*h**2/4
Suppose 0 = -c + 3*b + 20, 207*b + 22 = -c + 203*b. Find s such that -2/15*s**c + 0*s + 2/15 = 0.
-1, 1
Let t(m) be the third derivative of 0 + 0*m**3 - 1/70*m**7 + 0*m**4 + 1/5*m**6 + 185*m**2 + 0*m - 3/4*m**5. Find z such that t(z) = 0.
0, 3, 5
Let n(d) be the third derivative of d**7/105 - d**6/20 - 2*d**5/15 - 1711*d**2. Suppose n(r) = 0. Calculate r.
-1, 0, 4
Let s(i) be the second derivative of i**6/15 + 7*i**5/5 - i**4/2 - 44*i**3/3 - 28*i**2 - 281*i. Factor s(p).
2*(p - 2)*(p + 1)**2*(p + 14)
Let u(j) = 43*j + 10. Let l be u(0). Suppose -l*c - 2140 + 2170 = 0. Find o, given that -2/3*o**c + 0*o + 2/3*o**2 + 0 = 0.
0, 1
Factor -312*g - 2322*g**2 - 5207*g**2 - 3853*g**2 + 219*g**3.
3*g*(g - 52)*(73*g + 2)
Let i be (-51)/(-34)*(-2)/(-3). Suppose 0*c + 4 = 4*r - 4*c, 0 = c - i. Solve 3*x**2 - 7*x + 10 - 2*x**r + 4*x**2 - 8*x = 0 for x.
1, 2
Suppose r + s - 120 = 0, 0 = -7*r + 8*r + 4*s - 129. Suppose 0 = i + 11 - r. Solve -62*l**2 - 147*l**3 - i*l**2 - 19*l + 6 + 4*l = 0 for l.
-1, -2/7, 1/7
Let p(r) be the second derivative of -135*r**4/14 - 289*r**3/3 + 10*r**2/7 - 4*r + 256. Let p(w) = 0. What is w?
-5, 2/405
Let i(a) be the first derivative of 34/27*a**3 - 2/9*a**4 - 4/9*a**2 - 52 + 0*a. Factor i(c).
-2*c*(c - 4)*(4*c - 1)/9
Let 13124*x**4 - 2128*x**2 + x**5 - 2688 + 3*x**5 + 120*x**3 - 4768*x - 12952*x**4 = 0. What is x?
-42, -2, -1, 4
Factor -72980 - 93327 + 9*z**3 - 490*z**2 - 15980*z - 16*z**3 - 7093 + 2*z**3.
-5*(z + 30)*(z + 34)**2
Let t = -98 - -57. Let m = 54 + t. Suppose -16*k**4 - m*k**3 - 4*k**2 - 3*k**5 - k**5 + 4*k**4 + k**3 = 0. Calculate k.
-1, 0
Let p(m) be the first derivative of m**6/1620 + m**5/90 - 7*m**4/108 - 9*m**3 - 233. Let q(r) be the third derivative of p(r). Determine b, given that q(b) = 0.
-7, 1
Let y be (-16)/(-20)*(-430)/(-602). Let a(r) be the third derivative of 2/35*r**5 + 26*r**2 + 64/21*r**3 + 0 + y*r**4 + 1/420*r**6 + 0*r. Factor a(w).
2*(w + 4)**3/7
Suppose 30 = 5*n, -2*v - 475*n + 477*n = 6. Let c(q) be the second derivative of 0 + 1/2*q**2 - 1/48*q**4 + 7*q + 1/8*q**v. Factor c(m).
-(m - 4)*(m + 1)/4
Suppose 4*a = -5*p - 14, -5*p - 6 = 2*a + 6. Let g = 287 + a. Factor -g*z - 2 + 2*z**2 + 286*z.
2*(z - 1)*(z + 1)
Suppose 0 = -4*k + 5*k + 6. Let y be ((-252)/(-30))/(k/(-15)). Factor -y*x + 12 - 3*x**3 + 7*x**2 + 11*x**2 + 6 - 12*x.
-3*(x - 3)*(x - 2)*(x - 1)
Let h(t) = -3*t**3 - 189*t**2 - 4890*t + 48372. Let p(g) = 3*g**3 + 202*g**2 + 4891*g - 48374. Let v(c) = 5*h(c) + 6*p(c). Factor v(y).
3*(y - 7)*(y + 48)**2
Let l(f) be the first derivative of -f**6/6 + 2*f**5 - 33*f**4/4 + 40*f**3/3 - 8*f**2 - 1620. Find a, given that l(a) = 0.
0, 1, 4
Let z = 50 + -60. Let g be z/15*3/(-2)*3. Solve 3 - 2 - 4*j**3 + 2*j**g + 1 + 2*j - 2*j**2 = 0.
