r) be the third derivative of r**7/1365 - r**6/780 - 7*r**5/390 + r**4/12 - 2*r**3/13 + 4*r**2 + 2. Find j such that k(j) = 0.
-3, 1, 2
Suppose 0 = -j - 0*j + 17. Let y = j + -29/2. Factor -g - y*g**2 + 0 + 7/2*g**3.
g*(g - 1)*(7*g + 2)/2
Let u(z) = -49*z**3 - 99*z**2 + 19*z + 109. Let x(k) = -15*k**3 - 33*k**2 + 6*k + 36. Let i(b) = -3*u(b) + 10*x(b). Let i(n) = 0. Calculate n.
-11, -1, 1
Suppose x + v = -v - 15, 2*x + 6 = 2*v. Let d(f) = -f**3 - 8*f**2 - 7*f. Let h be d(x). Factor 5*o - 1 + h + 6*o**3 - 3*o**2 - 2*o - 5*o**3.
(o - 1)**3
Let c(s) = 2*s**2 - s - 1. Let r(z) = 14*z**3 - 56*z**2 - 16*z - 6. Let w(f) = -6*c(f) + r(f). Solve w(u) = 0.
-1/7, 0, 5
Let l(t) = -12*t**4 - 3*t**3 + 66*t**2 + 57*t. Let h(i) = -3*i**4 - i**3 + 16*i**2 + 14*i. Let c(v) = -9*h(v) + 2*l(v). Solve c(a) = 0 for a.
-2, -1, 0, 2
Suppose 0 = -14*w - 1840 + 1910. Suppose 6/7*r**3 - 9/7*r**4 + 3/7 + 6/7*r**2 - 9/7*r + 3/7*r**w = 0. What is r?
-1, 1
Suppose -12*p + 285 - 249 = 0. Let t(i) be the second derivative of 0 + 1/6*i**p + 0*i**2 + 4/5*i**5 + i + 2/3*i**4. Suppose t(o) = 0. What is o?
-1/4, 0
Factor 95 + 19 + 4*b**2 + 92*b - 26.
4*(b + 1)*(b + 22)
Let c(y) be the second derivative of y**4/6 - 14*y**3/3 + 24*y**2 - 21*y - 4. What is w in c(w) = 0?
2, 12
Find c such that -2*c + 168 - 3*c**2 - 156 - 7*c = 0.
-4, 1
Let b(r) be the first derivative of -r**7/3360 - r**6/96 - 5*r**5/32 - 125*r**4/96 + 13*r**3/3 - 19. Let p(y) be the third derivative of b(y). Factor p(i).
-(i + 5)**3/4
Let k(i) be the third derivative of -i**5/210 + 3*i**4/7 - 108*i**3/7 - 2*i**2 + 58. Factor k(u).
-2*(u - 18)**2/7
Suppose 29 = 4*q - 2*c - 3, 0 = -4*q + c + 36. Let j be (-3 - (-81)/21)/(q/14). Factor -2/5*v**2 + 0 + j*v.
-2*v*(v - 3)/5
What is x in -2420*x**2 + 1209*x**2 - 145*x + 1206*x**2 = 0?
-29, 0
Let x(f) = -3*f**2 - 39*f - 41. Let a(j) = 10*j**2 + 118*j + 124. Let p(m) = 5*a(m) + 16*x(m). Factor p(b).
2*(b - 18)*(b + 1)
Let k(j) be the third derivative of j**5/120 - 7*j**4/24 + 4*j**3 + 272*j**2 - j. Factor k(c).
(c - 8)*(c - 6)/2
Let u = -6940/7 + 992. Find q, given that 1/7*q**4 + 4/7*q - 4/7*q**3 - u + 3/7*q**2 = 0.
-1, 1, 2
Find a such that 27/10*a**3 - 79/10*a + 27/5 - 3/10*a**2 + 1/10*a**4 = 0.
-27, -2, 1
Let o be (-2392)/(-78) - 29 - (-20)/204. Factor 4/17*a**3 + 72/17*a - 56/17 - o*a**2.
2*(a - 2)**2*(2*a - 7)/17
Suppose 8 + 8 = 8*t. Let d be t + 21/(-12) - (-28)/16. Determine j so that -2/13 - 8/13*j - 6/13*j**d = 0.
-1, -1/3
Factor 12/19*w - 54/19 + 2/19*w**2.
2*(w - 3)*(w + 9)/19
Let a(d) be the second derivative of d**7/14 + 7*d**6/10 + 12*d**5/5 + 3*d**4 + 4*d + 10. What is g in a(g) = 0?
-3, -2, 0
Suppose -q - 4 = 10. Let d = -11 - q. Suppose -4 + 4*o**2 - 4*o - 6*o + o**d + 9*o**3 = 0. Calculate o.
