(w - 8)
Let z(o) be the first derivative of 231*o**2 + 105 + 12*o - 4563/8*o**4 + 1443*o**3. Factor z(i).
-3*(i - 2)*(39*i + 2)**2/2
Factor 4/3*q**3 - 40/3*q**2 - 4/3*q + 40/3.
4*(q - 10)*(q - 1)*(q + 1)/3
Let v = 20/2949 - 124082/19165551. Let p = 311938/45493 + v. Find o such that p*o + 2/7*o**2 + 288/7 = 0.
-12
Let d(h) = h**3 - 25*h**2 + 89*h - 20. Let b be d(4). Let i(c) = 7*c - 4. Let n be i(1). Suppose 1/3*j**n - 2*j**2 + b + 8/3*j = 0. What is j?
0, 2, 4
Let x(r) be the second derivative of -17*r - 1/10*r**3 - 1/10*r**2 + 1 - 1/100*r**5 - 1/20*r**4. Factor x(m).
-(m + 1)**3/5
Suppose 5*o - 230 = -c, 4*c - 3*o = 290 + 722. Factor -130*i**2 - i**5 - 12*i**3 + c*i**2 - 128*i**2 - 6*i**4.
-i**2*(i + 2)**3
Let a(j) = -1. Let q(o) = -8*o + 280. Let b(m) = -2*a(m) - 2*q(m). Let f be b(35). Solve 1/2*z**f - z + 1/2 = 0 for z.
1
Factor -116/13*j**2 + 0 - 2/13*j**4 + 0*j - 62/13*j**3.
-2*j**2*(j + 2)*(j + 29)/13
Let j(k) be the third derivative of -k**5/75 - 233*k**4/30 - 892*k**3/3 + 8973*k**2. Factor j(z).
-4*(z + 10)*(z + 223)/5
Let t(m) be the first derivative of -m**4/20 - 119*m**3/15 - 348*m**2 + 720*m - 1243. Factor t(w).
-(w - 1)*(w + 60)**2/5
Let c(t) be the first derivative of -t**4/22 + 2*t**3 - 59*t**2/11 - 186*t/11 + 1404. Factor c(h).
-2*(h - 31)*(h - 3)*(h + 1)/11
Suppose -40*i = -76*i. Let z = -1 - -7/6. Factor 0*r + i + 1/6*r**2 - 1/6*r**4 + 1/6*r**3 - z*r**5.
-r**2*(r - 1)*(r + 1)**2/6
Let k(o) be the third derivative of o**8/420 + 458*o**7/525 + 13447*o**6/150 + 12769*o**5/25 + 2751*o**2. Solve k(v) = 0 for v.
-113, -3, 0
Let w(a) = -10*a - 10. Let f(s) = -s**2 - 4*s + 5. Let g(n) = 2*f(n) + w(n). Find l, given that g(l) = 0.
-9, 0
Let k(i) be the first derivative of -18/5*i - 55 + 2/15*i**3 + 0*i**2. Determine l so that k(l) = 0.
-3, 3
Let z = 16512393/2120 - 62305/8. Let c = -18/53 + z. Determine o so that c*o - 2/5*o**3 + 0*o**2 + 0 = 0.
-1, 0, 1
Let o(m) be the third derivative of -m**5/210 + 44*m**4/3 - 54208*m**3/3 - 248*m**2 - 10. Factor o(r).
-2*(r - 616)**2/7
Suppose 63*u + 38589 = 82*u. Suppose -2034*x + 6 = -u*x. Factor 3/2*l**x - 3/4*l - 3/4*l**3 + 0.
-3*l*(l - 1)**2/4
Let j(r) be the first derivative of -3*r**4/4 + 77*r**3 + 471*r**2/2 + 237*r - 2344. Find v, given that j(v) = 0.
-1, 79
Suppose 9 = 2*v - 2*w + 3*w - 1, -24 = -4*w. Factor -10 - 2/5*p**v + 4*p.
-2*(p - 5)**2/5
Let g(f) be the second derivative of -f**9/12096 + f**8/3360 - f**7/3360 + 67*f**3/6 - 43*f. Let z(r) be the second derivative of g(r). Factor z(j).
-j**3*(j - 1)**2/4
Let j(s) be the third derivative of -s**8/336 - 2*s**7/105 + s**6/40 + 7*s**5/30 + s**4/3 + 545*s**2. Factor j(p).
-p*(p - 2)*(p + 1)**2*(p + 4)
Factor 156640*n - 3*n**3 + 21*n**3 - 1229*n**2 - 7*n**3 - 536*n**2 - 6*n**3 - 154880.
