f -z**5/60 + 35*z**4/24 - 17*z**3/3 - z**2 - 40. Factor s(h).
-(h - 34)*(h - 1)
Let u(h) be the first derivative of -h**4/30 + 146*h**3/45 + 304*h**2/15 + 616*h/15 - 1598. Factor u(y).
-2*(y - 77)*(y + 2)**2/15
Let v = -228751/2 + 114382. Suppose 1/2*k**4 + 5 - 5/2*k**3 - 3/2*k**2 + v*k = 0. Calculate k.
-1, 2, 5
Let h = 381 + -425. Let i(u) = -3*u**3 + u**2 - 1. Let j(a) = -68*a**3 + 18*a**2 + 6*a - 22. Let q(f) = h*i(f) + 2*j(f). Determine c, given that q(c) = 0.
-3, 0, 1
Let j = -59 - -55. Let b(s) = -46*s - 184. Let i be b(j). Factor -6/7*p**4 - 16/7*p**2 + i + 8/7*p - 22/7*p**3.
-2*p*(p + 2)**2*(3*p - 1)/7
Find d, given that -34*d**3 - 224 + 176*d - 110*d**3 + 10*d**4 + 189*d**3 - 121*d**3 + 114*d**2 = 0.
-7/5, 1, 4
Let y(t) = 10*t - 145. Let f be y(15). Factor 3813 - f*v**2 + 8*v**2 + 3099 - 288*v.
3*(v - 48)**2
Let z(i) be the second derivative of -1/330*i**5 + i**2 + 0*i**3 - 10*i + 1/66*i**4 + 0. Let f(b) be the first derivative of z(b). Factor f(u).
-2*u*(u - 2)/11
Let p = -6194 + 6194. Let c(d) be the first derivative of -1/3*d**5 - 2/9*d**6 - 15 + 7/12*d**4 + p*d + 2/9*d**3 + 0*d**2. Suppose c(b) = 0. Calculate b.
-2, -1/4, 0, 1
Let w(s) be the third derivative of 5*s**6/16 - 211*s**5/8 + 11639*s**4/16 - 10609*s**3/4 - 1201*s**2. Factor w(b).
3*(b - 1)*(5*b - 103)**2/2
Let c(s) be the second derivative of -5/168*s**7 + 0*s**2 - 1/12*s**3 + 17/120*s**6 + 0 - 54*s + 11/48*s**4 - 21/80*s**5. Factor c(f).
-f*(f - 1)**3*(5*f - 2)/4
Let k(v) = 19*v**4 - 30*v**3 + 144*v**2 - 244*v - 12. Let j(o) = -41*o**4 + 61*o**3 - 288*o**2 + 486*o + 26. Let a(t) = 6*j(t) + 13*k(t). Factor a(q).
q*(q - 16)*(q - 4)**2
Let l be ((-4935)/245 - -19)/(-9 + 1). Suppose 5/7*z**2 + l*z**3 + 2/7*z - 8/7 = 0. What is z?
-4, -2, 1
Suppose 0 = -88*q - 14*q. Let v(j) be the second derivative of 0 + q*j**5 + 1/36*j**4 + 0*j**2 + 0*j**3 - 17*j - 1/90*j**6. Solve v(a) = 0.
-1, 0, 1
Let t(c) be the second derivative of 3/8*c**6 + 0*c**3 + 1 - 42*c + 0*c**2 + 7/16*c**5 - 5/24*c**4. Factor t(k).
5*k**2*(k + 1)*(9*k - 2)/4
Factor -143 - 10*w - 1 + 74*w + 4*w**2.
4*(w - 2)*(w + 18)
Let f be 1712/12 + (-2)/3. Suppose f*o = 141*o. Factor 2/17*w - 2/17*w**2 + o.
-2*w*(w - 1)/17
Let 135/11*x + 11*x**3 - 25/11 - 21*x**2 = 0. What is x?
5/11, 1
Factor 62/3 - 1/6*a**3 + 61/3*a**2 + 247/6*a.
-(a - 124)*(a + 1)**2/6
Let z(w) be the first derivative of w**5 - 20*w**4 - 170*w**3 - 180*w**2 + 945*w + 3146. Factor z(o).
5*(o - 21)*(o - 1)*(o + 3)**2
Suppose -32*n = 3*n - 175. Let i be 99/12 - (-2)/(-8). Let -279 + 99 + i*l - n*l**2 + 54*l - 2*l = 0. Calculate l.
6
Let r(q) be the first derivative of -q**4/84 - 12*q**3/7 - 648*q**2/7 - 8*q - 56. Let z(m) be the first derivative of r(m). Suppose z(c) = 0. What is c?
-36
Suppose 33/4*b + 1/4*b**3 - 9/2*b**2 + 121 = 0. Calculate b.
