 k(z) be the third derivative of -2/3*z**m + 2*z**2 - 1/15*z**6 + 1/3*z**5 + 0 + 0*z + 2/3*z**3. Factor k(a).
-4*(a - 1)**2*(2*a - 1)
Let r(t) be the second derivative of t**7/210 + 19*t**6/25 + 1083*t**5/25 + 13718*t**4/15 + 2*t + 125. Let r(j) = 0. Calculate j.
-38, 0
Let y(p) be the second derivative of -9*p + 0*p**3 - 3/110*p**5 + 0*p**2 + 1/77*p**7 + 0 - 2/165*p**6 + 1/33*p**4. Determine o, given that y(o) = 0.
-1, 0, 2/3, 1
Let x(y) be the second derivative of -y**4/4 + 14*y**3/3 - 57*y**2/2 + 2*y + 375. Find o such that x(o) = 0.
3, 19/3
Let i = 5/233 - -559/6524. Let p(c) be the first derivative of i*c**4 - 3/14*c**2 - 1/21*c**3 - 4 + 2/7*c - 1/35*c**5. Factor p(t).
-(t - 2)*(t - 1)**2*(t + 1)/7
Let c(q) be the second derivative of 16*q + 1/11*q**2 + 1/66*q**4 + 0 - 2/33*q**3. Factor c(f).
2*(f - 1)**2/11
Let t(i) be the first derivative of 5*i**2 + 0*i + 21 + 5/2*i**4 + 25/3*i**3. Factor t(a).
5*a*(a + 2)*(2*a + 1)
Let t(r) = -5*r + 21. Let c(a) = 4*a - 20. Let h(x) = 6*c(x) + 5*t(x). Let k be h(-18). Find v such that -1/5*v**4 + 0*v**k - 1/5*v**5 + 0*v + 0 + 0*v**2 = 0.
-1, 0
Let z = 133/18 - 19/18. Let s = z + -35/6. Factor s*a**2 + 0*a - 3/2*a**3 + 0 + a**4.
a**2*(a - 1)*(2*a - 1)/2
Determine h, given that 110 - 5/2*h**2 + 274*h = 0.
-2/5, 110
Let i be 6/(-39) - (29/(-39) - -3). Let a = i + 40/13. Solve 0*l + 0 + 2/3*l**2 + a*l**3 = 0.
-1, 0
Let -4 - 45*n**2 - 2*n - 12*n - 40*n**2 - 6*n + 76*n**2 = 0. Calculate n.
-2, -2/9
Suppose -45*u - 12 = -48*u. Let v(n) be the third derivative of 5*n**2 - 1/140*n**5 - 1/14*n**3 + 0*n + 1/28*n**u + 0. Factor v(y).
-3*(y - 1)**2/7
Let i = 3751 - 11183/3. Let 8/3*v + i*v**3 + 0 + 52/3*v**2 - 49/3*v**4 = 0. What is v?
-2/7, 0, 2
Suppose -2*u = -5*t - 7*u - 85, 3*t + 55 = u. Let y be (-52)/t + 5/45. Solve 2/7*z**5 - 4/7*z**4 + 0 + 4/7*z**2 - 2/7*z**y + 0*z = 0 for z.
-1, 0, 1, 2
Let r be -3 + 1 + -2 + 7. Suppose 0 = -4*m + r*m + 3. Factor -5*l**2 - m*l + 3*l**3 + 4 + 1 + 2*l**2 - 2.
3*(l - 1)**2*(l + 1)
Let i(o) = 9*o**3 - 127*o**2 + 1162*o - 1014. Let g(a) = 4*a**3 - 64*a**2 + 580*a - 508. Let q(b) = -5*g(b) + 2*i(b). Let q(w) = 0. What is w?
1, 16
Let y be 9 + -1 + 24/(-6). Let -36/13*z**2 - 14/13 + 2/13*z**y + 40/13*z + 8/13*z**3 = 0. Calculate z.
-7, 1
Let u(x) be the third derivative of -x**8/168 - 4*x**7/105 - x**6/20 + x**2 - 8*x. Determine r so that u(r) = 0.
-3, -1, 0
Let a be 10/(-2) - (40/(-32) + -7 - 0). Suppose 7/2*v**2 - 3/4*v**3 - a*v - 3/2 = 0. Calculate v.
-1/3, 2, 3
Let j(p) be the first derivative of 25*p**6/2 - p**5 - 235*p**4/4 - 45*p**3 + 20*p**2 + 20*p - 35. Suppose j(i) = 0. What is i?
-1, -1/3, 2/5, 2
Suppose -6/13*f - 4/13 - 2/13*f**2 = 0. Calculate f.
