 Find n, given that q(n) = 0.
0, 1
Suppose 90*u - 75 = 20 + 85. Let g = -730 + 5122/7. Factor 2/7*f - g*f**u + 0.
-2*f*(6*f - 1)/7
Let o(b) be the second derivative of b**5/180 + 53*b**4/108 + 935*b**3/54 + 5491*b**2/18 - 14*b + 26. Factor o(a).
(a + 17)**2*(a + 19)/9
Let p(f) be the first derivative of -46*f**3/21 - 37*f**2 - 132*f/7 - 2049. Solve p(m) = 0 for m.
-11, -6/23
Suppose -7*z + 1609 = -981. Let i be 17/(425/z) + -4. Factor -i*x + 3/5*x**2 + 243/5.
3*(x - 9)**2/5
Let b = -159533/5 + 31784. Let h = 123 + b. Find f such that h + 2/5*f**2 + 4/5*f = 0.
-1
Suppose 105025*j - 111 - 52515*j - 52513*j + 111*j**2 + 3*j**3 = 0. Calculate j.
-37, -1, 1
Let g be ((-2)/(-7))/(28/(-343)*(-70)/15). Factor -3/8*k**3 + g*k + 0 + 3/8*k**2.
-3*k*(k - 2)*(k + 1)/8
Let q(y) = 15*y**3 + 103*y**2 - 15*y - 137. Let w(a) = 5*a**3 + 34*a**2 - 5*a - 46. Let r = 141 - 135. Let l(n) = r*q(n) - 17*w(n). Factor l(t).
5*(t - 1)*(t + 1)*(t + 8)
Let w(z) = 2406*z + 52935. Let m be w(-22). Factor 32/3*q + 4/3*q**2 - 4/9*q**m + 112/9.
-4*(q - 7)*(q + 2)**2/9
Let x(h) be the third derivative of 8 - 1/135*h**5 + h**2 + 0*h**3 - 1/270*h**6 + 0*h + 0*h**4. Find l, given that x(l) = 0.
-1, 0
Let b(n) be the second derivative of n**5/30 + 113*n**4/72 - 326*n**3/9 - 111*n**2/4 - 4*n + 44. Factor b(p).
(p - 9)*(p + 37)*(4*p + 1)/6
Let w(g) = -g**2 - 5*g + 9. Suppose -5*j - 32 + 2 = 0. Let u be w(j). Factor 4 + 0 - 3*k**u + 2*k**2 - 12*k + k**3 + 7*k**2.
-(k - 2)**2*(2*k - 1)
Suppose 0 = -6*q + 5*q + 7, -3*x - 5*q = -41. Let p(t) be the first derivative of 22 - 10*t**x - 80/3*t**3 - 25/4*t**4 + 0*t + 25*t**5. Factor p(g).
5*g*(g - 1)*(5*g + 2)**2
Suppose b + 3 + 15 = 7*u, -3*u = b - 12. Let a(j) be the first derivative of -5 + 0*j + 1/4*j**4 - 1/6*j**6 - 1/5*j**5 + 1/3*j**u + 0*j**2. Factor a(f).
-f**2*(f - 1)*(f + 1)**2
Determine d so that 3/4*d**2 - 249/2*d + 0 = 0.
0, 166
Let b(w) be the first derivative of w**5 + 5*w**4/4 - 10*w**3 - 11367. Factor b(x).
5*x**2*(x - 2)*(x + 3)
Let r(u) = -2*u**4 - 29*u**3 + 25*u**2 + 6*u + 2. Let y(h) = -113*h**4 + 1 - h + 58*h**4 + 56*h**4. Let m(t) = 5*r(t) - 10*y(t). Let m(j) = 0. What is j?
-8, -1/4, 0, 1
Suppose -648 = -177*n + 169*n. Let 48*s**2 - 6200*s**3 - 12*s**2 - n*s + 42 + 6203*s**3 = 0. Calculate s.
-14, 1
Suppose -4*t + 7*t + 8 = -2*h, 2*t + 8 = 0. Factor -3*y**2 + 9*y**2 - 8*y**h - 20 + 0 - 22*y.
-2*(y + 1)*(y + 10)
Let z(r) be the first derivative of -3*r**2 + 0*r - 3/4*r**4 + 3/2*r**6 - 21/5*r**5 + 7*r**3 + 14. Suppose z(c) = 0. Calculate c.
-1, 0, 1/3, 1, 2
Let p(l) be the second derivative of -l**4/4 + 17*l**3/2 - 105*l**2 + 1360*l - 1. Solve p(j) = 0.
7, 10
Suppose -60*i - 418*i + 1437 = i. Factor 0 - 7/2*f**2 - 1/4*f**4 + 7/4*f**i + 2*f.