-4, 11
Solve 54*f - 120 + 69*f**2 - 3*f**4 - 2*f**3 + 2*f**3 - 54*f**3 + 0*f**4 + 54*f**2 = 0 for f.
-20, -1, 1, 2
Let l be 2 + 9 - (-1090)/(-100). Let s(b) be the first derivative of -13 + 6/5*b**2 - l*b**4 + 0*b + 2/3*b**3. Factor s(r).
-2*r*(r - 6)*(r + 1)/5
Let d(k) be the third derivative of -k**5/135 - 7*k**4/9 + 470*k**3/27 + 764*k**2. Let d(g) = 0. What is g?
-47, 5
Let m(s) be the first derivative of s**5/5 - 50*s**4 + 10768*s**3/3 - 38400*s**2 + 147456*s - 1045. Factor m(f).
(f - 96)**2*(f - 4)**2
Let g(b) = -2*b**3 - b**2 - 3*b - 1. Let l be g(-1). Let -391*x**3 + 5*x**4 - 90 + 65*x**2 + 0*x**2 + 15*x + 203*x**3 + 153*x**l = 0. What is x?
-1, 2, 3
Let o(w) be the third derivative of -w**7/1575 - 211*w**6/900 - 209*w**5/150 - 125*w**4/36 - 208*w**3/45 - 6*w**2 - 5*w. Factor o(f).
-2*(f + 1)**3*(f + 208)/15
Suppose -7*a + 6*a - 68 = -3*t, 4*a = 4*t - 96. Suppose -t*d**2 - 113463 - 2*d**4 + 14*d**3 + 113463 + 10*d = 0. What is d?
0, 1, 5
Let p(a) be the first derivative of a**5/50 - 1111*a**4/40 + 20609*a**3/2 - 61605*a**2/4 + 6979. Solve p(d) = 0 for d.
0, 1, 555
Let d be -5*(3 + 1 - 7). Solve -30*m - 5*m + 6*m + 104 - d*m - 4*m**2 = 0.
-13, 2
Let f be 0 + -5 + (48188/1968)/7. Let g = -1/492 - f. Factor -6*v - g*v**2 - 9/2.
-3*(v + 1)*(v + 3)/2
Let i = 2539548824/813645 - 10/162729. Factor 6/5*r**2 + 612/5*r + i.
6*(r + 51)**2/5
Suppose 2*r + 5*f - 40 = 0, -3*f - 3345 + 3369 = -4*r. Factor -60/7*k**3 - 24/7*k + 12/7*k**4 + 4/7*k**5 + 68/7*k**2 + r.
4*k*(k - 1)**3*(k + 6)/7
Let y = -256/85 + 3149/340. Factor 0 - 5*q**3 - 5/2*q + y*q**2 + 5/4*q**4.
5*q*(q - 2)*(q - 1)**2/4
Let t be (-15)/(-9) + 16/(-6). Let n be 5 + (-4 - -7)*(0 + t). Find m such that 12/13*m**3 + 2/13*m**4 + 2/13*m**n + 32/13 - 48/13*m = 0.
-4, 1
Let c be ((-14)/28)/((3/(-62))/3). Factor -59 - z**5 + c + 28 + z**3.
-z**3*(z - 1)*(z + 1)
Let z = 14 + -11. Factor -2 + 312*v**4 + 10*v - 3 - 10*v**z - 307*v**4.
5*(v - 1)**3*(v + 1)
Solve 162/13*v**5 + 4032*v - 288*v**4 + 15530/13*v**3 + 832 + 70836/13*v**2 = 0 for v.
-2, -4/9, 13
Let c(r) be the third derivative of -r**7/7560 + r**6/2160 + 31*r**4/24 - 69*r**2. Let j(z) be the second derivative of c(z). Let j(o) = 0. Calculate o.
0, 1
Factor 3*v**4 + 294*v + 0*v**4 - 7180*v**2 + 276*v - 192*v - 12*v**3 + 7063*v**2.
3*v*(v - 7)*(v - 3)*(v + 6)
Let i be -38 - -45 - (9 - -1). Let k be ((-30)/36*3)/(i/2). Find n, given that k*n + 0 + 35/6*n**2 + 15/2*n**3 + 5/6*n**5 + 25/6*n**4 = 0.
-2, -1, 0
Let j = 21932/3 + -108508/15. Factor j*o + 222/5*o**2 + 6*o**3 + 24.
6*(o + 2)*(o + 5)*(5*o + 2)/5
Let v be (-20439)/(-4542)*(12/13)/3. Determine i, given that 4/13*i**3 - v*i + 0 - 24/13*i**2 + 8/13*i**4 - 2/13*i**5 = 0.
