/10
Let b(m) be the first derivative of -3*m**5/5 - 93*m**4/4 - 168*m**3 - 590. Factor b(f).
-3*f**2*(f + 7)*(f + 24)
Suppose 7*c - 49*c + 1806 = 0. Let t be (-1 + c/49)/(300/(-700)). Factor -8/7 + 6/7*q**2 + t*q**4 + 8/7*q**3 - 8/7*q.
2*(q - 1)*(q + 1)*(q + 2)**2/7
Let b(s) be the first derivative of -1/396*s**6 + 15 - 1/660*s**5 + 0*s + 0*s**4 + 0*s**2 - 13/3*s**3. Let o(h) be the third derivative of b(h). Factor o(y).
-2*y*(5*y + 1)/11
Let x(h) = -3995*h + 583272. Let c be x(146). Determine q so that 9/5*q**c + 288/5 + 438/5*q = 0.
-48, -2/3
Let k(d) be the first derivative of -2*d**3/9 + 188*d**2/3 + 126*d + 1195. Let k(b) = 0. Calculate b.
-1, 189
Factor 14611 + 172*d + 17*d**2 - 3*d**2 - 14323.
2*(d + 2)*(7*d + 72)
Factor 0*l**3 + 22201*l**2 + 409600 - 3*l**4 + 7*l**4 + 1565*l**2 - 3222*l**2 + 608*l**3 - 194560*l.
4*(l - 4)**2*(l + 80)**2
Let r be (2 - (-988)/126) + 1190/(-765). Let 60/7 - 2/7*z**2 - r*z = 0. What is z?
-30, 1
Let k(t) = -t**2 - t - 2. Let x(r) = 2*r**2 + 88*r - 240. Let g(o) = -12*k(o) - 4*x(o). Factor g(p).
4*(p - 82)*(p - 3)
Suppose -31*b + 2 = -42*b + 35. Let d(c) be the second derivative of -13*c + 1/9*c**b + 0 + 5/54*c**4 - 2/9*c**2. Factor d(m).
2*(m + 1)*(5*m - 2)/9
Let y(m) = 8*m**3 + 596*m**2 - 1224*m + 612. Let t(b) = 9*b**3 + 594*b**2 - 1225*b + 612. Let k(g) = -4*t(g) + 5*y(g). Solve k(h) = 0.
-153, 1
Let g be (7644/245 - 32)/(1152/615 + -2) - 6. Let -2/13*a**3 - 4/13*a**2 + 2/13*a + g = 0. What is a?
-2, -1, 1
Let h be (252/819)/(70/35). Factor -36/13*g - 80/13 + h*g**2.
2*(g - 20)*(g + 2)/13
Let t(o) = -3*o + 13. Let m be t(10). Let s = m - -21. Factor 95*h**2 + 114*h**2 + 36*h**s - 240*h**3 - h**2 + 213 + 43 + 640*h.
4*(h - 4)**2*(3*h + 2)**2
Let b(d) = -5*d**4 - 65*d**3 + 10*d**2 + 55*d + 5. Let y = -34 - -32. Let m(k) = 3*k**4 + 32*k**3 - 5*k**2 - 28*k - 2. Let a(n) = y*b(n) - 5*m(n). Factor a(h).
-5*h*(h - 1)*(h + 1)*(h + 6)
Let p(x) be the first derivative of -x**4/32 + 5*x**3/12 + 487*x**2/16 + 119*x/2 - 251. Factor p(u).
-(u - 28)*(u + 1)*(u + 17)/8
Let y(d) = d**3 - 11*d**2 + 10*d + 2. Let l be y(10). Let u be 2/(-4) + 34/4. Solve 3*a**2 + a**l + u*a**4 + a**2 + 10*a**3 - a**2 + 2*a**5 = 0 for a.
-2, -1, 0
Let q be 2354/(-308) - (-3)/21 - -8. Factor 6*s**2 + q*s**4 + 3/2 - 5*s - 3*s**3.
(s - 3)*(s - 1)**3/2
Suppose 2*h**2 + 4528*h + 1161271 + 1400124 + 952942 - 453829 - 497660 = 0. Calculate h.
-1132
Let c(f) be the first derivative of 2*f**5/85 + 15*f**4/17 + 506*f**3/51 + 420*f**2/17 + 392*f/17 + 2412. Factor c(r).
2*(r + 1)**2*(r + 14)**2/17
Suppose 0*q + j - 5 = -2*q, -11 = -5*q - 4*j. Determine n, given that -152*n**2 - 148*n - 52*n**3 + 8*n**4 + 23*n**3 - 19*n**q + 4*n**5 - 48 = 0.