-1, 1
Suppose -1/4*y**2 + 202*y - 40804 = 0. What is y?
404
Let h(o) be the third derivative of -o**8/16800 + o**7/2100 - 167*o**3/6 + 12*o**2 - 4. Let n(f) be the first derivative of h(f). Factor n(c).
-c**3*(c - 4)/10
Let t(i) = 7*i**2 - 27*i - 25. Let h(n) be the second derivative of -5*n**4/4 + 55*n**3/6 + 49*n**2/2 - 36*n. Let g(y) = -3*h(y) - 7*t(y). Factor g(x).
-4*(x - 7)*(x + 1)
Let v(w) be the third derivative of -w**5/60 + 49*w**4/24 - 209*w**3/3 + 7452*w**2. Determine x, given that v(x) = 0.
11, 38
Let b(s) be the second derivative of s**6/720 + s**5/180 - s**4/144 - s**3/18 + 29*s**2/2 - 39*s. Let c(p) be the first derivative of b(p). Factor c(r).
(r - 1)*(r + 1)*(r + 2)/6
Suppose -3*a = 2*y - 1 - 11, 2*a - 8 = 5*y. Factor 2*o**a - 5*o - 16*o**2 + 34 - 7 + 18*o**3 - 21 - 5*o**5.
-(o - 1)**3*(o + 2)*(5*o + 3)
Let a(g) = 14*g**3 - 504*g**2 - 570*g - 70. Let y(m) = -8*m**3 + 505*m**2 + 571*m + 73. Let z(u) = 5*a(u) + 6*y(u). Factor z(l).
2*(l + 1)*(l + 22)*(11*l + 2)
Let r be ((1/1)/10)/(((-1575)/(-1400))/9). Solve -8/5*n**2 + 0*n**3 + 8/5*n**4 + 4/5*n**5 + 0 - r*n = 0.
-1, 0, 1
Determine h, given that -32*h**4 + 8*h**4 - 202*h**2 - 276*h**3 + 22*h**4 + 300 - 38*h + 218*h**3 = 0.
-25, -3, -2, 1
Let p(c) be the third derivative of c**7/105 + 23*c**6/180 + 59*c**5/90 + 19*c**4/12 + 2*c**3 - 3151*c**2. What is y in p(y) = 0?
-3, -1, -2/3
Let c(p) be the first derivative of p**8/84 - 4*p**7/105 - p**6/10 + 11*p**2 - 67. Let u(z) be the second derivative of c(z). Determine b so that u(b) = 0.
-1, 0, 3
Let d(r) be the second derivative of -2*r**6/135 + 2*r**5/15 + 47*r**4/27 + 56*r**3/9 + 88*r**2/9 + 912*r. Solve d(h) = 0 for h.
-2, -1, 11
Solve -33*g**3 + 3/2*g**4 + 972*g + 243/2*g**2 - 3240 = 0 for g.
-5, 3, 12
Suppose 3*u = a + 10, 3*u + 4*a + 10 = -0*a. Suppose -u*d - g = 0, 2*d + g + 8 = -2*g. Find j such that -6*j - j - 1 + 4*j**d - j + 5 = 0.
1
Suppose c = 4*c - 9, -2*c = -2*d + 78. Let i = -35 + d. Factor i*g**3 - 2*g**3 - 4*g**5 - 4*g**5 + 3*g**5.
-5*g**3*(g - 1)*(g + 1)
Suppose 2711*o - 2709*o - 26 = 2*q, 5*q + 53 = o. Factor -5/3 - 1/3*x + 5/3*x**2 + 1/3*x**o.
(x - 1)*(x + 1)*(x + 5)/3
Factor 4*z**4 - 13*z**2 - 261*z**3 - 241*z**3 + 518*z**3 - 6*z - z**4.
z*(z - 1)*(z + 6)*(3*z + 1)
Factor -3/8*k**2 + 39/8*k + 0.
-3*k*(k - 13)/8
Suppose 4*s + 25 - 50 = -5*f, 3*s + 42 = 3*f. Let r(l) be the first derivative of 8*l + 17*l**4 - 8*l**3 + 56/5*l**5 - 14*l**2 - f. Find u such that r(u) = 0.
-1, 2/7, 1/2
Let d(r) = 4*r**5 - r**4 + r**2 + r + 1. Let x(v) = 35*v**5 - 7*v**4 + 12*v**3 + 23*v**2 + 14*v + 9. Let g(p) = 36*d(p) - 4*x(p). Factor g(f).