-2, -1
Let j(x) = 7*x**2 - 11*x + 7. Let h(d) = 4*d**2 - 6*d + 3. Let s(f) = 11*h(f) - 6*j(f). Let y be s(-4). Solve -7*u**3 + 6 - 20*u - 4 - 6 - y*u**2 = 0 for u.
-2, -1, -2/7
Let w(j) be the third derivative of j**6/120 + j**5/20 - j**4/4 - j**3 - 5*j**2. Let s be w(-4). Factor -6 + 3 - 3*g**s + 5*g**2 + g**2.
3*(g - 1)*(g + 1)
Let p be (1844/1383)/(1 + 0). Factor p + 2/9*s - 2/9*s**2.
-2*(s - 3)*(s + 2)/9
Suppose -3*q + 48*q = -80*q. Find o, given that 14/3*o**2 + 4/3*o + 4/3*o**3 + q - 2*o**4 = 0.
-1, -1/3, 0, 2
Let i(w) = 5*w**3 - 52*w**2 - 4*w + 2. Let o(c) = -2*c**3 + 23*c**2 + 2*c - 2. Let l(y) = 3*i(y) + 7*o(y). Factor l(z).
(z - 1)*(z + 2)*(z + 4)
Let b(r) be the second derivative of 2*r**5/25 + 7*r**4/15 + 14*r**3/15 + 4*r**2/5 - 84*r - 3. Factor b(j).
4*(j + 1)*(j + 2)*(2*j + 1)/5
Suppose -161*m + 48 = -157*m. Determine h so that -12 + 14*h - 50*h**2 + 5*h**5 - 30*h**4 + m + 60*h**3 + h = 0.
0, 1, 3
Let n(c) = 7*c**4 + 11*c**3 - 5*c**2 - 5*c - 5. Let q(i) = 2*i**4 + i**3 - i**2 - i - 1. Let w(o) = n(o) - 5*q(o). Let w(l) = 0. What is l?
0, 2
Let a be ((-12)/15)/(18/(-435)). Let d = 20 - a. Suppose d*i - 1/3*i**4 + 1/3 - 2/3*i**3 + 0*i**2 = 0. What is i?
-1, 1
Find c such that -116/3*c - 4/3*c**2 - 104 = 0.
-26, -3
Let u(v) be the second derivative of -v**7/2 + 12*v**6/5 + 69*v**5/20 - 6*v**4 - 8*v**3 - v - 20. Solve u(n) = 0 for n.
-1, -4/7, 0, 1, 4
Suppose -4*x = -u - 17, 0 = 4*u + 4*x - 12 - 20. Determine f so that -20 + 180*f + 298*f**3 - 76*f**3 - 50*f**4 + 138*f**u - 485*f**2 - 30*f**4 = 0.
1/4, 2
Let b(r) be the second derivative of -r**5/80 + 11*r**4/48 + 232*r. Suppose b(n) = 0. What is n?
0, 11
Let g(t) = 17 + 13 + 15 + 1 - 9*t. Let q be g(5). Factor -j**2 + 5/2*j - 1/2*j**5 - 2*j**3 - q + 2*j**4.
-(j - 2)*(j - 1)**3*(j + 1)/2
Let z(i) be the second derivative of 40*i**7/21 + 76*i**6/15 - 67*i**5/20 - 121*i**4/12 - 20*i**3/3 - 2*i**2 + 72*i. Let z(k) = 0. Calculate k.
-2, -2/5, -1/4, 1
Suppose 4*r + 5*d - 19 = 2*d, -5*d - 7 = -3*r. Let w(o) be the first derivative of 0*o**2 + 1/2*o**r + 0*o**3 + 1/5*o**5 - 3 + 0*o. Solve w(y) = 0 for y.
-2, 0
Let t(z) be the first derivative of -7 + 9/20*z**4 + 3/25*z**5 + 0*z + 0*z**3 - 6/5*z**2. Factor t(s).
3*s*(s - 1)*(s + 2)**2/5
Suppose 5*u + 28 = 7*u. Let m be ((-9)/u)/((-24)/140*5). Let -m*o**3 - 3/4 + 3/4*o + 3/4*o**2 = 0. What is o?
-1, 1
Let m(j) be the second derivative of -j**4/12 + 6*j**3 - 162*j**2 + 415*j. What is k in m(k) = 0?
18
Suppose 2/5*a + 1/5*a**2 - 3/5 = 0. Calculate a.
-3, 1
Let w(c) = 4*c**2 + 2*c + 7. Let m(q) = -7*q + q - 60*q**2 + 43*q**2 - q - 29. Let u(i) = 6*m(i) + 26*w(i). Let u(t) = 0. What is t?
-4, -1
Let t(p) be the first derivative of -40 - 5/7*p**3 + 18/7*p - 69/14*p**2 + 3/7*p**4. Suppose t(y) = 0. What is y?
-2, 1/4, 3
Let w(q) be the second derivative of q**4/24 - 13*q**3 + 1521*q**2 + 8*q. Solve w(p) = 0 for p.
