/7 - 488. Find r, given that a(r) = 0.
-15, 9
Let u(r) be the third derivative of 5/3*r**3 + 0 + 32*r**2 + 85/24*r**4 + 0*r + 2/3*r**6 + 10/3*r**5. Factor u(s).
5*(s + 2)*(4*s + 1)**2
Let t(c) be the third derivative of c**5/15 + 23*c**4/3 + 30*c**3 - 2*c**2 - 160*c. Factor t(z).
4*(z + 1)*(z + 45)
Let o be 32/6 + (-88)/66. Suppose 2*p - 2*d = -10, 3*p - 20 = -0*d - 4*d. Factor 2/13*q**3 + p*q**2 + 0 + 0*q + 2/13*q**5 - 4/13*q**o.
2*q**3*(q - 1)**2/13
Let n(v) = 2*v**5 + v**4 - v**3 - v - 1. Let r(b) = -7*b**5 - 3*b**4 + 13*b**3 - 20*b**2 + 18*b - 1. Let m(d) = 12*n(d) + 4*r(d). Factor m(h).
-4*(h - 1)**4*(h + 4)
Let t(w) be the first derivative of 2*w**6/15 - 16*w**5/25 + 3*w**4/5 + 16*w**3/15 - 8*w**2/5 + 78. Determine l so that t(l) = 0.
-1, 0, 1, 2
Let x(u) be the third derivative of -u**8/252 + 2*u**7/63 - u**6/10 + 7*u**5/45 - u**4/9 + 147*u**2. Solve x(i) = 0.
0, 1, 2
Let l(d) = 10*d - 41. Let u be l(4). Let z be 5/35 + u + 2. Solve 20/7*q**4 + z*q - 20/7*q**2 - 80/7*q**3 + 0 + 72/7*q**5 = 0 for q.
-1, -1/2, 0, 2/9, 1
Solve -4*a**4 - 6724 - 7384*a**2 - 6*a**3 + 12903*a - 9750*a + 10623*a + 342*a**3 = 0.
1, 41
Suppose -5 = 5*y - 0*y - 5*l, 19 = y + 3*l. Find g, given that -65*g**5 + 90*g**2 + 5*g**5 + 41*g - g - 95*g**y + g**3 + 5 + 19*g**3 = 0.
-1, -1/3, -1/4, 1
Suppose -5*k + 342 = 3*u, -3*u - 29 = -k + 43. Let w = k - 66. Find z such that 0 + 2/7*z**w - 2/7*z**4 + 0*z**2 + 0*z = 0.
0, 1
Factor 14427*u**3 - 56*u - 240*u**2 - 4*u**4 - 14367*u**3 + 376*u - u**4.
-5*u*(u - 4)**3
Solve -43*y**3 + 88*y**3 + 40*y - 16*y**2 - 47*y**3 = 0 for y.
-10, 0, 2
Let t(u) be the third derivative of u**6/30 - 2*u**5/15 - u**4/6 + 4*u**3/3 - 35*u**2 + u. Solve t(z) = 0 for z.
-1, 1, 2
Factor 0*t**2 + 2/7*t**3 + 0 - 2/7*t.
2*t*(t - 1)*(t + 1)/7
Let l be (-5120)/(-2080) + 6/(-13). Factor 1/8*u**l + 3/8*u - 1/2.
(u - 1)*(u + 4)/8
Let 11/5*v**2 - 1/5*v**4 - 36/5 - 2/5*v**3 + 12/5*v = 0. What is v?
-3, 2
Let g(q) = q**3 + q**2 + q + 2. Let c(s) = -4*s**4 - 17*s**3 + 127*s**2 - 217*s + 86. Let m(y) = -c(y) - 5*g(y). Factor m(t).
4*(t - 3)*(t - 1)**2*(t + 8)
Suppose 0 = -2*m + 4*m - 14. Let r be 12/(-42) - (-23)/m. Determine u so that 14*u**2 + 3*u**4 + 0*u**3 - 4*u + r*u**4 - 9*u**3 - 7*u**3 = 0.
0, 2/3, 1
Let m(d) = -40*d**2 - 240*d - 420. Let b(o) = 3*o**2 + 17*o + 30. Let g(t) = -55*b(t) - 4*m(t). Factor g(r).
-5*(r - 6)*(r + 1)
Let y(a) be the third derivative of -a**6/40 + a**5/20 + 5*a**4/4 + 4*a**3 + 90*a**2 + 1. Suppose y(j) = 0. Calculate j.
-2, -1, 4
Let p(u) be the third derivative of -11/30*u**5 + 0*u**3 - 10*u**2 + 2*u + 1/24*u**6 + 1/3*u**4 + 0. Find r such that p(r) = 0.
