*q**5 + 3/160*q**6 - 1/448*q**8. Find i, given that o(i) = 0.
-2, -1, 0, 1
Let m be (-7)/70*359/(-19). Let h = -11/38 + m. Factor -2/5*v**2 + 2*v - h.
-2*(v - 4)*(v - 1)/5
Let o(l) = -2*l - 1. Let z = 202 + -201. Let y(c) = -5*c**3 - 375*c**2 - 9355*c - 78115. Let g(j) = z*y(j) + 10*o(j). Suppose g(a) = 0. What is a?
-25
Solve -505 + 82*p**2 + 373*p**2 + 44*p**3 - 45*p - 5*p**4 + p**3 + 55 = 0 for p.
-6, -1, 1, 15
Let v = -267 + 270. Factor 4*s**3 - 8*s**2 - 4*s + 5*s**3 - 3*s**3 + 10 - 2*s**v - 2.
4*(s - 2)*(s - 1)*(s + 1)
Suppose -2/3*d**3 - 84 + 2/3*d**4 + 86*d - 70/3*d**2 = 0. Calculate d.
-7, 2, 3
Let s = -16761 + 16764. Let y(z) be the second derivative of -64*z**2 + 1/15*z**6 + 0 - 16/3*z**s - 11/10*z**5 + 6*z**4 + 29*z. Suppose y(i) = 0. What is i?
-1, 4
Let l(j) be the first derivative of -16*j**5/7 - 11*j**4 + 8*j**3/3 + 16*j**2/7 - 1238. Find d, given that l(d) = 0.
-4, -1/4, 0, 2/5
Let q(y) be the third derivative of 2*y**7/105 - y**6/5 + y**5/5 + 5*y**4/3 + 7*y**2 + 33*y. Factor q(i).
4*i*(i - 5)*(i - 2)*(i + 1)
Let s(p) be the second derivative of -9/4*p**4 - 50*p**2 + 19/100*p**5 - 231*p - 1/150*p**6 + 0 + 85/6*p**3. Factor s(k).
-(k - 5)**3*(k - 4)/5
Let k be (-101)/(-808) - (47/8)/(-1). Determine s so that -s**4 - s**2 + k*s**2 + 10*s**3 - 20*s**3 + 6*s**4 = 0.
0, 1
Find u such that -2210*u**3 - 27*u**4 - 120*u - 1732*u**3 + 1649*u**2 + 3216*u**3 - 116 = 0.
-29, -2/9, 1/3, 2
Let z(q) be the first derivative of 1/36*q**6 + 0*q - 1/30*q**5 + 0*q**3 - 13/2*q**2 + 1 - 1/18*q**4. Let x(b) be the second derivative of z(b). Factor x(r).
2*r*(r - 1)*(5*r + 2)/3
Let c(o) be the third derivative of -1/168*o**8 + 0*o - o**2 + 1/4*o**6 + 23/30*o**5 + 0*o**3 + 1/105*o**7 + 5/6*o**4 - 14. Suppose c(d) = 0. Calculate d.
-2, -1, 0, 5
Let g(s) be the second derivative of 1/2*s**4 + 7/15*s**6 + 7 + 0*s**2 - s**5 + 6*s + 0*s**3. Find o such that g(o) = 0.
0, 3/7, 1
Suppose 8*i - 16 - 24 = 0. Let k(x) be the second derivative of 6/5*x**i + 13/3*x**4 + 8*x**3 + 0 - 10*x + 8*x**2 + 2/15*x**6. Factor k(z).
4*(z + 1)**2*(z + 2)**2
Let h(x) = 3*x**3 - 4*x**2 + 25*x - 24. Let t be h(1). Let j = 14 + -11. Factor 3/5*k + 0 + t*k**2 - 3/5*k**j.
-3*k*(k - 1)*(k + 1)/5
Let y(n) be the first derivative of -4*n**5/35 + 12*n**4/7 + 192*n**3/7 + 640*n**2/7 + 5164. Factor y(q).
-4*q*(q - 20)*(q + 4)**2/7
Let n(h) be the third derivative of -h**5/12 - 3145*h**4/6 - 3956410*h**3/3 + 7*h**2 + 58*h - 2. Find v such that n(v) = 0.
-1258
Let f be ((-33)/(-36) + -1)/((-486)/(-34344)) + 7. Determine s, given that 8/3 - 80/9*s - f*s**4 + 8/3*s**3 + 14/3*s**2 = 0.
-2, 2/5, 1, 3
Let c(a) = -28*a - 4. Let b be c(-9). Let q = -991/4 + b. Factor 1/4*g**2 - 1/4*g + q*g**3 - 1/4.
