r) be the third derivative of 0*r**4 + 1/120*r**5 + 0*r + 3*r**c + 0 - 1/12*r**3. Solve a(i) = 0 for i.
-1, 1
Let b(q) be the first derivative of 8*q**3/9 - 7*q**2/3 + 2*q + 13. Factor b(r).
2*(r - 1)*(4*r - 3)/3
Suppose 13 + 14 = 3*k. Let u = k + -7. Factor -2/3*s**u + 4/3*s - 2/3.
-2*(s - 1)**2/3
Suppose -5*l + 17 = -h, -3*l - 5*h = -1 + 2. Let n(j) be the first derivative of 5*j**2 + 8/3*j**l - 1 + 2*j. Find q such that n(q) = 0.
-1, -1/4
Solve -3/4*o**3 + 3/4*o**5 + 1/2*o**4 - 1/2*o**2 + 0*o + 0 = 0.
-1, -2/3, 0, 1
Let q(a) = a + 8. Let c be q(-6). Let -i - 2*i - i**c + 3*i = 0. Calculate i.
0
Let f(g) be the third derivative of -7*g**6/180 - g**5/10 - g**4/18 - 17*g**2. What is v in f(v) = 0?
-1, -2/7, 0
Let t(x) = -x + 8. Let w be t(8). Suppose 0 = 2*l - w*l - 6. Factor 1/3*k**l - 1/3*k - 1/3*k**4 + 0 + 1/3*k**2.
-k*(k - 1)**2*(k + 1)/3
Let k(f) be the second derivative of -f**10/12096 - f**9/15120 + f**4/12 + 2*f. Let q(t) be the third derivative of k(t). What is i in q(i) = 0?
-2/5, 0
Let f(j) be the first derivative of 5/12*j**3 + j - 4 + 1/16*j**4 + j**2. Factor f(l).
(l + 1)*(l + 2)**2/4
Let a(r) be the second derivative of -r**7/105 + 2*r**6/75 + 3*r**5/25 - 2*r**4/3 + 19*r**3/15 - 6*r**2/5 - 19*r. Find b, given that a(b) = 0.
-3, 1, 2
Suppose 4*b + 3 = -3*q - 1, 3*q + 8 = -2*b. Factor 2/13*i**b - 6/13*i + 4/13.
2*(i - 2)*(i - 1)/13
Let v = -3 - -7. Let f = -2 + v. Find i, given that 2 + 4*i**2 + 6*i**3 - 8*i**4 - 8*i**5 - 4 - f*i + 2 = 0.
-1, 0, 1/2
Let i(a) = 28*a + 171. Let x be i(-6). Factor -1/2*l**x - 1/2*l**2 + 1/2*l + 1/2.
-(l - 1)*(l + 1)**2/2
Let b(i) be the second derivative of i**9/22680 - i**8/10080 - i**7/3780 + i**6/1080 - 7*i**4/12 + 3*i. Let v(m) be the third derivative of b(m). Factor v(j).
2*j*(j - 1)**2*(j + 1)/3
Let o(m) = -m + 1. Let v be o(-3). Suppose 3*q = -v*y - 10, -3*q + y = q - 12. Solve 8/5*x - 8/5 - 12/5*x**3 - 18/5*x**4 + 22/5*x**q = 0.
-1, 2/3
Suppose -11*h + 5 = 5. Let h*u**2 + 0 - 2/3*u + 2/3*u**3 = 0. What is u?
-1, 0, 1
Let j(c) be the third derivative of -c**6/900 + c**5/75 - c**4/15 + 4*c**3/3 + 7*c**2. Let y(x) be the first derivative of j(x). Factor y(v).
-2*(v - 2)**2/5
Let m(k) be the third derivative of -3*k**6/80 + k**5/6 - 13*k**4/48 + k**3/6 + 7*k**2. What is i in m(i) = 0?
2/9, 1
Let r(b) be the first derivative of b**6/9 - 2*b**5/15 - b**4/6 + 2*b**3/9 + 18. Factor r(u).
2*u**2*(u - 1)**2*(u + 1)/3
Let u be -3*4*((-111)/27 - -4). Factor u*q - 2/3*q**2 - 2/3.
-2*(q - 1)**2/3
Let q(k) be the second derivative of k**8/1440 - k**7/420 + k**6/540 - k**4/12 - k. Let z(h) be the third derivative of q(h). Factor z(p).