78
Let j(t) = 6*t**3 + 128*t**2 - 239*t + 112. Let g(m) = 4*m**3 + 64*m**2 - 120*m + 56. Let q(p) = -7*g(p) + 4*j(p). Suppose q(d) = 0. Calculate d.
1, 14
Let f(k) be the third derivative of 0*k**4 - 1/510*k**5 + 0*k + 0 - 1/1020*k**6 + 1/2856*k**8 + 1/1785*k**7 + 0*k**3 - 43*k**2. Factor f(p).
2*p**2*(p - 1)*(p + 1)**2/17
Let u(y) be the second derivative of 5*y**4/12 - y**2 - 17*y. Let c be u(1). Factor 1/4*n**2 - 1/4 + 1/4*n**c - 1/4*n.
(n - 1)*(n + 1)**2/4
Factor -108/7 + 53/7*f**2 + 1/7*f**3 - 8*f.
(f - 2)*(f + 1)*(f + 54)/7
Let t(x) be the third derivative of -14*x**2 - 1/60*x**6 + 0 + 0*x**4 + 1/168*x**8 - 1/30*x**5 + 0*x**3 + 0*x + 1/105*x**7. Factor t(z).
2*z**2*(z - 1)*(z + 1)**2
Let 2/9*c**5 - 8/9 - 2/9*c**2 + 2/9*c**4 - 10/9*c**3 + 16/9*c = 0. Calculate c.
-2, 1
Let z(u) = 4*u + 10. Let n be z(-2). Let -9*j**n + 27*j**2 - 2*j**3 + 139 - 30*j - 96 - 93 = 0. What is j?
-1, 5
Let p(r) be the third derivative of -r**8/50400 - r**7/6300 + r**6/225 + 17*r**5/60 + 18*r**2. Let z(m) be the third derivative of p(m). Factor z(v).
-2*(v - 2)*(v + 4)/5
Let t(l) be the first derivative of 0*l - 3*l**2 + 2/3*l**3 - 12. Determine r, given that t(r) = 0.
0, 3
Let j(y) = 4*y**4 - 3*y**3 + 4*y**2 - 16*y + 11. Let u = 69 - 72. Let q(z) = -z**4 + z**3 + z**2 - 1. Let h(b) = u*j(b) - 21*q(b). Solve h(n) = 0.
-2, 1/3, 1, 2
Suppose 0 = -3*s - p + 12, -3*p + 0*p + 15 = 2*s. Suppose 5*n - 17 = 3. Factor 3*z**4 - z**3 - n*z**5 + 7*z**4 - 4*z**s - z**5.
-5*z**3*(z - 1)**2
Let i = -2 + 5. Suppose -8 = -5*n - 3*l + 1, 0 = -3*n - 3*l + i. Factor 0 + 8/7*j - 6/7*j**2 - 2/7*j**n.
-2*j*(j - 1)*(j + 4)/7
Let s(n) be the second derivative of n**4/54 + 14*n**3/27 - 16*n. Let s(z) = 0. Calculate z.
-14, 0
Let s be 64*(1 - 2 - (-11)/22). Let o be s + 38 - (-16)/(-6). Factor o*d + d**2 + 1.
(d + 3)*(3*d + 1)/3
Determine c so that -5*c**4 + 16*c**4 - 6*c - 4*c**4 - 2*c**4 - 5*c**2 + c**5 + 5*c**3 = 0.
-3, -2, -1, 0, 1
Let k(n) be the third derivative of 0 + 0*n**3 - 1/40*n**6 + 1/2*n**4 + 1/140*n**7 - 5*n**2 - 1/10*n**5 + 0*n. Factor k(f).
3*f*(f - 2)**2*(f + 2)/2
Let i(p) be the second derivative of -1/14*p**6 - 1/7*p**4 + 0*p**3 + 6/35*p**5 + 0 + 1/98*p**7 - 8*p + 0*p**2. Let i(b) = 0. What is b?
0, 1, 2
Let w(y) = -y**2 - 16*y + 15. Let n be w(-17). Let r(s) = 24*s**3 + 72*s**2 + 32*s - 130. Let x(k) = -k**4 + k**3 - 1. Let g(c) = n*x(c) + r(c). Factor g(m).
2*(m - 1)*(m + 4)**3
Let z = -30805 + 30808. Solve -8/5*i - 6/5*i**2 + 2/5*i**z + 0 = 0.
-1, 0, 4
Let x be (8 - (5 + -6))/(3/2). Find i such that i**3 + 4 - 9*i**2 + 15*i**2 + 3*i + x*i = 0.
-4, -1
Let b be 4/(16/4) - (1 + 2). Let r be (-105)/10*(24/15 + b). What is i in r*i**2 + 0 - 