(g - 1)*(g + 1)**2/4
Suppose -99 = 7*a + 41. Let f be (-10)/12*((-128)/a)/(-16). Solve -f*c**2 + 7/6*c**3 - 5/6*c**4 + 0*c + 0 = 0.
0, 2/5, 1
Let p(b) = -220*b - 2626. Let q be p(-12). Let w(i) be the second derivative of -1/54*i**4 + 0 + 1/27*i**3 - 1/90*i**5 + 1/135*i**6 + 0*i**2 - q*i. Factor w(m).
2*m*(m - 1)**2*(m + 1)/9
Suppose 13*v - 397 - 578 = 0. Suppose -6*c = 19*c - v. Factor 0*a - c + 3/4*a**2.
3*(a - 2)*(a + 2)/4
Let j(c) be the first derivative of -c**8/112 - c**7/14 - 7*c**6/40 - 3*c**5/20 + 17*c**2/2 + 4*c - 67. Let h(f) be the second derivative of j(f). Factor h(m).
-3*m**2*(m + 1)**2*(m + 3)
Let a(n) = 40 - 23*n**2 - 22 - n**3 - 53*n + 53 + 73. Let j be a(-20). Suppose 4/7 - 8/7*q**j - 2/7*q**5 + 10/7*q + 4/7*q**2 - 8/7*q**3 = 0. What is q?
-2, -1, 1
Let v(u) be the third derivative of -u**5/20 - 5*u**4/8 - 5*u**3 - 13*u**2. Let w(o) = 1. Let s(c) = v(c) + 18*w(c). Find l such that s(l) = 0.
-4, -1
Let q be 12/(-10) - (-4128)/3440. Suppose q*o + 0 - 1/3*o**3 + 1/6*o**2 + 1/6*o**4 = 0. Calculate o.
0, 1
Let d be 1/(-1)*1*30/(-6). Let y(r) be the third derivative of 1/360*r**d + 0 + 1/36*r**4 + 0*r**3 - 23*r**2 + 0*r. Determine n, given that y(n) = 0.
-4, 0
Suppose -259 = 5*y - u - 740, -197 = -2*y + 5*u. Factor -369 + 3*h**5 + 1215*h - 810*h**2 + 174*h**3 - 360 + y*h**3 - 45*h**4.
3*(h - 3)**5
Let n(s) be the second derivative of 729*s**4 + 2125764*s**2 + 2 + 153*s + 1/60*s**6 - 52488*s**3 - 27/5*s**5. Let n(p) = 0. Calculate p.
54
Let p = 23739 + -10170. Factor 32 + 4 - 13565*a**2 - 24*a + p*a**2.
4*(a - 3)**2
Let v(d) = 2*d**2 - 2. Let n(g) = 16*g**2 - 12*g - 12. Let h(j) = -n(j) + 6*v(j). Factor h(r).
-4*r*(r - 3)
Let n(a) = a**2 - 216*a - 4340. Let j(o) = -3*o**2 + 429*o + 8682. Let m(r) = -4*j(r) - 9*n(r). Solve m(u) = 0 for u.
-38
Let y(k) be the first derivative of -k**3 + 3093*k**2 - 3188883*k - 938. Factor y(m).
-3*(m - 1031)**2
Factor -8/5*r - 7/5*r**2 + 1/5*r**3 + 0.
r*(r - 8)*(r + 1)/5
Let q(n) be the first derivative of n**6/15 + 8*n**5/25 - 6*n**4/5 + 4*n**3/15 + 11*n**2/5 - 12*n/5 - 3443. Determine v, given that q(v) = 0.
-6, -1, 1
Let l(k) = k**2 - 69*k - 112. Let i(q) = -2*q**2 + 70*q + 112. Let m(g) = -5*i(g) - 6*l(g). Suppose m(a) = 0. Calculate a.
-14, -2
Suppose -z + 28 = -33. Solve 15*m**3 - 12*m**2 - 23*m**2 - 16*m**2 + 5*m**4 + z*m**2 = 0.
-2, -1, 0
Let f(t) = -t**3 + 1152*t**2 - 2367*t - 3490. Let c(r) = 384*r**2 - 789*r - 1164. Let v(q) = -10*c(q) + 3*f(q). Find z such that v(z) = 0.
-130, -1, 3
Let p(z) be the first derivative of 2*z**3/27 - 1034*z**2/3 + 534578*z - 5294. Factor p(q).
2*(q - 1551)**2/9
Let b(z) be the third derivative of z**8/1008 - 4*z**7/315 - 23*z**6/360 + 67*z**5/90 + 119*z**4/18 + 196*z**3/9 - 632*z**2 - 3. Factor b(o).
