c(s) be the third derivative of s**7/1260 - s**6/240 + s**4/36 + 18*s**2 - s. Find z, given that c(z) = 0.
-1, 0, 2
Suppose -30 = -14*n - 17 + 43. What is o in 8/5*o**2 - 2/5*o**n + 4/5*o**3 - 16/5*o + 0 = 0?
-2, 0, 2
Let s(o) be the first derivative of -3*o**3 + 165*o**2/2 + 114*o + 48. Factor s(t).
-3*(t - 19)*(3*t + 2)
Suppose -293*n + 351*n = 0. Determine q, given that 0 + 2/9*q**2 + n*q = 0.
0
Suppose -489 = -51*b - 112*b. Factor 0*x**2 + 0 + 0*x + 2/11*x**b + 1/11*x**5 + 3/11*x**4.
x**3*(x + 1)*(x + 2)/11
Let p(d) = 13*d**5 - 480*d**4 + 11522*d**3 + 2*d + 2. Let o(w) = -17*w**5 + 480*w**4 - 11523*w**3 - 3*w - 3. Let c(f) = -2*o(f) - 3*p(f). Solve c(x) = 0 for x.
0, 48
Find y, given that -392/9 - 94/3*y**2 - 728/9*y - 2/9*y**4 + 52/9*y**3 = 0.
-1, 14
Let b be 0*((-35)/14 + 3). Let k(h) be the third derivative of 1/210*h**7 + 6*h**2 - 1/30*h**5 + 1/6*h**3 + b*h + 0*h**4 + 0 + 0*h**6. Factor k(v).
(v - 1)**2*(v + 1)**2
Factor -547*o - o**3 - 559*o - o**2 + 1112*o.
-o*(o - 2)*(o + 3)
Let l be 4 - 1/((-4)/4). Let g be (1/5 - (-9)/l)/1. Determine z so that 3/5*z**g + 27/5 - 18/5*z = 0.
3
Suppose 0*d - 3*d - 4 = 2*r, -5*r - 15 = 5*d. Factor 0*a + 0 - 2/7*a**d - 2/7*a**3.
-2*a**2*(a + 1)/7
Let q(u) be the third derivative of -u**7/35 + 7*u**6/60 + u**5/30 - 7*u**4/12 + 2*u**3/3 - 2*u**2 + 35. Let q(f) = 0. Calculate f.
-1, 1/3, 1, 2
Suppose -434 - 190 = -312*d. Factor 4/5*m**3 + 16/5 - 12/5*m**d + 0*m.
4*(m - 2)**2*(m + 1)/5
Factor -3945/7*p**3 - 3477/7*p**4 - 264/7*p - 12/7 - 1083/7*p**5 - 1803/7*p**2.
-3*(p + 1)**3*(19*p + 2)**2/7
Let k be ((-13)/5 + 3 - 2)/((-22)/55). Factor -6/5*t**2 + 4/5*t**3 + 0 + 0*t + 2/5*t**k.
2*t**2*(t - 1)*(t + 3)/5
Factor -g**2 + 322 - 58 - 1288 + 64*g.
-(g - 32)**2
Let h(v) be the third derivative of v**7/70 + 23*v**6/40 + 63*v**5/20 + 61*v**4/8 + 10*v**3 - 515*v**2. Factor h(m).
3*(m + 1)**3*(m + 20)
Factor -13467/2*n - 201/2*n**2 - 300763/2 - 1/2*n**3.
-(n + 67)**3/2
Let q(h) be the second derivative of 2*h**6/75 - 3*h**5/25 - 2*h**4/3 - 219*h. Factor q(w).
4*w**2*(w - 5)*(w + 2)/5
Let q(a) = -2*a**2 - 6*a - 1. Let g(z) = -z**2 - z + 1. Let k(j) = -j + 18. Let b be k(12). Let v(l) = b*g(l) - 2*q(l). Let v(h) = 0. Calculate h.
-1, 4
Let v = 8 + -4. Determine p, given that -4*p + p**2 - 2 - 4*p**3 + 11*p + v*p**2 = 0.
-1, 1/4, 2
Suppose 5*z - x = -3*x - 68, -5*x + 28 = -4*z. Let y be (z/8)/(3/(-6)). Factor 2*m**2 - 2*m**y + 0*m**2 + 2*m**3 - 2*m**3.
-2*m**2*(m - 1)
Let v(h) be the second derivative of -h**5/50 + h**3/15 - 187*h. Let v(i) = 0. What is i?
-1, 0, 1
Factor 6/5*b**2 + 54/5*b + 48/5.
6*(b + 1)*(b + 8)/5
Let r(s) = -6*s**3 - 24*s**2 - 30*s + 1. Let d(c) = 3*c**3 + 12*c**2 + 15*c. Let m(n) = -13*d(n) - 6*r(n). Factor m(t).
