be the first derivative of s(t). Factor g(l).
3*(l + 4)*(5*l - 6)/4
Let c be 33453/35 + 3/15. Factor 14240*q**3 + 7*q**5 + 12352*q**2 + 24*q**5 + 109824*q - 105952*q**2 - c*q**4 + 114176*q + 40000 - 7*q**5.
4*(q - 10)**4*(6*q + 1)
Suppose 5*y + 117 = 4*y. Let z = 119 + y. Let 5*p**z - 6*p**2 + p**2 - 30*p**4 + 62*p**3 - 8*p = 0. What is p?
-1/3, 0, 2/5, 2
What is z in -94773 + 2*z**4 + 168*z**2 - 1668*z + 96789 + 75*z**3 + z**4 = 0?
-21, -8, 2
Suppose 0 = 25*b + 1 - 51. What is x in 16*x - 8*x**3 - 46*x + 98 + 52*x**b - 78 - 7*x - 27*x = 0?
1/2, 1, 5
Let p(v) be the first derivative of v**4/4 + v**3/2 - 3*v**2 + 7*v/2 + 1754. Factor p(o).
(o - 1)**2*(2*o + 7)/2
Let x(o) be the second derivative of 3/20*o**2 + 0 - 3/100*o**6 + 3/50*o**5 + 19/60*o**4 + 89*o + 1/3*o**3. Determine h so that x(h) = 0.
-1, -1/3, 3
Let a(k) = 34*k**3 - 136*k**2 + 60*k + 31. Let x(r) = 7*r**3 - 27*r**2 + 12*r + 6. Let p(z) = 2*a(z) - 11*x(z). Let p(q) = 0. What is q?
-2/9, 1, 2
Solve 907*b**2 - 1612*b**2 + 265*b + 737*b**2 + b**3 + 234 = 0.
-18, -13, -1
Let r(a) be the third derivative of a**6/1080 - 11*a**5/90 - 5*a**4/8 + 24*a**3 + 74*a**2. Let l(s) be the first derivative of r(s). Factor l(d).
(d - 45)*(d + 1)/3
Let w be 150/1500*(-105)/(-2). Let p be -3*(1 + 0)*-1. Factor w*k**2 - 3/2*k - 3*k**p - 3/4.
-3*(k - 1)**2*(4*k + 1)/4
Let h(i) be the second derivative of -4/21*i**3 + 1/42*i**4 + 59 - 12/7*i**2 + i. Factor h(j).
2*(j - 6)*(j + 2)/7
Let q(c) = -10*c + 272. Let f be q(26). Let j be 2/4*(f + -17 + 9). Factor -1/4*p + 3/4*p**5 - 2*p**4 + 0*p**j + 3/2*p**3 + 0.
p*(p - 1)**3*(3*p + 1)/4
Let n(z) = -3*z**3 + 141*z**2 - 198*z + 272. Let g(i) = 6*i**2 + 2. Let m(t) = -16*g(t) + n(t). Factor m(f).
-3*(f - 8)*(f - 5)*(f - 2)
Let n = -6 + 3. Let c(y) = 4*y**2 + 176 - 175 - 5*y**2. Let w(u) = -3*u**4 - 7*u**3 - 4*u**2 + 3*u + 3. Let k(m) = n*w(m) + 3*c(m). Factor k(v).
3*(v + 1)**3*(3*v - 2)
Let a(v) = 3*v**4 + 27*v**3 + 96*v**2 + 135*v + 63. Let o(d) = d**3 + d**2 - d - 1. Let p(n) = -a(n) - 3*o(n). Determine r, given that p(r) = 0.
-5, -2, -1
Factor 690*m**3 + 21*m**4 - 53391*m + 5402*m**2 + 455877/5 + 1/5*m**5.
(m - 3)**2*(m + 37)**3/5
Let a(q) = 10*q - 18. Let w = 133 - 131. Let n be a(w). Factor -3*p - 2173*p**2 + 2175*p**n - p.
2*p*(p - 2)
Factor -4*w**2 - 2*w**4 + 23*w**3 - 16*w**3 - 312*w + 188*w**2 + 160 - 37*w**3.
-2*(w - 2)**2*(w - 1)*(w + 20)
Let r = 2830 - 8489/3. Let c(f) be the second derivative of -4/3*f**3 - r*f**4 + 0 - 17*f - 2*f**2. Factor c(w).
-4*(w + 1)**2
Determine n, given that 56/3*n**3 + 88/3 - 4/3*n**5 + 112/3*n**2 - 212/3*n - 40/3*n**4 = 0.
-11, -2, 1
Let s(n) = n**2 + 2012*n + 1006003. Let h(f) = 3*f - 3. Let r(g) = 10*h(g) - 5*s(g). Factor r(b).