(o - 7)**2*(o + 2)**3/3
Determine h so that 14/3*h + 132 - 2/3*h**2 = 0.
-11, 18
Suppose g + 8 - 11 = 0. Suppose -4*v - l + 7 + 4 = 0, 0 = v + g*l. Determine d, given that -5*d**3 - 2*d**2 + 4*d**3 + 0*d**v - d**3 = 0.
-1, 0
Let -45*p**3 - 259*p - 5*p**4 + 79*p - 80 - 188*p**2 + 48*p**2 = 0. What is p?
-4, -2, -1
Solve 6*s + 6*s**2 - 3*s**3 - 15/2*s**4 + 3/2 - 3*s**5 = 0 for s.
-1, -1/2, 1
Let c(s) be the first derivative of 0*s + 74 + s**4 + 0*s**2 - 52/3*s**3. Suppose c(h) = 0. Calculate h.
0, 13
Let p = 548687/1540 - 2494/7. Let i(z) be the third derivative of 0*z**3 + 1/132*z**4 - 1/1155*z**7 - 1/110*z**5 + p*z**6 + 0 + 22*z**2 + 0*z. Factor i(c).
-2*c*(c - 1)**3/11
Let -75*p**4 + 145*p**2 - 5/2*p**5 + 0*p + 0 - 135/2*p**3 = 0. Calculate p.
-29, -2, 0, 1
Suppose 49*r**2 - 52*r**2 + 1728*r - 345333 + 96501 = 0. Calculate r.
288
Let d(u) be the first derivative of 2*u**5/5 + 61*u**4 + 482*u**3/3 + 120*u**2 + 1169. Factor d(q).
2*q*(q + 1)**2*(q + 120)
Let b(x) be the third derivative of 323/18*x**4 + x**2 + 1/360*x**6 - 39 + 0*x - 7/18*x**5 - 1156/9*x**3. Solve b(a) = 0 for a.
2, 34
Let p(g) be the third derivative of g**5/160 - 49*g**4/64 - 25*g**3/8 + 776*g**2. Suppose p(w) = 0. What is w?
-1, 50
Factor 20/3*k - 4/9*k**4 + 0 + 116/9*k**2 + 52/9*k**3.
-4*k*(k - 15)*(k + 1)**2/9
Let g(x) = 2*x**2 + 28*x - 11. Suppose 3*c - 23 = -44. Let k(a) = 25*a - 3 - 6*a + a**2 - 4. Let h(u) = c*k(u) + 5*g(u). Let h(n) = 0. What is n?
-3, 2/3
Let n(r) be the third derivative of r**8/112 + 229*r**7/70 - 231*r**6/20 + 3893*r**2. Factor n(d).
3*d**3*(d - 2)*(d + 231)
Factor 21 - 156*j - 19*j**2 + 76*j**2 - 10*j**2 + 88*j**2.
3*(j - 1)*(45*j - 7)
Let r(b) be the third derivative of 1/24*b**4 + 0*b - 1/30*b**5 + 1 + 1/120*b**6 + 0*b**3 + 18*b**2. Factor r(t).
t*(t - 1)**2
Let t(r) be the first derivative of 2/5*r**4 - 1/30*r**6 + 0*r**5 + 2/5*r**3 - 7/10*r**2 + 127 - 6/5*r. Suppose t(i) = 0. What is i?
-2, -1, 1, 3
Let b be (4/(-16))/(55/(-132))*(15 - 0). Find z such that 3/2 + 15/2*z**2 - b*z = 0.
1/5, 1
Find k such that -8 - 12*k + 7/2*k**2 = 0.
-4/7, 4
Let n(m) be the second derivative of -m**7/3150 - m**6/225 + 17*m**4/12 + 17*m. Let b(z) be the third derivative of n(z). Factor b(u).
-4*u*(u + 4)/5
Let t(i) be the third derivative of -i**8/264 - 146*i**7/1155 + 511*i**6/660 - 203*i**5/165 + 4*i**4/11 + 14*i**2 - 91. Determine j so that t(j) = 0.
-24, 0, 1/7, 1, 2
Let v(u) be the second derivative of -u**6/80 - 27*u**5/32 + 193*u**4/32 - 147*u**3/16 + 263*u. Let v(l) = 0. What is l?
-49, 0, 1, 3
Let m(n) be the third derivative of -n**5/120 + 17*n**4/8 - 665*n**3/12 - 5014*n**2. Suppose m(w) = 0. What is w?
7, 95
Let x(t) = 4*t**2 - t**2 - 17 + 16. Let i be x(-1). Solve -4*m**3 - 5*m**2 + 5*m**i - 4*m**2 = 0.
-1, 0
Let k(f) = -4*