-3*(t + 1)**2*(t + 2)
Let j(y) = y**2 + y + 1. Let r be ((-8)/(-10))/((-2)/(-5)). Let m(n) = -9*n**2 + 22*n**2 + 3*n - 18*n**2 + 5. Let i(l) = r*m(l) - 2*j(l). Factor i(x).
-4*(x - 1)*(3*x + 2)
Let u be (-1)/(43/(-129)*(1 - -2)). Let w(j) be the first derivative of -u + 2/7*j - 1/21*j**3 + 1/14*j**2. Factor w(p).
-(p - 2)*(p + 1)/7
Suppose -10 = -5*w - 0*w, -3*r = -4*w + 2. Factor -c**3 - 6*c**r + 2*c**2 + 9*c - 7*c + 3*c**3.
2*c*(c - 1)**2
Factor -2*n - 2/13*n**4 - 30/13*n**2 - 14/13*n**3 - 8/13.
-2*(n + 1)**3*(n + 4)/13
Let y be ((-617)/154)/1 - (4 + -8). Let q = 313/770 + y. Factor -q*a**2 + 8/5*a - 8/5.
-2*(a - 2)**2/5
Determine m so that 0 + 24*m**2 - 576*m - 1/4*m**3 = 0.
0, 48
Let n(v) be the third derivative of -v**6/60 - 11*v**5/30 + v**4 + 17*v**2 - 4. Find r, given that n(r) = 0.
-12, 0, 1
Let u(q) = 7*q**4 - 10*q**3 - 26*q**2 - 14*q + 5. Let h(i) = 6*i**4 - 10*i**3 - 26*i**2 - 14*i + 4. Let b(c) = 5*h(c) - 4*u(c). Suppose b(y) = 0. What is y?
-1, 0, 7
Suppose -121*t + 31 = -211. Factor 1/7*s**t + 1/7*s**3 - 4/7 - 4/7*s.
(s - 2)*(s + 1)*(s + 2)/7
Let w(h) be the third derivative of -h**5/15 - 101*h**4/3 - 20402*h**3/3 + 533*h**2. Find r such that w(r) = 0.
-101
Let w = 5 - -3. Suppose 70*k**2 - 150*k**2 + 68*k**2 + 4*k**3 + w*k = 0. What is k?
0, 1, 2
Let j(x) be the third derivative of x**6/960 - x**5/80 - x**4/12 + 41*x**2. Determine w, given that j(w) = 0.
-2, 0, 8
Let d = -125 - -128. Let t(o) be the second derivative of -5*o - 1/4*o**2 + 0 + 1/48*o**4 - 1/24*o**d. Suppose t(p) = 0. What is p?
-1, 2
Let n = 919 - 914. Let a(v) be the second derivative of -n*v - 1/105*v**6 - 9/7*v**2 + 1/21*v**4 - 4/7*v**3 + 0 + 2/35*v**5. Factor a(m).
-2*(m - 3)**2*(m + 1)**2/7
Suppose -2*z - 4*n + 12 + 52 = 0, -5 = -5*n. Suppose 19 = 2*v + 5*j, -4*v - 2*j + z = -0*v. Let 6*c - 17*c + 7*c - c**2 + v*c = 0. Calculate c.
0, 3
Suppose 9 = -4*w + 41. Factor 0 + 4*b - w + 2*b**2 + 2*b**2.
4*(b - 1)*(b + 2)
Let i(s) be the first derivative of -4*s**2 - 19 - 4/3*s**3 + 0*s. What is q in i(q) = 0?
-2, 0
Let v(z) be the third derivative of -z**7/840 + z**6/96 + z**5/240 - 17*z**4/96 - z**3/2 + 6*z**2 + 8. Factor v(j).
-(j - 4)*(j - 3)*(j + 1)**2/4
Let x(f) be the first derivative of -1/4*f - 3/32*f**4 + 3/16*f**2 + 1/40*f**5 - 15 + 1/24*f**3. Factor x(o).
(o - 2)*(o - 1)**2*(o + 1)/8
Let z(g) be the second derivative of g**6/9 - 7*g**5/30 + 11*g**4/90 - g**3/45 - 2*g + 23. Solve z(d) = 0 for d.
0, 1/5, 1
Let f(h) be the first derivative of h**3/2 - 23*h**2/2 + 15*h/2 + 288. Factor f(m).
(m - 15)*(3*m - 1)/2
Determine p so that -12/7*p**3 - 20/7*p + 0 - 36/7*p**2 + 4/7*p**4 = 0.
-1, 0, 5
Let y(u) be the second derivative of 7/2*u**2 - 2/75*u**5 - 7*u + 1/30*u**4 + 0 + 2/15*u**3. Let n(z) be the first derivative of y(z). Factor n(k).
