ivative of -4/3*w**3 - 6 + 1/2*w**4 + c*w**2 + 0*w. Find i such that o(i) = 0.
0, 2
Let s(z) = -z**2 - 14*z**3 - 3*z**3 + 7*z**2 + 3*z**3. Let n = 6 - 17. Let q(t) = -5*t**3 + 2*t**2. Let x(k) = n*q(k) + 4*s(k). Factor x(g).
-g**2*(g - 2)
Let f(w) = 52*w - 49. Let k be f(1). Let x(p) be the third derivative of 0 + 1/144*p**4 - 8*p**2 + 1/360*p**5 - 1/18*p**k + 0*p. Factor x(g).
(g - 1)*(g + 2)/6
Let z(k) be the second derivative of -17*k**4/12 + 16*k**3/3 + 2*k**2 + 144*k. Solve z(q) = 0 for q.
-2/17, 2
Let h = 19 + 17. Suppose 5*m - h = -21. Factor 0*c + 0 + 2/9*c**2 - 2/9*c**m.
-2*c**2*(c - 1)/9
Let c(f) = -2*f**3 + 8*f**2 + 22*f + 12. Let s(k) = -k**3 + 4*k**2 + 11*k + 6. Suppose -7*n + 9*n + 6 = 0. Let x(w) = n*c(w) + 7*s(w). Factor x(a).
-(a - 6)*(a + 1)**2
Let y be (-708)/(-4602) + (2 - 48/(-26)). Suppose 2/7*g**y + 2/7*g**2 - 6/7*g**3 - 4/7 + 6/7*g = 0. What is g?
-1, 1, 2
Let s be 126/(-168) + 6869/28. Let p = 2690 - 18798/7. Determine h so that s*h**2 + p + 384/7*h + 480*h**3 + 350*h**4 = 0.
-2/5, -2/7
Let n(p) = p**3 - 24*p**2 - 23*p - 21. Let y be n(25). Factor 40 + y*f + 0*f + 2*f**2 + 3*f**2 + 16*f.
5*(f + 1)*(f + 8)
Suppose -4 = -2*g - 0. Let p(l) be the first derivative of -49/6*l**4 + 6 - 56/9*l**3 + 0*l - 4/3*l**g. Solve p(s) = 0.
-2/7, 0
Let b be (-2168)/(-1815) - (4 - 4). Let i = b + 2/363. Factor 0*w**2 + 3/5*w**5 + 3/5*w**3 + 0*w + 0 - i*w**4.
3*w**3*(w - 1)**2/5
Let y(i) be the third derivative of i**5/30 + 34*i**4/3 - 92*i**3 - 4*i**2 - 43*i. Factor y(b).
2*(b - 2)*(b + 138)
Let h(k) be the second derivative of -k**5/180 - 2*k**4/9 - 32*k**3/9 - 27*k**2/2 + 5*k + 4. Let m(c) be the first derivative of h(c). Let m(l) = 0. What is l?
-8
Let t = 1/5279 + 42227/26395. Find z such that z**3 + 1/5*z**4 + t*z**2 + 0 + 4/5*z = 0.
-2, -1, 0
Let f(j) be the third derivative of 1/10*j**4 + 0 + 0*j + 4/15*j**3 + 1/75*j**5 + 3*j**2. Suppose f(h) = 0. What is h?
-2, -1
Let n = -68 + 117. Suppose -2*o + 59 - n = 0. Factor -4/3*p**4 + 0 - 4/9*p**o + 0*p**2 - 8/9*p**3 + 0*p.
-4*p**3*(p + 1)*(p + 2)/9
Suppose 5*t = 122 - 197. Let d be (2/(-5))/(12/t). Factor -d + 1/4*w**2 + 1/4*w.
(w - 1)*(w + 2)/4
Let f be 4/62 - 44080/(-10602). Factor 14/9*n**4 + f*n**3 + 2/9*n**5 + 32/9*n + 50/9*n**2 + 8/9.
2*(n + 1)**3*(n + 2)**2/9
Let j be (((-9)/7)/(-3))/((-14)/(-98)). Let b(v) be the second derivative of v**j - 1/2*v**4 + 5*v - v**2 + 1/10*v**5 + 0. Let b(a) = 0. Calculate a.
1
Let j(u) be the second derivative of -2/3*u**3 + 0 - 3*u + 2/3*u**4 - 1/5*u**5 + 0*u**2. Factor j(z).
-4*z*(z - 1)**2
Let p(v) = -v**4 + v**2 - v - 1. Let g(k) = -k**4 + 64*k**3 - 223*k**2 + 3*k + 3. Let r(x) = g(x) + 3*p(x). Factor r(n).
-4*n**2*(n - 11)*(n - 5)
Let v(h) be the second derivative of 6*h + 1/30*h**4 + 1/3*h**3 + 6/5*h**2 + 0. Suppose v(q) = 0. What is q?