4*f*(f - 5)*(f + 1)**3
Let s be 324/1215 - 2/12. Let i(t) be the first derivative of 12/5*t + 20 - 6/25*t**5 - s*t**4 + 34/15*t**3 - 19/5*t**2. Determine z so that i(z) = 0.
-3, 2/3, 1
Let t(n) = 25*n**2 + 56*n + 784. Let p(a) = 54*a**2 + 112*a + 1568. Suppose -5*q = -2*q - 3*u + 3, -q + 4*u = -14. Let l(b) = q*p(b) + 13*t(b). Factor l(f).
(f + 28)**2
Let p(w) be the third derivative of w**7/1050 + 19*w**6/600 + 3*w**5/10 + 41*w**4/30 + 52*w**3/15 - 6*w**2 - 147. Find g such that p(g) = 0.
-13, -2
Let q(z) be the third derivative of 12 - 2*z**2 - 1/15*z**4 + 0*z + 7/300*z**5 + 0*z**3 + 1/600*z**6. Factor q(n).
n*(n - 1)*(n + 8)/5
Suppose 5*j - 310*h + 287*h + 312 = 0, -3*j - 5*h + 76 = 0. Solve 0*o - 3/7*o**3 + 0 - 3/7*o**j = 0.
-1, 0
Determine l, given that 45*l**2 - 3*l**4 - 24*l**3 + 122155720 + 162*l - 122155720 = 0.
-9, -2, 0, 3
Let j(r) be the third derivative of -r**5/20 - r**4/2 + 5*r**3/2 + 11*r**2 - 26*r. Factor j(d).
-3*(d - 1)*(d + 5)
Let m(v) be the third derivative of -v**5/20 + 153*v**4/4 + 307*v**3/2 + 2*v**2 + 58. Determine t, given that m(t) = 0.
-1, 307
Suppose 2*c - 33 = -27. Suppose 70 + 14 = c*u. Let 49*x**3 - 24*x**3 - 19*x**2 - 33*x - u*x**3 - 9 = 0. Calculate x.
-3, -1/3
Let t be ((-52)/6)/((-42)/(-63)). Let f(r) = -7*r**2 + 21*r - 14. Let p(a) = 16*a**2 - 43*a + 27. Let b(s) = t*f(s) - 6*p(s). Factor b(y).
-5*(y - 1)*(y + 4)
Let t(k) be the third derivative of -47*k**6/60 + k**5/20 + 47*k**4/12 - k**3/2 - 689*k**2 + 2. What is x in t(x) = 0?
-1, 3/94, 1
Let o(k) be the second derivative of 87*k + 0*k**3 + 0 + 0*k**2 + 1/2*k**4 - 33/20*k**5. Solve o(c) = 0.
0, 2/11
Let s = 24 + -21. Let t(k) = k**2 - 4*k + 5. Let u be t(s). Factor -2*v**u - 18 - 4*v - v + 17*v.
-2*(v - 3)**2
Let k(d) be the first derivative of d**4/16 - 275*d**3/12 - 553*d**2/8 - 277*d/4 + 1942. Factor k(x).
(x - 277)*(x + 1)**2/4
Suppose -132 = -67*p + 64*p. Factor -3 + 15 + 51*j - p*j + j**2.
(j + 3)*(j + 4)
Let d be (-8)/6*(6/8)/((-2544)/3180). Let a(k) be the first derivative of 10*k**3 - 45/2*k**2 + 20*k - d*k**4 - 32. Find g, given that a(g) = 0.
1, 4
Let d(l) be the second derivative of -100000/7*l**2 + 0 + 21*l - 5000/21*l**4 - 50000/21*l**3 - 1/147*l**7 - 10/21*l**6 - 100/7*l**5. Let d(i) = 0. Calculate i.
-10
Let i(x) be the third derivative of x**5/15 + 91*x**4/6 - 78*x**2 + 11. Find w, given that i(w) = 0.
-91, 0
Let m(u) = u**3 - 26*u**2 - 46*u + 65. Let a be m(28). Let o = -343 + a. Suppose 1/3*t**o + 0*t - 1/3 = 0. Calculate t.
-1, 1
Let u(q) = q**2 - 2*q - 4. Let i(b) = -b**2 + 10*b - 2. Let g be i(10). Let d be u(g). Factor -6*h**2 + 165*h**5 + 4*h**d - 2*h**3 + 2*h**2 - 163*h**5.
2*h**2*(h - 1)*(h + 1)*(h + 2)
Determine p, given that -4/3*p**2 - 1/3*p**3 + 10/3 + 7/3*p = 0.
-5, -1, 2
Let l(b) be the third derivative of -b**5/12 - 65*b**4/8 - 90*b**3 + 5*b**2 + 6*b. Solve l(m) = 0.
-36, -3
Suppose