-5*(b + 1003)**2
Let b(i) be the third derivative of i**8/1680 + 13*i**7/350 + 3*i**6/5 - 4*i**5/3 - 955*i**2. Factor b(c).
c**2*(c - 1)*(c + 20)**2/5
Let k(w) be the first derivative of -5/3*w**3 + 5*w**2 + 0*w - 5/4*w**4 + 46. Determine i so that k(i) = 0.
-2, 0, 1
Suppose -8*n**5 - 302*n**3 + 993*n**2 + 310*n - 587*n**2 + 154*n**4 - 492*n**2 - 68 = 0. Calculate n.
-1, 1/4, 1, 2, 17
Let m = 4132 - 4115. Let b(c) be the second derivative of -m*c + 1/80*c**5 - 1/24*c**3 + 1/16*c**4 + 0 - 1/4*c**2 - 1/120*c**6. Let b(j) = 0. Calculate j.
-1, 1, 2
Determine v, given that -126184301*v**4 - 75*v + 11*v - 21*v**2 + 68 + 126184302*v**4 + 16*v**3 = 0.
-17, -2, 1, 2
Let w be ((-199)/(-1592) - 62/240)*-20. Factor 8/3*z**2 - w + 1/3*z**3 - 1/3*z.
(z - 1)*(z + 1)*(z + 8)/3
Let y(t) be the second derivative of t**8/1680 + 4*t**7/315 + t**6/15 + 17*t**4/2 - 6*t - 4. Let r(j) be the third derivative of y(j). Factor r(p).
4*p*(p + 2)*(p + 6)
Let p(i) be the third derivative of i**5/12 + 145*i**4/8 + 636*i**2. Factor p(u).
5*u*(u + 87)
Let x be (-7)/(-3) - (5 + -4). Suppose -79 = -j + 4*g - 91, -g + 3 = 0. Solve 0*c + j - 2*c**3 + 2/3*c**4 + x*c**2 = 0 for c.
0, 1, 2
Let m be 3471/(-6) + 22/(286/(-39)). Let i = -579 - m. Suppose -5/2*s**3 - i - 5/2*s**4 + 5/4*s**5 + 5/4*s + 5*s**2 = 0. What is s?
-1, 1, 2
Let d(i) = -9*i**4 + 24*i**3 - 42*i**2 - 9*i + 48. Let f(w) = 2*w**4 - w**3 + 2*w**2 - w. Let a = -380 + 379. Let s(b) = a*d(b) - 3*f(b). Factor s(u).
3*(u - 4)*(u - 2)**2*(u + 1)
Let v be (-4)/16 + (-11937)/(-644). Factor -4/7*d**4 - v*d**2 - 128/7*d + 0 - 40/7*d**3.
-4*d*(d + 2)*(d + 4)**2/7
Let i be (-168)/(-140) + 12/108*-9. Factor 4*y**3 + 18/5*y**2 + i*y**4 - 19/5 - 4*y.
(y - 1)*(y + 1)**2*(y + 19)/5
Factor 9*m**4 + 3/2*m**3 + 0 - 3/4*m - 3*m**2 - 27/4*m**5.
-3*m*(m - 1)**2*(3*m + 1)**2/4
Let x be -2 - (-18 + 18/(-3)). Let d be (-54)/8*-3*x/99. Find l such that 3*l + d*l**2 - 3/2 = 0.
-1, 1/3
Let x(t) = -6*t**2 + 21*t - 16. Let o be x(2). Let i(f) be the third derivative of 0*f - 5*f**o + 0 - 1/450*f**5 - 1/90*f**4 + 0*f**3. Factor i(b).
-2*b*(b + 2)/15
Let a(w) = -w**3 + 43*w**2 - 40*w - 78. Let h be a(42). Let 17*u**2 + 4*u**2 - 19*u**2 + 0*u**2 + 10*u - 6 - h = 0. What is u?
-6, 1
Let q(c) be the first derivative of 3/19*c**2 - 6 - 1/57*c**3 - 1/38*c**4 + 1/190*c**5 - 4*c. Let u(o) be the first derivative of q(o). Factor u(m).
2*(m - 3)*(m - 1)*(m + 1)/19
Let g(f) = -13*f**2 + 301*f + 294. Let h(m) = -10*m**2 + 300*m + 295. Let p(y) = -3*g(y) + 4*h(y). Solve p(l) = 0.
-1, 298
Suppose -3*d + 0*d - 6 = 2*n, -2*n + 4*d = -22. Let t be (-1 - n/(-7))/((-36)/42). Suppose 2/3*k**3 - k**2 - 1/6*k**4 - 1/6 + t*k = 0. Calculate k.
1
Let g(c) be the second derivative of -c**5/60 + 7*c**4/36 + 113*c**3/18 + 35*c**2/2 - 2342*c. Solve g(w) = 0.