-3, -2
Let q = -341 - -341. Let r(z) be the third derivative of 0*z + 1/60*z**5 - 1/120*z**6 + 1/24*z**4 + q - 1/6*z**3 + 6*z**2. Let r(x) = 0. Calculate x.
-1, 1
Let c(l) be the third derivative of l**6/240 + 5*l**5/24 - 53*l**4/48 + 9*l**3/4 + 104*l**2 + 2. Suppose c(o) = 0. Calculate o.
-27, 1
Let q be (-1)/(-1*(4 - 3)). Let w be 32/((-3)/((-3)/q)). Determine p so that -16*p**3 + 2*p**2 + w*p**5 - p**3 + 3*p**3 + 15*p**4 + p**4 = 0.
-1, 0, 1/4
Let o = 21563/9 + -2395. Factor -2/3*j**2 - o*j + 8/9 + 4/9*j**3 + 2/9*j**4.
2*(j - 1)**2*(j + 2)**2/9
Suppose -4*y + 1054 - 1053 = a, 0 = -y + 5*a + 37. Factor -3/2*p**4 + 18*p**3 + 144*p - 78*p**y - 96.
-3*(p - 4)**2*(p - 2)**2/2
Let o(y) be the second derivative of 1/126*y**7 + 1/6*y**3 + 1/5*y**5 - 6*y + 5/18*y**4 + 0 + 0*y**2 + 1/15*y**6. Factor o(z).
z*(z + 1)**3*(z + 3)/3
Let j(f) be the first derivative of f**7/168 + f**6/36 + f**5/24 - 5*f**3/3 - 3. Let h(c) be the third derivative of j(c). Factor h(z).
5*z*(z + 1)**2
Factor 3/2*y + 3 - 3/2*y**2.
-3*(y - 2)*(y + 1)/2
Let n be (-18 - -12) + 9 + 0/(-6). Solve 3/4*u**2 - 1/4*u**4 + 0 + 0*u**n + 1/2*u = 0.
-1, 0, 2
Factor 0 - 11*s - 1/2*s**2.
-s*(s + 22)/2
Let x(t) = -3*t**3 - 303*t**2 + 462*t + 696. Let y(p) = p**3 + 77*p**2 - 116*p - 174. Let h(v) = 6*x(v) + 22*y(v). Determine a so that h(a) = 0.
-1, 3, 29
Suppose -y = -7 - 38. Factor -4*m - 5*m**2 - y - 22*m + 15*m - 19*m.
-5*(m + 3)**2
Find b, given that -23*b - 7 + 22 + 15 - 100 - 56 - b**2 = 0.
-14, -9
Let o(i) be the first derivative of i**4/6 - 16*i**3/27 - 5*i**2/9 + 4*i/3 + 88. Factor o(y).
2*(y - 3)*(y + 1)*(3*y - 2)/9
Suppose -74/7*d - 12/7*d**4 - 48/7*d**2 + 76/7*d**3 - 2/7*d**5 + 60/7 = 0. What is d?
-10, -1, 1, 3
Find c, given that -1/2*c**2 - 1/6 - 1/6*c**3 - 1/2*c = 0.
-1
Let o(g) be the third derivative of -g**10/10080 + g**8/1120 - g**6/240 - g**4/8 - 13*g**2. Let v(k) be the second derivative of o(k). Factor v(t).
-3*t*(t - 1)**2*(t + 1)**2
Let s(q) be the second derivative of q**7/315 + q**6/75 - q**5/30 - q**4/30 + 4*q**3/45 - 123*q. Solve s(i) = 0.
-4, -1, 0, 1
Let x = 120 + -93. Let s = x - 80/3. Factor 1/3*n**2 - 2/3*n + s*n**3 + 0.
n*(n - 1)*(n + 2)/3
Let k(x) be the second derivative of 0 - 27*x - 3*x**2 + 11/2*x**3 - 9/4*x**4. Factor k(p).
-3*(p - 1)*(9*p - 2)
Let s = 12644 + -12644. Let -4/9*g**2 + s*g - 4/9*g**3 + 0 = 0. Calculate g.
-1, 0
Suppose -17 = r + 5*q, 6 = -4*r + 4*q + 34. Factor -12/5*u**3 + 0 - r*u**2 - 3/5*u**4 - 6/5*u.
-3*u*(u + 1)**2*(u + 2)/5
Let j(b) be the first derivative of b**8/80 - 3*b**7/70 - b**6/30 + 19*b**3/3 - 11. Let v(g) be the third derivative of j(g). Find t such that v(t) = 0.
-2/7, 0, 2
Suppose 5*j - 27 = -12. Suppose -2*d = -5*r + 2*d + 47, 3*d - 12 = -j*r. Let -r + 7 + 2*s**2 - 6*s**2 + 2*s**3 = 0. What is s?