-1, -2/5, 1
Let w = -5 + 30. Let j = w - 22. Factor -4*n**j + 20*n - 16*n**2 - 8 + 3*n**3 + n**3 + 4*n**3.
4*(n - 2)*(n - 1)**2
Suppose -7*m**2 - 8 + 16*m**2 - 7*m**2 + 6*m = 0. What is m?
-4, 1
Let o(s) be the second derivative of -1/168*s**7 + 0*s**3 + 0 + 0*s**4 + 0*s**5 + 1/120*s**6 - 25*s + 0*s**2. Determine i, given that o(i) = 0.
0, 1
Let o(i) = -i**3 - i**2 + 3. Let r be o(0). Suppose -3*j**2 - 6*j**3 + j**2 + 4*j**r = 0. What is j?
-1, 0
Suppose -5*z - 3 + 18 = 0, 0 = -k + 4*z - 12. Let j = -10812 + 10812. What is h in k*h + 1/3*h**3 + j*h**2 + 0 = 0?
0
Suppose 27*t**2 + 54*t - 21/2*t**3 + 3/4*t**5 - 15/4*t**4 + 0 = 0. Calculate t.
-2, 0, 3, 6
Let z(k) be the third derivative of k**8/168 + k**7/210 - k**6/60 - k**5/60 + 176*k**2. Let z(j) = 0. Calculate j.
-1, -1/2, 0, 1
Let m(b) be the third derivative of b**8/672 + b**7/420 - b**6/48 + b**5/40 - b**2 + 1. Factor m(v).
v**2*(v - 1)**2*(v + 3)/2
Let c(x) = 21*x**3 - 41*x**2 - 18*x. Let o(f) = -43*f**3 + 83*f**2 + 34*f. Let b(s) = -7*c(s) - 4*o(s). Factor b(g).
5*g*(g - 2)*(5*g + 1)
Let k(i) = -25*i + 129. Let x be k(5). Let p(q) be the first derivative of -2*q**4 - 4 + 4/3*q**3 + 1/3*q**6 - x*q + 3*q**2 + 0*q**5. Factor p(z).
2*(z - 1)**3*(z + 1)*(z + 2)
Let f(o) = 7*o**3 + 27*o**2 + 43*o - 82. Let x(y) = 6*y**3 + 26*y**2 + 44*y - 80. Let h(k) = 4*f(k) - 5*x(k). Factor h(m).
-2*(m - 1)*(m + 6)**2
Let z be (-1 + (-6)/(-18))*-3. Let t(p) be the first derivative of -2/27*p**3 - 6 + 4/9*p + 1/9*p**z. Solve t(o) = 0.
-1, 2
Let q = -21883 + 21883. Factor 4/17*x + q + 32/17*x**3 + 22/17*x**2 + 14/17*x**4.
2*x*(x + 1)**2*(7*x + 2)/17
Let u = 21741/23 + -945. Let j = u + 45/92. Factor 0 + 0*h**2 + 3/4*h**3 + 0*h + j*h**5 - 3/2*h**4.
3*h**3*(h - 1)**2/4
Let w(n) be the second derivative of -10*n**7/27 + 197*n**6/135 - 61*n**5/30 + 49*n**4/54 + 13*n**3/27 - 2*n**2/3 - 953*n. Let w(x) = 0. What is x?
-2/7, 1/2, 3/5, 1
Let w(a) = a. Let v be w(3). Suppose 5*l - v*l - 4 = 0. Factor -7/5*k**l + 2/5*k + 0.
-k*(7*k - 2)/5
Let r be ((-11)/(-22))/(2/(-52)). Let w = r + 16. Factor 16 - b**w - 63*b**2 + 51*b**2 - 3*b**3.
-4*(b - 1)*(b + 2)**2
Suppose -678*g + 707*g = 87. Let r be (10/12)/(6/225). Factor -r + 75*a + 16*a**g - 60*a**2.
(4*a - 5)**3/4
Suppose 5*a = 28 - 13. Determine n, given that -18 - 38*n**2 - 32*n + 15*n - 5*n**a + 78*n = 0.
-9, 2/5, 1
Let x(j) be the second derivative of j**5/60 + j**4/36 - j**3/2 - 3*j**2/2 - 24*j - 12. Let x(o) = 0. What is o?
-3, -1, 3
Let n be (-3)/((-11 - -5) + 5). Let w(i) be the first derivative of -1 + 0*i + 16/21*i**n + 2/35*i**5 + 4/7*i**2 + 5/14*i**4. Factor w(y).
2*y*(y + 1)*(y + 2)**2/7
Let c(i) = -2*i - 9. Let p be c(-6). Factor -9*x**2 + 12*x**p - 3*x**4 + 2*x**4 - 2*x**4 - 3*x**2.