-1, 0, 3
Let y(d) = 16*d**3 - d**2 - 2*d + 2. Let b(q) = 75*q**3 + 140*q**2 + 4390*q + 24510. Let u(v) = b(v) - 5*y(v). Factor u(f).
-5*(f - 49)*(f + 10)**2
Let b(f) be the first derivative of 3/5*f**5 + 429*f**3 + 3468*f + 1938*f**2 + 86 + 57/2*f**4. Factor b(j).
3*(j + 2)**2*(j + 17)**2
Let m(v) be the third derivative of v**8/1848 - 18*v**7/385 + 63*v**6/44 - 882*v**5/55 + 934*v**2. Let m(t) = 0. Calculate t.
0, 12, 21
Determine z, given that -4*z**3 + 0*z - 26/7*z**2 + 0 - 2/7*z**4 = 0.
-13, -1, 0
Let m be -40*(-32)/(-40)*-2. Let -8 - 2*b + 1 - 1 + 65*b**2 - m*b**2 = 0. What is b?
-2, 4
Factor 825/7*s + 3/7*s**2 - 828/7.
3*(s - 1)*(s + 276)/7
Let c(n) be the third derivative of 2*n**7/105 + 2*n**6 + 229*n**5/15 + 47*n**4 + 224*n**3/3 + 6*n**2 - 10. Factor c(f).
4*(f + 1)**2*(f + 2)*(f + 56)
Factor -19*m**2 - 35/2*m + 37 - 1/2*m**3.
-(m - 1)*(m + 2)*(m + 37)/2
Let r(n) be the first derivative of 0*n**2 + 0*n - 15/4*n**4 + 0*n**3 + n**5 + 23. Let r(g) = 0. What is g?
0, 3
What is g in 34 - 1776*g + 171 - 420*g**3 - 15*g**4 + 358*g**2 + 31*g**4 + 147 + 1218*g**2 = 0?
1/4, 2, 22
Suppose 3520 = -36*v + 26*v. Let k = v + 356. Find o, given that 0 + 1/3*o**2 + 0*o - 1/6*o**k - 1/6*o**3 = 0.
-2, 0, 1
Find z such that 16*z + 10*z**3 + 718/11*z**2 - 88 - 38/11*z**4 + 2/11*z**5 = 0.
-2, 1, 11
Find o such that 11464/5*o + 2/5*o**2 + 16427912/5 = 0.
-2866
Solve 108 - 54/5*q**3 - 828/5*q + 339/5*q**2 + 3/5*q**4 = 0 for q.
1, 5, 6
Let n(f) be the first derivative of 3*f**4/8 - 39*f**2/4 + 18*f - 757. Factor n(k).
3*(k - 3)*(k - 1)*(k + 4)/2
Determine i so that 6333931*i - 15840*i**2 - 7762501*i - 15298470*i - 5*i**3 - 5887918080 = 0.
-1056
Let j(d) be the second derivative of d**5/40 - 3*d**4/4 + 5*d**3/4 + 17*d**2/2 - 53*d + 2. Factor j(t).
(t - 17)*(t - 2)*(t + 1)/2
Let a(v) be the first derivative of -v**7/42 + v**6/4 - 3*v**5/4 - 3*v**2/2 - 6*v - 200. Let w(f) be the second derivative of a(f). Factor w(j).
-5*j**2*(j - 3)**2
Let x(g) be the first derivative of 203 - 8/7*g**2 - 44/21*g**3 - 16/35*g**5 - 1/21*g**6 - 3/2*g**4 + 0*g. Find p such that x(p) = 0.
-4, -2, -1, 0
Let d(j) be the second derivative of -5*j**3/2 + 79*j**2/2 + 161*j + 1. Let u be d(5). Let 0 + 0*t**2 + 0*t - 1/3*t**3 + 1/2*t**u + 7/3*t**5 = 0. What is t?
-1/2, 0, 2/7
Let z(o) = -16*o**2 + 173*o + 1606. Let k(t) = -13*t**2 + 174*t + 1608. Let a be (9/(-3))/(21/49). Let d(i) = a*k(i) + 6*z(i). Solve d(r) = 0.
-18
Suppose 2*g - 87 = -83. Suppose -g*t = 5*m + 4 + 12, 16 = 4*t - 2*m. Factor -4/11*c**3 + 2/11 + 0*c**t - 2/11*c**4 + 4/11*c.
-2*(c - 1)*(c + 1)**3/11
Let g(w) = -w**3 - 562*w**2 - 77845*w - 6. Let j(l) = 3*l**3 + 1688*l**2 + 233537*l + 21. Let i(t) = -7*g(t) - 2*j(t). Factor i(b).
b*(b + 279)**2
Let t(y) = y**3 + 3