0, 2/5, 4
Let x be (-90)/(-27)*615/(-1372). Let f = 2/343 - x. Factor -3/4*w**2 - f*w + 0.
-3*w*(w + 2)/4
Factor -3*p - p**3 - 7*p - 4*p**2 + 5*p - 2.
-(p + 1)**2*(p + 2)
Let o(n) be the first derivative of -n**6/6 + 2*n**5/5 + 11*n**4/4 - 40*n**3/3 + 22*n**2 - 16*n - 108. Suppose o(k) = 0. Calculate k.
-4, 1, 2
Let s(n) be the first derivative of 3*n**5/20 + n**4 + 5*n**3/2 + 3*n**2 + 37*n - 1. Let u(r) be the first derivative of s(r). Factor u(t).
3*(t + 1)**2*(t + 2)
Let g(i) be the first derivative of 16 + 1/2*i - 1/3*i**2 + 1/18*i**3. Factor g(k).
(k - 3)*(k - 1)/6
Let r = 866 - 861. Suppose 0*y + 8/7*y**4 - 2*y**3 + 0 + 4/7*y**2 + 8/7*y**r = 0. What is y?
-2, 0, 1/2
Let y = 491 + -489. Find b, given that -7/4*b + 5/4*b**y + 1/2 = 0.
2/5, 1
Let r(o) be the third derivative of -o**8/1848 + 4*o**7/1155 - o**6/220 - 2*o**5/165 + o**4/33 - 136*o**2. Suppose r(w) = 0. Calculate w.
-1, 0, 1, 2
What is w in 4/3*w - w**3 - 5/3*w**4 + 5/3*w**2 + 0 - 1/3*w**5 = 0?
-4, -1, 0, 1
Let l(z) be the second derivative of -z**8/224 - z**7/140 + z**6/40 - 37*z**2/2 + 27*z. Let w(v) be the first derivative of l(v). Let w(p) = 0. What is p?
-2, 0, 1
Let g(o) be the second derivative of o**6/40 + o**5/5 + 3*o**4/8 - 27*o**2/2 - 26*o. Let w(v) be the first derivative of g(v). Let w(z) = 0. Calculate z.
-3, -1, 0
Let w(m) be the first derivative of -m**5 + 5*m**4/2 + 35*m**3/3 + 10*m**2 - 193. Factor w(a).
-5*a*(a - 4)*(a + 1)**2
Let p(n) be the first derivative of -2*n**4/3 + 2*n**3 - 2*n**2 - 2*n - 16. Let x(w) be the first derivative of p(w). Determine h so that x(h) = 0.
1/2, 1
Let f(a) = -11*a**3 - 100*a**2 - 437*a - 682. Let x(i) = -5*i**3 - 49*i**2 - 218*i - 340. Let p(d) = -2*f(d) + 5*x(d). Solve p(y) = 0 for y.
-7, -4
Factor -227/5*v - 45*v**2 - 2/5.
-(v + 1)*(225*v + 2)/5
Let z = -123 + 79. Let m = z - -44. Determine w so that 0*w**2 + m*w + 6/5*w**3 - 3*w**5 + 0 + 9/5*w**4 = 0.
-2/5, 0, 1
Let h(i) be the second derivative of 2*i + 0 + 245/8*i**4 + 35/3*i**3 + 5/3*i**2. Suppose h(u) = 0. Calculate u.
-2/21
Let k(m) = -27*m - 918. Let v be k(-34). Determine g so that v + 8/3*g - 92/3*g**2 = 0.
0, 2/23
Let y(b) = b**3 - 3*b**2 - b. Let z be -4 + -6*(0 - (-3)/9). Let u(t) = 10*t**3 - 32*t**2 - 10*t. Let s(i) = z*u(i) + 68*y(i). Suppose s(n) = 0. What is n?
-1/2, 0, 2
Let y(i) be the first derivative of -5*i**3/3 + 55*i**2/2 - 613. Find k such that y(k) = 0.
0, 11
Let u(j) be the third derivative of 0*j - 1/1380*j**6 - 38*j**2 - 25/276*j**4 + 0 - 1/69*j**5 + 0*j**3. Factor u(v).
-2*v*(v + 5)**2/23
Let a(h) be the second derivative of h**4/3 - 19*h**3/3 - 10*h**2 - 207*h. Let a(n) = 0. Calculate n.
-1/2, 10
Let r = -1449 - -1449. Let q(n) be the second derivative of 0*n**3 + 0*n**4 + 2/15*n**6 + 2*n + 0 + 1/5*n**5 + r*n**2. Let q(u) = 0. Calculate u.
