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1
Let x(r) be the first derivative of 12*r**5/35 - 213*r**4/28 + 26*r**3/7 + 1257*r**2/14 + 306*r/7 - 636. Determine h so that x(h) = 0.
-2, -1/4, 3, 17
Let p = -869357 + 115623906/133. Let f = p + 93/19. Factor 2/7*t - 2/7*t**2 + f.
-2*(t - 2)*(t + 1)/7
Suppose 0 = 2*s - 2*t, 3*t = 19*s - 15*s - 5. Factor -s - 720*w**3 + 260*w - 840*w**2 - 784*w + 399*w.
-5*(w + 1)*(12*w + 1)**2
Let d(q) be the second derivative of -q**5/50 + q**4/30 + 92*q**3/15 - 36*q**2 - 3058*q. Find c such that d(c) = 0.
-10, 2, 9
Let k(y) = y**3 + 7*y**2 + 14*y + 10. Let s be k(-4). Find w, given that -154*w**2 - 143*w**2 + 6*w + 48 + 293*w**s + 10*w = 0.
-2, 6
Let x = 163 + -162. Let f(a) = 12*a**4 + 63*a**3 + 258*a**2 + 540*a + 297. Let j(w) = -w**4 - w**3 + 2*w**2 - 2*w. Let b(v) = x*f(v) + 9*j(v). Factor b(u).
3*(u + 1)*(u + 3)**2*(u + 11)
Let v = 55 - 187. Let h be v/(-165)*5/2. Factor 1/3*l**h + l + 2/3.
(l + 1)*(l + 2)/3
Let g(s) = 3*s**2 - 9. Let y(h) = 8*h**2 - 29. Let z(t) = -13*t - 72. Let l be z(-5). Let c(v) = l*g(v) + 2*y(v). Factor c(d).
-5*(d - 1)*(d + 1)
Let w = 42859/51438 + 1/8573. Let f(g) be the first derivative of w*g**3 + 0*g - 5/16*g**4 - 5/8*g**2 + 6. Factor f(r).
-5*r*(r - 1)**2/4
Let r = 79 - 79. Suppose -u + 28 - 23 = r. Let -46*q**2 + 4 - 4 + 51*q**2 + u*q = 0. Calculate q.
-1, 0
Suppose 0 = -3*a - 14*d - 271, 39*a = 44*a + 3*d + 45. Factor 4/3*z**2 - 14/3*z**4 + 20/3*z**a + 2/3*z**5 - 22/3*z + 10/3.
2*(z - 5)*(z - 1)**3*(z + 1)/3
Let h(p) be the third derivative of -p**8/20160 + p**7/1260 + p**6/60 + 151*p**5/60 + 28*p**2 + 2. Let w(n) be the third derivative of h(n). Factor w(a).
-(a - 6)*(a + 2)
Suppose 54 = -4*u + 2*j, 9 - 48 = 3*u - j. Let d(t) = 2*t**3 + 25*t**2 + 9*t - 33. Let k be d(u). Solve 15/8*h + 0 - 9/4*h**2 + 3/8*h**k = 0.
0, 1, 5
Let m(y) be the first derivative of -32 - 125/9*y**2 + 38/45*y**5 - 65/9*y**4 - 1/27*y**6 + 700/27*y**3 - 1250/9*y. Factor m(q).
-2*(q - 5)**4*(q + 1)/9
Let k(q) be the first derivative of q**3 + 5457*q**2 + 9926283*q + 812. Solve k(r) = 0 for r.
-1819
Let x(y) be the first derivative of 1/15*y**3 + 32 - y**2 + 16/5*y. Factor x(o).
(o - 8)*(o - 2)/5
Let t = 775724 + -775722. Find k such that -75/7*k**t + 0*k + 3/7*k**4 + 72/7*k**3 + 0 = 0.
-25, 0, 1
Let m be (-2 - (-10)/6)/((-25)/(-2325)). Let z(c) = 3*c + 93. Let b be z(m). Solve -24/5*f**2 - 16/5*f + b - 1/5*f**4 - 9/5*f**3 = 0 for f.
-4, -1, 0
Let w(v) = -12*v + 501. Let y be w(40). Suppose y*n - 17 = 235. Let 144 + n*b**2 + 72*b + 2/3*b**3 = 0. What is b?
-6
Let l(m) = -2*m**3 + 0 - 12*m - 19*m**2 + 22*m**2 + 6 + 11*m. Let i(c) = -2*c**3 + 2*c**2 + 4. Let s(g) = -6*i(g) + 4*l(g). Determine z, given that s(z) = 0.
-1, 0, 1
Find n such that -2924 - 404*n**2 - 1388*n + 167*n**2 + 715*n - n**3 - 2255*n - 498*n**2 = 0.