5*(n - 176)**2*(n - 1)
Let u = -460348/75 - -6138. Let g(f) be the second derivative of 0*f**2 + u*f**6 + 14*f + 0*f**3 + 1/25*f**5 + 0 - 2/15*f**4. Solve g(r) = 0 for r.
-2, 0, 1
Let y = 29 + -16. Suppose y = -k + 21. Solve -k*o**3 - o**3 - 48*o + 15 - 2*o**2 + 53*o**2 - 9*o**3 = 0.
5/6, 1
Let q(d) = -2*d - 6. Let p be q(-3). Suppose -5 = x - p, 5*x = 3*t - 43. Factor 6*s**2 + t*s**3 - 19*s**2 + 11*s**2.
2*s**2*(3*s - 1)
Let s = -986 + 361. Let i = s - -630. Find f, given that 0*f**2 + 1/5*f**4 - 1/5*f**i + 0 + 0*f + 2/5*f**3 = 0.
-1, 0, 2
Let h(r) = -5*r**3 + 24*r**2 + 60*r - 4. Suppose b = -16 + 12. Let c(k) = -20*k**3 + 95*k**2 + 240*k - 15. Let u(z) = b*c(z) + 15*h(z). Factor u(t).
5*t*(t - 6)*(t + 2)
Factor -3 + 1/6*j**3 - 1/2*j + 2/3*j**2.
(j - 2)*(j + 3)**2/6
Let z = 35 - 33. Factor 40520 - 16*g + 4*g**3 - 2*g**2 - z*g**2 - 40504.
4*(g - 2)*(g - 1)*(g + 2)
Let a(w) = -2*w**4 - 2*w**2 + w + 7. Let h(j) = -9*j**4 + 105*j**3 + 1306*j**2 + 1202*j + 14. Let i(n) = 2*a(n) - h(n). Suppose i(k) = 0. What is k?
-8, -1, 0, 30
Let x(k) = 15*k - 31. Let c be x(3). Suppose -2*n = 4*q - 5*n - 6, 0 = -4*q - n + c. Factor -h + 1/4*h**5 + 1/4*h**q - 2 + 5/2*h**2 - h**4.
(h - 2)**3*(h + 1)**2/4
Factor 572 + 10/3*q**2 - 4294/3*q.
2*(q - 429)*(5*q - 2)/3
Let v(d) be the second derivative of -d**4/12 + 5*d**3/6 + 18*d**2 - 644*d. Determine u so that v(u) = 0.
-4, 9
Let l = -40 + 44. Factor -4580*q**3 + 35*q**l - 285 + 4280*q**3 - 174*q + 810*q**2 - 366*q - 120.
5*(q - 3)**3*(7*q + 3)
Let i(t) = t**3 - 2*t**2 - 3*t + 2. Let q = -127 + 130. Let d be i(q). Factor -2/11*s**d + 0*s + 2/11.
-2*(s - 1)*(s + 1)/11
Let a = 238 - 71. Let w = a + -164. What is d in 0 + 0*d**2 + 8/7*d - 2/7*d**w = 0?
-2, 0, 2
Let g = -9/155 + -11213/155. Let q = -1443/20 - g. Solve q*u**2 + 1/4 + 1/2*u = 0 for u.
-1
Let j = 737699/9 - 81963. Solve 4*g**2 + 2/9*g**4 + 10/9 + j*g + 16/9*g**3 = 0.
-5, -1
Let f(u) be the third derivative of -u**5/48 + 315*u**4/16 - 1885*u**3/24 + u**2 + 967. Factor f(g).
-5*(g - 377)*(g - 1)/4
Suppose -33 = 23*b + 36. Let i be (-5)/((-165)/(-22))*b. Factor -12/5*k**i + 3/5*k - 3/5*k**3 + 12/5.
-3*(k - 1)*(k + 1)*(k + 4)/5
Let b(s) be the second derivative of -s**7/147 - 2*s**6/105 + s**5 + 208*s**4/21 + 265*s**3/7 + 450*s**2/7 - 2277*s + 2. Let b(y) = 0. Calculate y.
-5, -3, -1, 10
Let s(i) be the third derivative of -7*i**5/150 - 103*i**4/30 - 29*i**3/5 + 5326*i**2. What is a in s(a) = 0?
-29, -3/7
Let u(m) be the third derivative of 1/1260*m**7 + 1/60*m**5 + 0*m**3 + 0*m - 7/720*m**6 + 0*m**4 - 81*m**2 - 1. Factor u(q).
q**2*(q - 6)*(q - 1)/6
Let r(w) be the second derivative of 0 + 15/32*w**5 - 6*w**2 - 319/16*w**3 - 395/16*w**4 + 60*w. Suppose r(v) = 0. Calculate v.