-7, -1, 15
Let i(g) be the third derivative of -g**6/30 + 14*g**5/15 - g**4/6 - 104*g**3 - 82*g**2 - 8. Determine d, given that i(d) = 0.
-3, 4, 13
Let -8/9*m**3 - 26/9*m**2 + 8/3 + 2/9*m**4 + 8/9*m = 0. Calculate m.
-2, -1, 1, 6
Let h(c) be the second derivative of 3/40*c**6 - 1/12*c**3 - 1/4*c**5 + 0*c**2 + 3 + 3*c + 13/48*c**4. Find y, given that h(y) = 0.
0, 2/9, 1
Suppose 3*z + 2*z = 2550. Suppose 672*t**4 + 118*t**3 + z*t**3 - 220*t**5 + 24*t**5 - 608*t**2 - 432*t - 64 = 0. What is t?
-1, -2/7, 1, 4
Let q(u) be the first derivative of 2*u**5/5 + 13*u**4 + 130*u**3/3 - 92*u**2 + 2536. Factor q(t).
2*t*(t - 1)*(t + 4)*(t + 23)
Let n(a) be the first derivative of -3*a**4/22 + 12*a**3 - 387*a**2/11 + 384*a/11 + 13592. Factor n(h).
-6*(h - 64)*(h - 1)**2/11
Let a(c) be the first derivative of c**3/3 + 13*c**2/2 - 168*c + 2125. Determine w, given that a(w) = 0.
-21, 8
Factor 99/2 + 197/4*o - 1/4*o**2.
-(o - 198)*(o + 1)/4
Suppose 2*u + 192 = 9*q + 362, 0 = 4*u - 4*q - 88. Determine x, given that 382/3*x**2 + 92/9*x**3 + 968/9 + 2024/9*x + 2/9*x**u = 0.
-22, -1
Suppose 0 = 613*b - 307*b - 303*b - 15. Let l(h) be the first derivative of -12/5*h**b - 15*h**3 - 39/4*h**4 - 21/2*h**2 - 3*h - 19. Factor l(q).
-3*(q + 1)**3*(4*q + 1)
Determine n so that -32/11*n**3 - 148/11*n**2 - 112/11*n + 294/11 - 2/11*n**4 = 0.
-7, -3, 1
Suppose 0 = -5*g + 3*w + 24, 4*g - g = -3*w. Suppose 6 = g*j - j. Let 6*l**3 - 10*l**j - 2*l**2 + 4*l**2 - l + 3*l**3 = 0. What is l?
0, 1
Suppose 67*q**2 - 2*q - 412*q + 600 - 3*q**3 + 95*q**2 - 198*q = 0. Calculate q.
2, 50
Let i be (-4)/20 + 245335/10425. Let -2/3*t**3 - i*t + 50/3 + 22/3*t**2 = 0. Calculate t.
1, 5
Let b(s) be the third derivative of -13*s**7/945 + 7*s**6/180 + 67*s**5/270 - 7*s**4/36 - 2*s**3 - 15*s**2 + 37. Find h such that b(h) = 0.
-18/13, -1, 1, 3
Let k(q) = -11*q - 66 + 35 + 17 - 10*q**2 - q**3. Let m be k(-9). Factor 2/13*h**5 + 0*h**2 + 2/13*h**3 + 0*h + 0 - 4/13*h**m.
2*h**3*(h - 1)**2/13
Let j(f) be the second derivative of -64 + 1/10*f**5 + 1/2*f**2 - 1/12*f**4 + 2*f - 1/3*f**3. Factor j(i).
(i - 1)*(i + 1)*(2*i - 1)
Suppose -2*b + 10 = -4*a, 4*b - 8*a + 4*a - 20 = 0. Suppose 5*m + 5*p = -15, -12*m = -17*m + b*p + 35. Factor -2/7*u**m + 2/7*u + 4/7.
-2*(u - 2)*(u + 1)/7
Let r be 4*(0 - (-2)/4). Let u = -13632 - -122713/9. Factor -u*t**r - 1/9 + 10/9*t.
-(5*t - 1)**2/9
Solve -2126*r - 523179 - 594979 - r**2 + 271141 - 282952 = 0 for r.
-1063
Suppose -7 = -3*f - 46. Let r = f + 15. Find t such that -6*t**r + 3*t - 23*t + 26*t**3 + 4*t**4 - 6 + 4*t**4 - 2*t**3 = 0.
-3, -1/2, 1
Suppose -8*i = 32 - 152. Factor -261*v**3 - 576 - 42*v**2 + 525*v**3 - 267*v**3 - 336*v - i*v**2.
-3*(v + 3)*(v + 8)**2
Let j(c) be the third derivative o