-3, -1, 4
Let i be (-1)/(-3) - (-77)/66 - (-38)/(-36). Let k(n) be the first derivative of 8/3*n**2 - 8 + 0*n - i*n**3. Factor k(g).
-4*g*(g - 4)/3
Let y(p) be the second derivative of -27*p**7/14 + 48*p**6/5 + 59*p**5/20 - 253*p**4/6 - 110*p**3/3 - 12*p**2 - 1278*p + 1. Find s such that y(s) = 0.
-1, -2/9, 2, 3
Suppose -116 = 5*i - 18*m + 27*m, 4*m = 2*i - 60. Find j, given that 5*j + 7/8*j**i - 1/8*j**3 + 11/2 = 0.
-2, 11
Let a = 2401 + -21607/9. Let h(s) be the first derivative of 8/3*s - 5/3*s**2 + 14 + a*s**3. What is b in h(b) = 0?
1, 4
Suppose 90*m**2 + 441*m**4 + 36*m - 97*m**2 - 219*m**4 - 221*m**4 - 6*m**3 + 36 = 0. What is m?
-2, -1, 3, 6
Let a be (4 + -1 - -6) + 6. Factor -63*y**3 + 10*y**2 - 19 - 156*y - 20 + 420*y - 141 - 15*y**2 - y**5 - a*y**4.
-(y - 1)**2*(y + 5)*(y + 6)**2
Let b(r) be the first derivative of -1/30*r**4 + 66 + 8/15*r - 2/75*r**5 + 2/5*r**3 - 11/15*r**2. Solve b(l) = 0 for l.
-4, 1
Let j(x) be the first derivative of x**7/1260 + x**6/270 - x**5/180 - x**4/18 - x**3 - x - 191. Let r(i) be the third derivative of j(i). Factor r(g).
2*(g - 1)*(g + 1)*(g + 2)/3
Suppose -30*m = 5 - 65. Factor -3*c**m + 809*c - 59 - 1013*c - 142.
-3*(c + 1)*(c + 67)
Let a be (-10 - -2) + -2 + 5. Let g be 6/((-120)/(-26)) + (-1)/a. Suppose h**2 + 5/2*h - g = 0. What is h?
-3, 1/2
Factor -108*j + 123*j**2 - 136/3*j**3 + 16/3*j**4 + 0.
j*(j - 4)*(4*j - 9)**2/3
Let k(v) be the second derivative of 4/9*v**3 + 2/3*v**2 + 10*v + 0 - 5/36*v**4. Suppose k(x) = 0. Calculate x.
-2/5, 2
Solve 23*t**3 + 100*t**2 + 41*t - 78*t + 17*t**3 - 5*t**4 + 37*t = 0 for t.
-2, 0, 10
Suppose -81/4*b**2 + 5*b**4 + 1 - 1/4*b**3 + b = 0. Calculate b.
-2, -1/5, 1/4, 2
Let s(f) be the second derivative of -f**4/12 - 7*f**3/6 + 99*f**2 + 152*f - 15. Suppose s(p) = 0. Calculate p.
-18, 11
What is u in -34/5*u**3 - 8/5*u + 32 + 2/5*u**4 - 24*u**2 = 0?
-2, 1, 20
Let j(s) be the second derivative of s**5/60 + 11*s**4/24 + 5*s**3/3 - 45*s**2/2 - 72*s. Let h(q) be the first derivative of j(q). Factor h(t).
(t + 1)*(t + 10)
Let x = -25 - 20. Let g = x - -46. What is f in 7 - 12 + f**2 + g = 0?
-2, 2
Let g(d) be the second derivative of -d**7/3150 + 31*d**6/450 - 961*d**5/150 - 9*d**4/2 + d + 63. Let p(v) be the third derivative of g(v). Factor p(w).
-4*(w - 31)**2/5
Suppose -5*p + 101 = -234. Let m = p + -64. Factor 62 - 5*f**4 - 15*f**2 + 15*f**m - 62 + 5*f.
-5*f*(f - 1)**3
Let h(f) = -f**4 + 12*f**3 - 7*f**2. Let c(n) be the third derivative of -n**6/24 + n**5/20 + 2*n**2 + 63*n. Let w(r) = -5*c(r) - 3*h(r). Factor w(b).
b**2*(b - 3)*(3*b - 2)
Let -5*y**3 - 113673*y - 630 + 162*y**2 + 113368*y + 158*y**2 = 0. What is y?
-1, 2, 63
Let x(v) = 179592*v**2 - 2031*v + 15. Let a(y) = 89797*y**2 - 1013*y + 8. Let q(h) = 9*a(h) - 5*x(h). Let q(o) = 0. What is o?