-3*x**2*(x - 2)**2
Suppose -3*g = -3*g - 2*g. Suppose -4*n + 2 = d, -4*n = -d - g*n + 2. Factor -2/3*z**d - 2/3 + 4/3*z.
-2*(z - 1)**2/3
Let b = -8908/35 - -3902/15. Let z = b - 16/3. Factor -z*p**5 - 18/7*p**3 + 10/7*p**4 + 0 - 4/7*p + 2*p**2.
-2*p*(p - 2)*(p - 1)**3/7
Let x be 18/8 - 4/16. Let p be (-2)/6 + 1/3. Determine c so that -c**2 + p*c**x + c**4 + 2 - 1 - c**2 = 0.
-1, 1
Suppose -10*j = -2*j - 160. Find c such that -j*c**2 + 4*c - 17*c - 4*c**3 - 14*c + 3*c = 0.
-3, -2, 0
Suppose -9*z - 10 = -14*z. Factor 2*i**2 + 19 + 96*i + 2*i**3 - 12*i**z - 1 - 90*i.
2*(i - 3)**2*(i + 1)
Suppose 202/3*w**4 + 36*w**3 + 70/3*w**5 + 0 - 40/3*w**2 - 16/3*w = 0. What is w?
-2, -1, -2/7, 0, 2/5
Let r(s) = -4*s**2 - 16*s - 12. Let o(b) = -4*b**2 - 16*b - 13. Suppose a + 3*a + 20 = x, -x = 5*a + 16. Let l(i) = x*o(i) - 3*r(i). Factor l(u).
-4*(u + 2)**2
Solve -8*t**4 - 13/3*t**3 - 2/3*t**2 + 0 - 3*t**5 + 0*t = 0 for t.
-2, -1/3, 0
Let b(v) be the second derivative of 1/60*v**6 + 1 + 17*v + 0*v**2 - 1/84*v**7 + 0*v**3 + 1/20*v**5 + 0*v**4. Factor b(u).
-u**3*(u - 2)*(u + 1)/2
Let h = -103/70 - -19/10. Let v be 0 - (3 - (14 + -7)). Factor -12/7*x**3 + 12/7*x**2 + 0 + 0*x + h*x**v.
3*x**2*(x - 2)**2/7
Factor -576*x**3 + 32*x**4 + 0 - 2/3*x**5 + 4608*x**2 - 13824*x.
-2*x*(x - 12)**4/3
Let t be 40/(-6)*252/(-70). Let h be (100/t)/(-5) - (1 - 2). Factor 0 - 1/2*m**2 + 1/3*m + h*m**3.
m*(m - 2)*(m - 1)/6
Let v(y) be the third derivative of y**8/6720 - y**7/1260 - y**6/240 - 3*y**4/8 + 10*y**2. Let g(r) be the second derivative of v(r). Factor g(m).
m*(m - 3)*(m + 1)
Let l be (-65)/(-150)*(-52 + 56). Factor -8/5*t**2 + l*t + 8/15.
-2*(3*t - 4)*(4*t + 1)/15
Let j = -3/2401 - -48089/55223. Determine t so that -24/23*t**2 - 6/23*t**4 - 12/23*t - j*t**3 - 2/23 = 0.
-1, -1/3
Suppose -3*l = 3, -8*y + 4*l + 12 = -4*y. Factor 0 + 2/3*g - 2/3*g**y.
-2*g*(g - 1)/3
Let c(w) = -w**4 - w**2 + 1. Let m(o) = -3*o**4 + 118*o**3 - 3599*o**2 + 6844*o - 3362. Let a(l) = 10*c(l) - 5*m(l). Factor a(q).
5*(q - 58)**2*(q - 1)**2
Let o = -16/225 - -139/900. Let t(w) be the third derivative of 0 - 5/6*w**4 + 0*w**3 + 0*w - o*w**5 - 10*w**2. Determine n, given that t(n) = 0.
-4, 0
Let f(k) be the second derivative of 2*k**6/15 - 7*k**5/5 - k**4/3 + 14*k**3/3 + 47*k + 1. Factor f(v).
4*v*(v - 7)*(v - 1)*(v + 1)
Let p(h) be the third derivative of -1/72*h**4 + 0*h - 1/180*h**5 + 1/360*h**6 + 0 + 1/18*h**3 + 7*h**2. Determine y so that p(y) = 0.
-1, 1
Suppose -g - 4*r = -12, 2*g - 2*r = -19 + 23. Let p(y) be the second derivative of 0 - 4*y + 1/2*y**2 + 1/4*y**3 + 1/24*y**g. Factor p(v).
(v + 1)*(v + 2)/2
What is r in 0*r**3 - 1/12*r**5 + 17/12*r - 1/2 + 1/3*r**4 - 7/6*r**2 = 0?
-2, 1, 3
Let d = 31 + -29. Let s be (-2 - 1)*d/(-18). Let -m + 0 