-4*(k - 1)*(2*k + 1)/5
Suppose 0*y = w - y - 4, -w - 11 = 2*y. Let g be -24*(w + 2)/(-1). Find n, given that -g*n**3 + 6*n**3 - 4*n**2 - 14*n + 14*n = 0.
-2/9, 0
Suppose 3*w - 361 = -2*p, -3*p - p = -3*w + 367. Factor -w + 246 - 125 - 9*f**3 + 6*f**4 + 3*f**5.
3*f**3*(f - 1)*(f + 3)
Suppose 0 = 5*r + z - 35, -r - 3*r + 3*z = -47. Factor 4*w + 2*w**5 + 2*w**5 - r*w**3 + 18 - 18.
4*w*(w - 1)**2*(w + 1)**2
Factor -3/5*k**2 + 0 - 3/5*k + 3/5*k**4 + 3/5*k**3.
3*k*(k - 1)*(k + 1)**2/5
Suppose -24 = 6*u - 18*u. Find j such that -35 + 0*j**2 + 15*j + 35 - 5*j**u = 0.
0, 3
Let f = -43/6 + 23/3. Let d(x) be the second derivative of 3/20*x**5 + 0 + f*x**4 + 0*x**2 - 2*x + 1/2*x**3. What is l in d(l) = 0?
-1, 0
Factor -18/13*r**2 + 8/13*r**3 + 0 + 10/13*r.
2*r*(r - 1)*(4*r - 5)/13
Let z = -1273 + 1276. Factor -1/10*u**z + 4/5 + 2/5*u - u**2 - 1/10*u**5 + 2/5*u**4.
-(u - 2)**3*(u + 1)**2/10
Suppose 8 = -d - 2*o, 19 = -3*d - 2*o - 3*o. Solve -4*k**2 - 952*k + 932*k - k**d - 22 + 2 = 0.
-2
Suppose -i = -5 - 0. Factor m**4 - 32*m**3 + i*m**2 + 7*m**3 - 31*m**4.
-5*m**2*(m + 1)*(6*m - 1)
Let n(r) be the third derivative of r**8/420 + 22*r**7/525 + 11*r**6/50 + 37*r**5/75 + 7*r**4/15 + 17*r**2 - 3*r. Find t such that n(t) = 0.
-7, -2, -1, 0
Let y(r) be the second derivative of 2*r**4/3 + 14*r**3/3 - 8*r**2 - 14*r + 1. Find m such that y(m) = 0.
-4, 1/2
Suppose 0 = -f + m - 1, -4*f + 4 + 0 = 4*m. Let v(d) be the third derivative of f + 0*d + 1/33*d**4 + 4*d**2 + 1/330*d**5 + 1/11*d**3. Factor v(y).
2*(y + 1)*(y + 3)/11
Suppose 5*k - 930 = m, 3*m = -3*k + 2*m + 550. Let o = 189 - k. Determine y, given that 3*y - 3/2*y**o - 15/2*y**2 + 6*y**3 + 0 = 0.
0, 1, 2
Let w(l) = -3*l**2 + l. Let y(n) = -3*n**2. Suppose -15 + 39 = 4*u. Let b(x) = u*w(x) - 5*y(x). Factor b(v).
-3*v*(v - 2)
Suppose 3*s - 4*w = 2 + 5, 3*w = 6. Suppose 7 + 13 = s*n. Find j such that -4*j**4 + 25*j**4 - 4*j + 16*j**2 + 0*j**2 - 24*j**3 - n*j**5 - 5*j**4 = 0.
0, 1
Let w(d) = -51*d**3 + 99*d**2 - 75*d + 27. Let a(n) = -7*n**3 + 14*n**2 - 11*n + 4. Let s(r) = 15*a(r) - 2*w(r). Factor s(z).
-3*(z - 2)*(z - 1)**2
Factor 6*d**5 - 13*d**2 + 0*d + 10*d**4 - 11*d**4 - 2*d**5 - 3*d**3 - 4*d + 17*d**4.
d*(d - 1)*(d + 4)*(2*d + 1)**2
Suppose 5*t = 5*c + 25, -3*t + 366*c + 18 = 362*c. Factor 18/5*y + 0 + 6/5*y**3 - 39/5*y**t.
3*y*(y - 6)*(2*y - 1)/5
Factor -6/5*i**3 + 0*i + 0 + 3/5*i**2 + 3/5*i**4.
3*i**2*(i - 1)**2/5
Suppose 2*x + 0*g - 4 = 2*g, 4*x - 5*g = 5. Let 5/2*q**3 - x*q**2 + 5/2*q + 0 = 0. What is q?
0, 1
Let p(m) be the third derivative of m**6/240 - m**5/30 - 5*m**4/16 + 3*m**3/2 + 260*m**2 - 1. Let p(o) = 0. Calculate o.
-3, 1, 6
Let h = -233807/34 - -6879. Let z = h - 14/17. Solve 3/4*d**4 + 0*d - z*d**3 + 0 + 0*d**2