-1, 0
Let f(d) = -d**3 - d**2 - d - 1. Let n(g) = -6*g**3 - 4*g**2 - 3*g - 5. Let w(l) = -5*f(l) + n(l). Solve w(i) = 0.
-1, 0, 2
Let h(i) be the first derivative of i**7/168 - i**6/18 + i**5/6 - 32*i**3/3 - 14. Let n(f) be the third derivative of h(f). Find d, given that n(d) = 0.
0, 2
Let s(t) = t**3 + 8*t**2 - 6*t - 24. Let p be s(-8). Let k be 4/p - -1*(-7)/(-30). Factor -1/5*o**2 + 3/5*o - k.
-(o - 2)*(o - 1)/5
Let q(f) be the third derivative of -f**8/1344 - f**7/280 + f**5/60 - 26*f**2. Factor q(s).
-s**2*(s - 1)*(s + 2)**2/4
Let p = 10041/4 - 2486. Let x = p - 24. Solve 1/2 + 1/4*c - x*c**3 - 1/2*c**2 = 0 for c.
-2, -1, 1
Suppose -50*b = -34 - 116. Factor 4/3*n - 2/3 + 8/3*n**b + 14/3*n**2.
2*(n + 1)**2*(4*n - 1)/3
Let r = 304 - 304. Let m(c) be the third derivative of -4*c**3 + 1/6*c**6 - 13*c**2 + 23/6*c**4 + 0*c + r - 22/15*c**5. Factor m(y).
4*(y - 3)*(y - 1)*(5*y - 2)
Let x(i) = -11*i**3 + 11*i**2 + 238*i + 240. Let q(l) = 10*l**3 - 10*l**2 - 240*l - 240. Let n(v) = 6*q(v) + 5*x(v). Factor n(p).
5*(p - 8)*(p + 1)*(p + 6)
Suppose -7*s = -8*s + 2. Find a, given that -3969*a**4 + 4956*a**3 - 2544*a**s + 0 + 1029*a**5 - 65 + 576*a + 17 = 0.
2/7, 1, 2
Let a(u) be the third derivative of u**5/105 + u**4/14 - 8*u**3/21 + 19*u**2 + 1. Factor a(x).
4*(x - 1)*(x + 4)/7
Suppose 4*y - 5*m = 7, y = -0*y - m + 4. Suppose -y*b + 16 = -b. Determine a so that -2*a**5 + 7*a**3 + 6*a**5 - b*a**4 - 3*a**3 = 0.
0, 1
Let b(h) = 26*h + 56. Let v be b(-2). Let x(q) be the first derivative of 7 + 1/8*q**4 - q**3 - v*q + 3*q**2. Factor x(l).
(l - 2)**3/2
Suppose 683*t + 12 = 689*t. Find y such that 1/2 - 1/4*y**t - 1/4*y = 0.
-2, 1
Suppose -b + 4*l + 0*l = 0, 2*b + 2*l = 10. Let w(d) be the first derivative of b + d**3 + 9/4*d**4 - 9/2*d**2 - 3*d. Factor w(c).
3*(c - 1)*(c + 1)*(3*c + 1)
Let x(v) be the third derivative of v**9/75600 - v**8/8400 + v**6/225 - 19*v**5/60 - 26*v**2. Let u(d) be the third derivative of x(d). What is q in u(q) = 0?
-1, 2
Let w(y) be the second derivative of y**6/15 + y**5/2 + 64*y. Factor w(f).
2*f**3*(f + 5)
Let a(t) be the second derivative of -t**9/1512 + t**8/420 - t**6/90 + t**5/60 + 11*t**3/6 - 11*t. Let k(m) be the second derivative of a(m). Factor k(l).
-2*l*(l - 1)**3*(l + 1)
Let o(v) = 8*v**5 + 7*v**4 + 26*v**3 + 25*v**2 + 2*v + 4. Let j(q) = q**5 + q**3 - 2*q. Let s(m) = -35*j(m) + 5*o(m). Factor s(h).
5*(h + 1)**3*(h + 2)**2
Let u(n) be the first derivative of 2*n**6/21 - 36*n**5/35 - n**4/7 + 12*n**3/7 + 140. Let u(w) = 0. Calculate w.
-1, 0, 1, 9
Suppose 72 = 13*k - k. Suppose -2*g + 2*d + 8 = 0, -2*g - 2*d - 3 = -3*g. Suppose j**5 + 0*j**g + 9*j**4 + k*j**3 + 2*j**5 + 0*j**3 = 0. What is j?
-2, -1, 0
Let p(y) be the second derivative of y**4/18 - 8*y**3/15 - y**2/3 + 2*y - 52. Factor p(t).
2*(t - 5)*(5*t + 1)/1