 Calculate r.
-1, 0
Let b be (-4)/(-18) - (-12)/(-54). Let y(z) be the third derivative of -1/60*z**4 + 1/300*z**5 + b*z + 1/30*z**3 + z**2 + 0. Factor y(j).
(j - 1)**2/5
Let l be (5/(-35))/(1/(-4)). Let p = 37 + -253/7. Let l - 6/7*h - 4/7*h**2 + p*h**3 = 0. What is h?
-1, 2/3, 1
Suppose -k = -13*k + 24. Factor 4/5*d**k - 2/5*d - 2/5*d**3 + 0.
-2*d*(d - 1)**2/5
Let v(c) be the second derivative of -c**7/336 - c**6/80 - 3*c**5/160 - c**4/96 - 6*c. Let v(f) = 0. What is f?
-1, 0
Let l = 349/3 - 115. Let i(c) be the first derivative of 1 + 0*c - 2/3*c**2 - l*c**6 + 10/9*c**3 + 7/3*c**4 - 2/3*c**5. Solve i(r) = 0.
-1, -2/3, 0, 1/4, 1
Let w = -17 + 4. Let d = -9 - w. Determine v, given that 1/4*v**d + 0*v**3 - 1/4*v**2 + 0*v + 0 = 0.
-1, 0, 1
Let h(a) be the first derivative of -4*a**3/15 + 16*a/5 - 23. Factor h(t).
-4*(t - 2)*(t + 2)/5
Let m(y) be the third derivative of 1/72*y**4 - 1/180*y**5 + 1/9*y**3 - 5*y**2 + 0*y + 0. Factor m(u).
-(u - 2)*(u + 1)/3
Factor -2/3*b**3 + 2/3*b + 1/3 - 1/3*b**4 + 0*b**2.
-(b - 1)*(b + 1)**3/3
Factor 0*t + 3/2*t**2 - 3/2.
3*(t - 1)*(t + 1)/2
Let v be 8 + -3 + 116/(-12) - -5. Solve 1/3*l - 2/3 + v*l**2 = 0 for l.
-2, 1
Let y be 1/(1/((-6)/(-3))). What is w in 4*w + 2*w**y - 4 - 1 + 3 + 4 = 0?
-1
Let f(w) be the first derivative of 2 - 1/8*w**4 + 0*w - 1/12*w**3 + 0*w**2 - 1/20*w**5. Factor f(k).
-k**2*(k + 1)**2/4
Factor 12*z - 11*z + 7*z - 2*z**3.
-2*z*(z - 2)*(z + 2)
Let k(y) = y**3 - y. Let b(s) be the second derivative of -1/15*s**6 + s**2 + 0*s**5 - s + 0*s**3 + 0 + 0*s**4. Let x(v) = -b(v) + 4*k(v). Factor x(l).
2*(l - 1)*(l + 1)**3
Let t be (-21)/6*(-6)/28*4. Let r(b) be the third derivative of -7/36*b**4 + 2/9*b**t + 0 + 0*b - 2/45*b**5 - 2*b**2. Solve r(d) = 0 for d.
-2, 1/4
Find d such that 2/5*d**4 + 0*d + 0*d**3 - 2/5*d**2 + 0 = 0.
-1, 0, 1
Let a be 6/3*(-5)/4 + 3. Factor 1/4 - a*i + 1/2*i**3 - 1/4*i**4 + 0*i**2.
-(i - 1)**3*(i + 1)/4
Let q be 4/6 - 8/(-6). Let -6*o - 6*o - 10*o**2 + q*o + 6*o = 0. Calculate o.
-2/5, 0
Suppose 5*c = 58 - 3. Let 5*a - 10*a + 4*a**2 - 4 + 16*a**3 - c*a + 0*a**2 = 0. Calculate a.
-1, -1/4, 1
Let s be (2 - 0)/(1 + -3). Let o(a) = 1. Let q = 15 - 9. Let b(d) = 2*d**2 - 4*d + 8. Let f(r) = q*o(r) + s*b(r). Factor f(y).
-2*(y - 1)**2
Suppose 0 = 3*u - 2*h - 19, -4*u + 0*h = -h - 17. Find k such that -4*k**4 + 3*k**2 - 19*k**3 + 7*k**u - 11*k**2 = 0.
-2, -1, 0
Let n(h) be the first derivative of -h**6/1800 - h**5/600 + h**3 + 3. Let d(u) be the third derivative of n(u). Let d(t) = 0. Calculate t.
-1, 0
Let v be ((-20)/110)/(-2 + 1). Factor -v*f**3 + 0*f**2 + 0 + 2/11*f.
-2*f*(f - 1)*(f + 1)/11
Let y be 15/(-3) - (-190)/20. Factor -1/2 - 3*i - y*i**2.