-731, -2
Suppose 15*a**4 - 359*a**2 + 726*a - 55*a**2 - 17*a**4 + 1234*a - 244*a**2 + 68*a**3 = 0. Calculate a.
0, 7, 20
Let x be (-1)/(-4 + 30/8). Let t be -10*(3 + (-36)/10). Factor s**4 + 10*s**3 + 5*s - 16*s**2 + 3*s - t*s**x + 3*s**4.
-2*s*(s - 2)**2*(s - 1)
Factor -576/7 + 3/7*j**3 + 285/7*j**2 - 42*j.
3*(j - 2)*(j + 1)*(j + 96)/7
Let k(i) = -i**3 + 12*i**2 + 118*i - 270. Let v be k(2). Let 2/3*a**2 - v*a + 16/3 = 0. Calculate a.
1, 8
Let g(v) = -23*v**3 - 195*v**2 - 66*v + 38. Let f(l) = -93*l**3 - 779*l**2 - 263*l + 153. Suppose 41*t + 52 = -317. Let m(h) = t*g(h) + 2*f(h). Factor m(k).
(k + 9)*(3*k + 2)*(7*k - 2)
Factor 27744 + 15413*h**2 + 3*h**3 + 4140*h - 14999*h**2 + 10548*h.
3*(h + 2)*(h + 68)**2
Let k(i) = 27*i + 210. Let s be k(-7). Find a, given that 71*a - s*a**3 + 21*a**2 + 16*a**2 + 44*a**3 + 35 - 22*a**3 = 0.
-35, -1
Let z be (-5)/((-10)/12) - (0 + 3). Determine m, given that 6*m**2 - 5 + 1160*m - 2*m**z - 2*m**4 + 1 - 1158*m = 0.
-2, -1, 1
Let v be (-152)/12*8/(-160) - (-29)/(-58). Factor 16/5*u - 24/5 + v*u**3 + 22/15*u**2.
2*(u - 1)*(u + 6)**2/15
Let g(o) be the first derivative of -o**4/42 - 11*o**3/21 + 12*o**2/7 + 30*o - 37. Let x(n) be the first derivative of g(n). Factor x(y).
-2*(y - 1)*(y + 12)/7
Suppose 0 = -22*h - 80 + 168. Let k(d) be the third derivative of -1/15*d**5 - 1/60*d**6 + 0*d**3 + 0 - 1/12*d**h - 11*d**2 + 0*d. Factor k(i).
-2*i*(i + 1)**2
Suppose -2*f - 2*v + 8 = 0, 0 = -4*f + 7*f + 5*v - 16. Factor f*i**3 - 20 - 12*i**2 - 4*i**2 + 120*i - 86*i.
2*(i - 5)*(i - 2)*(i - 1)
Factor -2335*q**3 + 34*q**2 - 2301*q**3 + 4671*q**3 + q**4.
q**2*(q + 1)*(q + 34)
Let o(l) be the first derivative of -5*l**4/4 + 460*l**3/3 - 9425*l**2/2 + 55770*l - 1666. Find k, given that o(k) = 0.
13, 66
Let n = -89 + 211. Let c = n - 364/3. Solve -4*z - c - 6*z**2 - 8/3*z**3 = 0.
-1, -1/4
Let w = 141 + -139. Let f be -4 - ((-48)/24 - (-2)/(-1)). Suppose 2/5*k**4 + f*k**w + 0 + 0*k + 6/5*k**3 = 0. Calculate k.
-3, 0
Factor 767 + 77 - 23 + 55*p + p**2 - 85.
(p + 23)*(p + 32)
Let v = -2716 + 2719. Let i(a) be the first derivative of 1/12*a**4 + 0*a - 4/9*a**v + 1/2*a**2 - 5. Suppose i(t) = 0. What is t?
0, 1, 3
Let s(q) = -q**2 - 1056*q - 7341. Let z be s(-7). Factor -u - 2/3 + 1/3*u**3 + 0*u**z.
(u - 2)*(u + 1)**2/3
Suppose -1269*z = -1265*z - 5*o + 107, -2*z + 4*o = 88. Suppose -26/3 + 2/3*n**3 + 18*n - 10*n**z = 0. Calculate n.
1, 13
Let h(g) = -13*g - 11. Let x be h(-1). Factor -2*a**x - 79*a - 32 + 22*a + 37*a.
-2*(a + 2)*(a + 8)
Let o be ((-19)/(-7))/1 - (-12)/42. Suppose u**3 + 35 + 6*u**o - 47 - 8*u**3 - 10*u**2 + 23*u = 0. Calculate u.
-12, 1
Let a be 55 + 1925/(140/(-4)). Solve -7/2*w**2 + w + a + 7/2*w**4 - w**3 = 0 for w.