0, 2
Let n(k) be the second derivative of k**5/120 + 5*k**4/36 + 25*k**3/36 + 23*k + 1. Factor n(q).
q*(q + 5)**2/6
Factor -3/5*n**2 - 84/5 + 48/5*n.
-3*(n - 14)*(n - 2)/5
Suppose -n = -0 - 5, 2*m + 5*n = 43. What is f in -2*f + 5*f**2 - m - 2*f**3 - 4*f**4 + 5*f - f**4 - f**5 + 9*f**2 = 0?
-3, -1, 1
Let r(s) = 9*s - 16. Suppose -4*m + 5*q - 2 + 10 = 0, 10 = 5*m - 3*q. Let n be r(m). Let -6/13*p - 2/13*p**n - 4/13 = 0. What is p?
-2, -1
Suppose -343 = -3*a - 322. Let c(h) be the third derivative of 0 - 4*h**2 - 1/15*h**5 + 1/30*h**6 - 1/6*h**4 + 0*h + 0*h**3 + 2/105*h**a. Factor c(q).
4*q*(q - 1)*(q + 1)**2
Solve -6*x**3 + 1/2*x**4 - 7*x + 0 - 27/2*x**2 = 0 for x.
-1, 0, 14
Let r(i) be the first derivative of -i**7/70 + i**6/20 + i**5/20 - i**4/4 + 19*i**2/2 - 17. Let b(x) be the second derivative of r(x). Factor b(f).
-3*f*(f - 2)*(f - 1)*(f + 1)
Let t(m) be the first derivative of 2*m**5/55 - 19*m**4/22 + 84*m**3/11 - 324*m**2/11 + 432*m/11 + 86. Factor t(b).
2*(b - 6)**3*(b - 1)/11
Factor 85*c**3 + 90 + 25*c**4 - 608*c**2 - 487*c**2 - 1840 + 1586*c - 6411*c.
5*(c - 7)*(c + 5)**2*(5*c + 2)
Let p(k) be the first derivative of -2*k**4/17 - 218*k**3/51 - 27*k**2/17 - 331. Determine l, given that p(l) = 0.
-27, -1/4, 0
Let z(w) be the first derivative of 127/36*w**4 + 32/9*w**2 - 15 - 131/27*w**3 - 4/3*w - 19/15*w**5 + 1/6*w**6. Suppose z(p) = 0. Calculate p.
2/3, 1, 3
Let f(v) be the third derivative of 0*v - 4*v**2 + 1/2*v**4 + 0 - 2/3*v**3 + 1/30*v**6 - 1/5*v**5. What is w in f(w) = 0?
1
Suppose -19 = 5*s - 4*h + 5, 5*s + 3*h + 17 = 0. Let o be ((-175)/40 - s)*2/(-3). Factor -1/4 + 1/4*z**2 - 1/4*z + o*z**3.
(z - 1)*(z + 1)**2/4
Let p(v) be the first derivative of -v**4/24 + v**3/3 - 3*v**2/4 - 27*v - 9. Let m(r) be the first derivative of p(r). Factor m(l).
-(l - 3)*(l - 1)/2
Suppose -4*t = t - 180. Let z = t + -34. Factor 2/7*p**5 + 2/7*p**z - 2/7*p**4 + 0*p - 2/7*p**3 + 0.
2*p**2*(p - 1)**2*(p + 1)/7
Let y(f) = 2*f**2 - 8*f + 16. Let o(l) = -l**2 + l + 2. Let a(x) = -3*o(x) - y(x). Let h be a(-8). Factor 4/9 - 2/9*z - 2/9*z**h.
-2*(z - 1)*(z + 2)/9
Let q be 21/9*-3 + 8 + -1. Factor 0*l**2 + q*l - 2/19*l**4 + 0 + 2/19*l**3.
-2*l**3*(l - 1)/19
Suppose 0 = -a - 1 + 3. Factor 2*t**3 + 45 - 2*t - t**a + 5*t**4 - 45 - 4*t**4.
t*(t - 1)*(t + 1)*(t + 2)
Let m(x) be the first derivative of -10/3*x - 5/4*x**4 - 8 + 5/2*x**2 + 10/9*x**3. Let m(n) = 0. What is n?
-1, 2/3, 1
Find v such that 2*v**5 - 12*v**4 - 4*v + 0*v - 39*v**3 + 21*v**2 + 10*v**5 + 22*v + 0*v = 0.
-3/2, -1/2, 0, 1, 2
Let l be 3/(2/(-16)*-3). Suppose 6*q = 5*v + q - 15, -2*q = -l. Factor 5*o**2 + 9*o - 4*o**3 + 7*o**3 + v*o**2.