-(3*i + 1)**2/2
Let b = -46 + 48. Let g(x) be the first derivative of 9/8*x**b - 1/2*x + 2 + 3/16*x**4 - 5/6*x**3. Factor g(h).
(h - 2)*(h - 1)*(3*h - 1)/4
Let d(w) = 2*w - 2. Let i be d(3). Suppose -9 = -i*a + a. Let -12*p**4 - 14*p**4 - 4*p**2 + 0*p**3 + 4*p - 7*p**5 - 27*p**a = 0. What is p?
-2, -1, 0, 2/7
Let j(d) = -d**2 + d + 6. Let g be j(0). Factor -h + 3*h**2 + 1 - g*h**2 + 2*h**2 + h**3.
(h - 1)**2*(h + 1)
Let d(k) be the first derivative of 5*k**3/3 - 25*k**2/2 + 20*k + 37. Let d(f) = 0. Calculate f.
1, 4
Determine z, given that 10/7*z**4 + 10/7*z + 2/7 + 20/7*z**2 + 2/7*z**5 + 20/7*z**3 = 0.
-1
Let c be -2 + 41/13 + (-10)/65. Let i(y) be the first derivative of -c - 1/4*y**4 + 1/2*y**2 + 2*y - 5/3*y**3 + 3/5*y**5. Factor i(d).
(d - 1)**2*(d + 1)*(3*d + 2)
Let u(q) be the second derivative of -1/66*q**4 + 0*q**2 - 1/33*q**3 + 4*q + 1/110*q**5 + 0 + 1/165*q**6. Factor u(p).
2*p*(p - 1)*(p + 1)**2/11
Let f = 0 - 1. Let o(g) = g**2 + 2*g + 1. Let y be o(f). Factor 2 - 6*d + 2*d**2 + 2*d + y*d.
2*(d - 1)**2
Suppose 53 = -4*b - 23. Let f = b - -22. Suppose 1/4*a**4 + 1/2*a**2 - 3/4*a**f + 0 + 0*a = 0. What is a?
0, 1, 2
Let q = 15 + -25. Let h = -6 - q. Let 1/3*k**h + 0*k**2 + 0 + 2/3*k**3 - 1/3*k**5 + 0*k = 0. What is k?
-1, 0, 2
Let z be (-55)/(-75) + 1/(0 + -3). Suppose 2/5*m**2 - z*m**3 + 2/5*m - 2/5 = 0. What is m?
-1, 1
Let r(z) be the second derivative of 0 + 3*z + 1/3*z**3 - 1/12*z**4 + 0*z**2. Let r(p) = 0. What is p?
0, 2
Let l(p) = -9*p**2 - 6*p + 7. Let q(k) = 3*k**2 + 2*k - 2. Let n(t) = -6*l(t) - 21*q(t). Let n(s) = 0. Calculate s.
-2/3, 0
Let w = 3/13 + 11/65. Factor 0*j + 2/5*j**3 + 0 - w*j**2.
2*j**2*(j - 1)/5
Let j(x) be the second derivative of x**7/840 - x**6/240 + x**5/240 - x**2 + 4*x. Let a(p) be the first derivative of j(p). Factor a(q).
q**2*(q - 1)**2/4
Let y(x) = -x**2 + x - 1. Let c(k) = -4*k**2 + 4*k - 8. Let i(l) = -c(l) + 5*y(l). Let v be i(0). Factor -154/3*s**2 - 8/3 - 98/3*s**v - 64/3*s.
-2*(s + 1)*(7*s + 2)**2/3
Let v(m) be the first derivative of -27*m**4/20 + 9*m**3/5 - 9*m**2/10 + m/5 - 11. Factor v(c).
-(3*c - 1)**3/5
Let r(v) be the second derivative of v**6/150 - 3*v**5/100 + v**4/20 - v**3/30 - 6*v. Factor r(b).
b*(b - 1)**3/5
Let t(v) = -14*v**3 - 4*v - 4. Let m be t(-2). Determine i, given that 110*i**4 + 287*i**2 + 32 - 190*i**4 - 84*i**3 + 201*i**2 - 240*i - m*i**4 = 0.
-2, 2/7, 1
Factor 2*t**4 + 132*t**2 - 132*t**2.
2*t**4
Factor 0*r + 0 + 1/4*r**4 - 1/4*r**2 + 0*r**3.
r**2*(r - 1)*(r + 1)/4
Let d = 2268 + -22900/9. Let t = -276 - d. Factor -t - 2/9*w**3 - 10/9*w - 8/9*w**2.
-2*(w + 1)**2*(w + 2)/9
Suppose 1/2*g**4 + 0 + 1/2*g**3 + 0*g + 0*g**2 = 0. What is g?
-1, 0
Let a(r) be the third derivative of 0*r**3 + 0*r**4 + 0 + 2*r**2 - 1/150*r**5 + 1/300*r**6 + 0*r. Factor a(z).