1/173
Suppose 500*c - 1642 = -321*c. Factor -35/2 + 35/2*n**c + 1/2*n - 1/2*n**3.
-(n - 35)*(n - 1)*(n + 1)/2
Factor 10 + 31*p**2 + 50 - 63*p**2 - 100*p - 33*p**2.
-5*(p + 2)*(13*p - 6)
Let k be -4 - (-26 - 8*(-2)/(-4)). Suppose 0 = -d + 33 - k. Solve -9 + 11 + 2*s**4 - 2*s**4 - d*s**2 + 5*s**4 - 3*s + 3*s**3 = 0 for s.
-1, 2/5, 1
Let m(h) = 48*h**3 + 4127*h**2 - 8949*h + 1066. Let c(o) = 72*o**3 + 6190*o**2 - 13425*o + 1598. Let t(k) = -5*c(k) + 7*m(k). Let t(q) = 0. What is q?
-88, 1/8, 2
Let x(t) be the first derivative of t**5/40 - 5*t**4/8 + 20*t**2 - 1. Let l(n) be the second derivative of x(n). Factor l(w).
3*w*(w - 10)/2
Suppose -4*y + 320 = 5*z, 3*y - 310 = -5*z + y. Find p, given that z*p**4 + 12*p - 89*p**3 - 28*p - 16*p**5 + 121*p**3 - 60*p**2 = 0.
-1, -1/4, 0, 1, 4
Let t(u) be the second derivative of u**5/20 + 5*u**4/4 + 5*u**3/3 - 53*u**2/2 + 29*u + 8. Let r be t(-14). Factor -1/2*z**4 + 1/2*z**2 + 0 + 1/2*z**r - 1/2*z.
-z*(z - 1)**2*(z + 1)/2
Let m(f) be the first derivative of -18*f**5/35 + 879*f**4/28 - 528*f**3 + 4320*f**2/7 - 3574. Factor m(i).
-3*i*(i - 24)**2*(6*i - 5)/7
Let m(r) be the third derivative of 2*r**7/315 - 13*r**6/45 - 316*r**5/45 + 13*r**4/9 + 70*r**3 + 2818*r**2. Suppose m(n) = 0. Calculate n.
-9, -1, 1, 35
Let c = -6/6289 + 6307/18867. Factor -1/3*p**4 + 0 + 1/3*p + c*p**2 - 1/3*p**3.
-p*(p - 1)*(p + 1)**2/3
Let t(u) be the second derivative of 0*u**3 + 0*u**2 + 5*u + 0*u**4 + 0 - 1/60*u**5. Let t(x) = 0. What is x?
0
Let v(f) be the second derivative of f**5/4 - 5*f**4/12 - f**3/2 + f - 2. Let c(h) = -12*h**3 + 11*h**2 + 7*h. Let w(p) = 3*c(p) + 7*v(p). Factor w(l).
-l**2*(l + 2)
Let k(r) be the first derivative of -145 + 625/2*r**2 - r**5 - 125*r**3 + 0*r + 75/4*r**4. Solve k(t) = 0.
0, 5
Let f(g) = -14*g + 151. Let t be f(9). Suppose 2632 + t*h - 1308 + 5*h**2 - 1309 - 5*h**3 = 0. What is h?
-1, 3
Let a be (-16)/48 - (-115)/(-15). Let x be (6 - a) + -10 + -1. Factor -4/9*f**x + 8/9*f**2 + 0 + 4/3*f.
-4*f*(f - 3)*(f + 1)/9
Let n(m) be the first derivative of -m**3/12 + 57*m**2/4 - 3249*m/4 + 1092. Factor n(k).
-(k - 57)**2/4
Let v be -2 + ((-130)/(-5))/1. Let l be (v/100)/(27/15). Determine d so that 0 + 2/3*d**4 - 16/15*d**3 + 8/15*d**2 + 0*d - l*d**5 = 0.
0, 1, 2
Let b = 1910738 + -5732209/3. Factor -b*h + 35/6*h**2 + 0.
5*h*(7*h - 2)/6
Let i(q) be the first derivative of -17 + 5/7*q**2 + 0*q + 2/21*q**3. Factor i(h).
2*h*(h + 5)/7
Suppose 92*v + 6314 - 6774 = 0. Let -12150/11*n + 86/11*n**4 + 2/11*n**v + 4140/11*n**2 + 1172/11*n**3 + 6750/11 = 0. What is n?
-15, 1
Let a(m) be the first derivative of m**5 + 41*m**4/2 + 132*m**3 + 108*m**2 + 309*m - 113. Let b(p) be the first derivative of a(p). Suppose b(r) = 0. What is r?
-6, -3/10
Factor 0 + 