-1/5, 32
Find d, given that -1648/3*d - 124958*d**3 + 238521/2*d**5 + 1887829/6*d**4 + 8 + 13232*d**2 = 0.
-3, 2/43, 2/9
Let s(i) be the third derivative of -i**7/630 + i**6/10 + 9*i**5/10 - 243*i**4/2 - 6561*i**3/2 - 98*i**2 - 5*i. Factor s(x).
-(x - 27)**2*(x + 9)**2/3
Suppose 70 = 26*b + 9*b. Factor 38*h**b + 2*h**2 + 96 - h - 4*h**3 + 3*h - 28*h - 86*h.
-4*(h - 6)*(h - 2)**2
Let g = 165 - 114. Let d(s) = -43*s**2 - 240*s + 1783. Let c(t) = -5*t**2 - 30*t + 223. Let h(q) = g*c(q) - 6*d(q). Let h(n) = 0. What is n?
15
Let t = 198239 + -396393/2. Suppose 15/2*l**3 + 10*l**2 - t*l - 15 = 0. What is l?
-3, -1/3, 2
Let x(m) = 918*m**2 - 463*m**2 - 454*m**2 - 2*m + 2. Let d be (-1 + -1)/(3 + -2). Let g(i) = i**2 - i + 1. Let b(n) = d*g(n) + x(n). Factor b(l).
-l**2
Determine o so that -85/6*o + 0 + 387*o**4 - 384*o**3 - 9/2*o**5 + 383/3*o**2 = 0.
0, 1/3, 85
Let r(k) = -2*k**2 + 2*k - 1. Let m(t) = -3*t**2 + 59*t - 176. Let f(d) = 3*m(d) - 6*r(d). Suppose f(s) = 0. What is s?
-58, 3
Let n(z) be the first derivative of 5*z**4/12 - 5*z**3/6 + 103*z - 38. Let y(g) be the first derivative of n(g). Determine h, given that y(h) = 0.
0, 1
What is k in k**2 - 1/3*k**3 + 16/3*k - 16 = 0?
-4, 3, 4
What is b in -3/7*b - 12/7*b**2 - 3/7*b**5 + 6/7*b**3 + 6/7 + 6/7*b**4 = 0?
-1, 1, 2
Suppose -3*g - f + 13 = 0, 114*g = 119*g - 3*f + 39. Suppose 8/9*q**3 + 2/9*q**4 + 0*q**2 + 0 + g*q = 0. Calculate q.
-4, 0
Let c(z) be the third derivative of 3*z**7/49 + 83*z**6/140 + 47*z**5/21 + 29*z**4/7 + 88*z**3/21 - 2918*z**2. Suppose c(m) = 0. Calculate m.
-11/5, -2, -2/3
Let o be (-858)/(-3003)*(-1 + 3 + 1). Determine c, given that 16/7*c - o*c**2 - 8/7 + 2/7*c**4 - 4/7*c**3 = 0.
-2, 1, 2
Let y(g) = -9*g**3 + 9*g**2 - 18*g + 12. Suppose 47*b = 51*b - 24. Let n(t) = -8*t**3 + 10*t**2 - 19*t + 12. Let q(w) = b*n(w) - 5*y(w). Factor q(c).
-3*(c - 2)**2*(c - 1)
Let x(c) be the third derivative of c**7/735 + 716*c**6/105 + 512656*c**5/35 + 367061696*c**4/21 + 262816174336*c**3/21 - 646*c**2 + 2. Factor x(u).
2*(u + 716)**4/7
Suppose 5*l = 4*d - 2*d, -59*l + 63*l = -4*d. Let c(r) be the first derivative of -18 + 63/2*r**4 + d*r - 68/3*r**3 + 81/5*r**5 + 4*r**2. Solve c(u) = 0 for u.
-2, 0, 2/9
Let f = -165/13 - -508/39. Let w(u) be the third derivative of -5/3*u**3 - 25/24*u**4 + 0 - f*u**5 + 0*u - 1/24*u**6 + 6*u**2. Factor w(c).
-5*(c + 1)**2*(c + 2)
Let j(z) = -155*z**2 + 86*z + 471. Let y(b) = 69*b**2 - 42*b - 236. Let o(r) = -4*j(r) - 9*y(r). Find t such that o(t) = 0.
-6, 40
Let p be 34/((-1666)/(-21))*(-154)/(-33). Solve 19/4*u + 2*u**p + 3 + 1/4*u**3 = 0.
-4, -3, -1
Factor -14/3 + 10/9*p**2 + 2/9*p**3 - 34/9*p.
2*(p - 3)*(p + 1)*(p + 7)/9
Suppose -6 = 5*g + 3*s, -35*s + 39*s = -8. Let p(d) be the third derivative of 0 