2*z**2*(z - 1)/5
Let r(x) be the first derivative of 3 + 2/5*x + 1/15*x**3 + 3/10*x**2. Determine a, given that r(a) = 0.
-2, -1
Let r = 108 + -1295/12. Let a(k) be the third derivative of 0*k + 0 + 1/30*k**5 + 0*k**3 + k**2 - r*k**4. Factor a(q).
2*q*(q - 1)
Let m = -2 + 5. Factor 4*o - 3*o**2 + 3*o**2 + 2*o**m + 6*o**2.
2*o*(o + 1)*(o + 2)
Suppose -j + 44 = 3*j. Suppose -3*q**3 + j*q**3 - 2*q**5 + 4*q**2 - 9*q - 4 + 3*q = 0. What is q?
-1, 1, 2
Let a(z) be the second derivative of 2*z**3/3 - 5*z. Let k(v) = v**2 + 8*v. Let y(r) = -7*a(r) + 4*k(r). Factor y(p).
4*p*(p + 1)
Let l(n) = n**3 + 7*n**2 - 7*n - 1. Let i be l(-8). Let c be (2 - 1)*(-3)/i. Let 0*v - c + 1/3*v**2 = 0. Calculate v.
-1, 1
Let i(t) = t**3 + 2*t**2 - 9*t - 2. Let k be i(-4). Let 0 + 0*a + 0*a**3 + 0*a**k + 1/2*a**4 = 0. Calculate a.
0
Let d(y) be the third derivative of -5*y**8/1008 + 2*y**7/63 - 5*y**6/72 + y**5/18 + 50*y**2. Find g such that d(g) = 0.
0, 1, 2
Let a = 22 + -20. Factor -2*q - q**3 + 0 + 0 - a*q**2 - q**2.
-q*(q + 1)*(q + 2)
Let w(k) be the first derivative of -k**6/3 - 4*k**5/5 + k**4 + 16*k**3/3 + 7*k**2 + 4*k - 19. Factor w(o).
-2*(o - 2)*(o + 1)**4
Suppose -6*z + 2*z = -4*t + 4, -t - 3 = -3*z. Factor -5 + b**4 - b + 4 - z*b**3 + 3*b.
(b - 1)**3*(b + 1)
Let k(p) = 5*p**2 - p + 5. Let i(n) = 8*n**2 - 5*n - 3. Let r(t) = t**2 - t - 1. Let z(x) = i(x) - 5*r(x). Let q(b) = 2*k(b) - 5*z(b). What is h in q(h) = 0?
-2/5, 0
Suppose j = 3*t - j - 6, 5*j - 8 = -4*t. Let s(f) be the first derivative of 3 - 2/21*f**3 + 0*f**t + 1/14*f**4 + 0*f. Determine r, given that s(r) = 0.
0, 1
Let p(j) = -55*j + 222. Let w be p(4). Determine h so that 0*h - 3/4*h**w + 0 = 0.
0
Let b = -19 + 56. Let v = b - 37. Let -2/7 + v*h + 2/7*h**2 = 0. What is h?
-1, 1
Let v(n) be the third derivative of -3*n**6/160 - 7*n**5/80 + 17*n**4/96 - n**3/8 + 13*n**2. Let v(b) = 0. Calculate b.
-3, 1/3
Let n(q) be the third derivative of 0*q + 0*q**3 + 1/140*q**7 + 0 + 1/80*q**6 - 1/40*q**5 - 1/16*q**4 - 5*q**2. Factor n(d).
3*d*(d - 1)*(d + 1)**2/2
Suppose -3*n + 4*w + 6 = -4*n, 5*w + 18 = 4*n. Solve y**5 + y**4 + 0*y**4 - 6*y**n + 6*y**2 = 0.
-1, 0
Let g(l) = 2*l**3 - l**2 - 4*l + 1. Let b = 6 - 9. Let j(d) = -2*d**3 + 2*d**2 + 5*d - 2. Let c(z) = b*g(z) - 2*j(z). Find n such that c(n) = 0.
-1, -1/2, 1
Let k be (-2)/6 + 3/(0 + 9). Determine o, given that -1/3*o**5 + 0 + 2/3*o**3 + 0*o**4 + k*o**2 - 1/3*o = 0.
-1, 0, 1
Suppose 4*j + 6 = 18. Factor 2*k**2 - 2*k + j*k + 2*k**2 - 3*k**2.
k*(k + 1)
Let z(m) be the first derivative of 3/2*m**3 - 3*m + 8 - 3/4*m**2. Determine y, given that z(y) = 0.
-2/3, 1
Let d = -124/3 + 626/15. Let r be (-36)/15*(-1)/2. Solve 0 - d*t + r*t**2 - 6/5*t**3 + 2/5*t**4 = 0 for t.
0, 1
Let a be -4 + 65/15 + 1. Let f(s) be the f