-1, 0, 2/7, 1
Let v be -53 + 9146/238 - -15. Factor -15/7*d**2 - v*d**3 - 3*d - 9/7.
-3*(d + 1)**2*(d + 3)/7
Suppose 0 = 3*g + 3, -10 = -3*v - 12*g + 10*g. Solve 4*u**v - 489*u**5 + 0*u**2 + 0*u**2 + 487*u**5 = 0.
0, 2
Let y(a) = -a**3 + 9*a**2 - 24*a + 18. Let s = -104 + 108. Let c be y(s). Suppose -6/5*b**c + 12/5*b - 6/5 = 0. What is b?
1
Let b(m) = m**3 - 12*m**2 + 34*m + 12. Let j be b(7). Find p such that -72*p**2 + 187*p**j - 1443*p + 74*p**3 + 55*p**5 + 396*p**4 + 1451*p = 0.
-1, 0, 2/11
Let g(r) be the second derivative of r**4/36 - 467*r**3/72 - 39*r**2/8 - 4569*r. Determine f so that g(f) = 0.
-1/4, 117
Find j such that 327*j - j - j**2 + 145 - 99*j - 83*j = 0.
-1, 145
Factor -35*w**2 - 553 - 4*w**2 + 302 - 15*w**3 + 39*w + 314.
-3*(w + 1)*(w + 3)*(5*w - 7)
Suppose -9*u + 22 = -32. Suppose 37*h**3 - u*h**4 - 69*h**3 - 3*h**5 + 29*h**3 = 0. Calculate h.
-1, 0
Let t(u) be the first derivative of 0*u**2 + 69 + 0*u - 3/25*u**5 - 1/15*u**3 - 3/20*u**4 - 1/30*u**6. Let t(k) = 0. Calculate k.
-1, 0
Let a(x) be the second derivative of -x**7/42 - 12*x**6/5 + 111*x**5/10 - 56*x**4/3 + 25*x**3/2 - 2043*x. Determine c, given that a(c) = 0.
-75, 0, 1
Let p be (2460/(-72))/(-41) - 5/(270/21). Let c(v) be the first derivative of -14/45*v**5 - 2*v**3 - p*v + 23/18*v**4 + 13/9*v**2 + 22. Factor c(n).
-2*(n - 1)**3*(7*n - 2)/9
Let h(l) be the second derivative of 0*l**2 + 2*l - 100 + 4/3*l**3 - 22/15*l**6 + 3*l**5 - 3*l**4 + 2/7*l**7. Find u, given that h(u) = 0.
0, 2/3, 1
Factor 6/5*r + 3/5*r**2 - 144/5.
3*(r - 6)*(r + 8)/5
Let k(q) be the third derivative of q**5/45 - 25*q**4/18 - 56*q**3/3 + 45*q**2 + 18*q. Find c such that k(c) = 0.
-3, 28
Let v(f) be the second derivative of 7*f**6/180 - 6*f**5/5 + 329*f**4/24 - 1127*f**3/18 + 1223*f. Factor v(m).
m*(m - 7)**2*(7*m - 46)/6
Determine u, given that 102/7*u**2 + 1048/7*u - 1152/7 + 2/7*u**3 = 0.
-36, -16, 1
Determine u so that -15/8*u**4 - 1/8*u**5 - 9*u**3 + 0 + 0*u - 27/2*u**2 = 0.
-6, -3, 0
Let b(g) be the third derivative of g**5/150 - 271*g**4/30 - 5531*g**2. Factor b(m).
2*m*(m - 542)/5
Let a(w) = w**2 + 798 + 166*w + 2*w**2 + 1721. Let p(t) = -3*t**2 - 168*t - 2520. Let m(y) = -3*a(y) - 4*p(y). Factor m(u).
3*(u + 29)**2
Let m(o) = 28*o + 19. Let p = 62 + -50. Let r be m(p). Factor -16*c**2 + 21*c**3 + r*c**4 - 359*c**4 - c**3.
-4*c**2*(c - 4)*(c - 1)
Let o(u) be the second derivative of u**9/1512 + u**8/105 - u**3/3 + 128*u. Let m(z) be the second derivative of o(z). Factor m(w).
2*w**4*(w + 8)
Let z = 347528/2606685 - -2/173779. Suppose -z*i**2 - 16/15*i - 8/5 = 0. Calculate i.
-6, -2
Suppose -4*w - 4*z = 8, -z = 7*w - 4*w. Suppose 0 = 4*k - 1 - 19. Factor -11*s + k - 3*s**2 + w + 17*s - 9*s.
-3*(s - 1)*(s + 2)
Factor -61*c - 1/5*