2*p*(p - 1)*(7*p - 2)/3
Let d(i) be the second derivative of -1/60*i**5 - 1/36*i**4 + 1/90*i**6 + 0 + 0*i**2 + 1/18*i**3 + 6*i. Determine o, given that d(o) = 0.
-1, 0, 1
Let h(s) = s**5 - s**4 + s**3 - s**2 + s - 1. Let w(a) = -2*a**5 + 3*a**4 - 4*a**3 + 3*a**2 - 3*a + 3. Let f(m) = 3*h(m) + w(m). Let f(b) = 0. What is b?
-1, 0, 1
Suppose 5*v = -25, -3*l - 4*v = 4 + 16. Let x(u) = -u**3 - u**2 + u + 2. Let z be x(l). Factor 1/2*c + 1/2*c**z - 1.
(c - 1)*(c + 2)/2
Let v = -47 - -49. Let -2/7 - 2/7*r**v - 4/7*r = 0. Calculate r.
-1
Let i(c) be the third derivative of -c**6/900 - c**5/100 - c**4/30 + 2*c**3/3 - 4*c**2. Let b(o) be the first derivative of i(o). Factor b(l).
-2*(l + 1)*(l + 2)/5
Let b(j) = j + 4. Let v be b(-4). Let z(o) be the second derivative of v*o**4 - 2/3*o**3 + o**2 + 1/5*o**5 + 0 - 1/15*o**6 - o. Factor z(g).
-2*(g - 1)**3*(g + 1)
Suppose -4*z + 30 = z + 2*a, z - 3*a + 11 = 0. Let o(b) be the first derivative of 3 + 16/3*b**3 + z*b + 3/2*b**4 + 7*b**2. Let o(h) = 0. What is h?
-1, -2/3
Let z = 278/3 - 92. Find f such that -z*f**3 - 2/9*f**5 + 0 + 2/3*f**4 + 2/9*f**2 + 0*f = 0.
0, 1
Let g = -55 + 496/9. Let f(p) be the second derivative of 0*p**2 + 0 - 1/18*p**4 - g*p**3 + 3*p. Find s such that f(s) = 0.
-1, 0
Let v(x) = -x**4 + 2*x**3 + 2*x**2 + 2. Let s(n) = -2*n**4 + 4*n**3 + 5*n**2 + 5. Let r(t) = 4*s(t) - 10*v(t). Let r(p) = 0. Calculate p.
0, 2
Let j(s) be the third derivative of s**8/4200 - s**7/700 + s**6/450 + s**3/2 - 3*s**2. Let n(x) be the first derivative of j(x). Factor n(c).
2*c**2*(c - 2)*(c - 1)/5
Let o(f) be the first derivative of f**3/15 + 3*f**2/10 - 4*f/5 - 21. Factor o(z).
(z - 1)*(z + 4)/5
Let q(s) = -2*s + 2. Let b be q(-3). Let i = -6 + b. Factor 0*y**2 - i + y**3 + 0 - 3*y + 0*y**2.
(y - 2)*(y + 1)**2
Find f such that 0*f - f + 8*f**2 + 4*f**3 - 8 - 3*f = 0.
-2, -1, 1
Factor -2/9*h**3 + 8/9 + 10/9*h**2 - 16/9*h.
-2*(h - 2)**2*(h - 1)/9
Let f = 1741/10 + -174. Let x(o) be the first derivative of 1 + 0*o + 1/20*o**4 + 1/25*o**5 - 1/15*o**3 - f*o**2. Solve x(u) = 0.
-1, 0, 1
Let u be -1 - (8/3)/(7/(-21)). Let d(p) be the third derivative of -1/21*p**u + 0*p**5 + 0*p**4 + 0 + 0*p + 0*p**3 - p**2 - 1/30*p**6. Factor d(a).
-2*a**3*(5*a + 2)
Let a(j) be the second derivative of -j**5/30 - j**4/12 - 3*j**2/2 - j. Let h(i) be the first derivative of a(i). Factor h(b).
-2*b*(b + 1)
Solve -4/5 - 36/5*t**2 + 26/5*t = 0.
2/9, 1/2
Let p(i) = i + 10. Let x be p(-7). Factor -4*r**2 - r**2 - 2*r**x + 4*r + 5*r**2 + 2*r**2.
-2*r*(r - 2)*(r + 1)
Let z(n) = -n**2 + 6*n - 6. Let t(h) = 6*h**2