-f*(f - 4)*(f - 2)*(f - 1)/4
Let t be -1 - (0/(-3) + -4). Let b be (-3017)/(-2586) - (4/(-3))/(-2). Factor 2 - 9/2*n + 3*n**2 - b*n**t.
-(n - 4)*(n - 1)**2/2
Let y(b) = 6*b**2 + 4*b - 25. Let d be y(6). What is o in 28*o**3 + 512*o + 128 - 191*o**2 - d*o**2 + 638*o**2 = 0?
-4, -2/7
Let k(i) be the second derivative of i**7/56 + 13*i**6/20 - 279*i**5/20 - 211*i**4/8 + 371*i**3/8 + 297*i**2/2 + 3005*i. Determine x so that k(x) = 0.
-36, -1, 1, 11
Let 280/3*v**2 - 19600/3*v + 0 - 1/3*v**3 = 0. Calculate v.
0, 140
Let f = -449 + 475. What is o in 13 - 2*o**2 + 16 - 53 + 0*o**2 - f*o = 0?
-12, -1
Suppose -y - 433 = -k - 421, -5*k = -70. Find q, given that 4/5*q + 2/5 + 2/5*q**y = 0.
-1
Let s(t) be the first derivative of 11*t**3 + 261*t**2/2 - 24*t - 5325. Factor s(v).
3*(v + 8)*(11*v - 1)
Let m(i) be the third derivative of -i**7/70 - 37*i**6/80 + 3*i**5/2 - i**4/16 - 5*i**3 - 11*i**2 - 6*i. Solve m(s) = 0.
-20, -1/2, 1
Let x(l) be the first derivative of l**3/12 - 1245*l**2/4 + 1550025*l/4 - 2350. Factor x(v).
(v - 1245)**2/4
Factor 86 + 26*f + f**2 - 70 + 14*f + 79 + 80.
(f + 5)*(f + 35)
Let n(i) = i**4 + 17*i**3 + 96*i**2 + 208*i + 108. Let u(w) = -w**4 - 17*w**3 - 96*w**2 - 208*w - 103. Let h(q) = 5*n(q) + 4*u(q). Let h(v) = 0. Calculate v.
-8, -4, -1
Suppose -56*c + 41*c = 17*c - 448. Let b(u) be the second derivative of 1/17*u**3 - 2/17*u**2 + c*u + 0 - 1/102*u**4. Factor b(i).
-2*(i - 2)*(i - 1)/17
Factor -1552*j - 1/8*j**5 - 12673/8*j**2 - 512 - 131/8*j**4 - 4483/8*j**3.
-(j + 1)**3*(j + 64)**2/8
Let z(b) be the first derivative of b**5/150 - 2*b**4/5 + 48*b**3/5 + 23*b**2/2 - 75. Let r(n) be the second derivative of z(n). Factor r(o).
2*(o - 12)**2/5
Let c(b) be the second derivative of -219*b + 32*b**2 + 32/3*b**3 - 16/5*b**5 - 2/21*b**7 - 14/15*b**6 + 0 - 8/3*b**4. Suppose c(a) = 0. What is a?
-2, 1
Let g(k) be the second derivative of k**5/60 + 19*k**4/36 - 7*k**3/3 + 226*k - 3. Suppose g(n) = 0. Calculate n.
-21, 0, 2
Suppose 2*y - 1162 = -6*i + 2*i, 0 = 2*i - 4*y - 596. Let o = -192 + i. Factor -177*l + 21*l + o*l**3 - 90*l**2 - 10*l**2 - 16 - 260*l**2.
4*(l - 4)*(5*l + 1)**2
Let 4*j**2 - 313 - 144479089*j - 647 + 144480045*j = 0. Calculate j.
-240, 1
Factor 2403/2*h - 603*h**2 - 600 + 3/2*h**3.
3*(h - 400)*(h - 1)**2/2
Let b(y) be the second derivative of -y**6/210 - 3*y**5/35 - y**4/28 + 50*y**3/21 + 66*y**2/7 + 3540*y. Let b(a) = 0. Calculate a.
-11, -2, 3
Let b(c) = 25*c**3 + 181*c**2 + 11*c - 169. Let f(m) = -145*m**3 - 1085*m**2 - 65*m + 1015. Let v(q) = 35*b(q) + 6*f(q). Factor v(x).
5*(x - 35)*(x - 1)*(x + 1)
Let n be 228 - (8 + 5 + -16). Let o be 22/n - (-492)/126. Suppose 0 + 15*y**5 + 0*y + 40/3*y**2 + 10*y**o - 100/3*y**3 = 0. Calculate y.
-2, 0, 2/3
Suppose -5*a + 15 = 5*t, 0 = -22*t + 25*t + 2*a - 9. Suppose 160*w + t*w**2 + 2*w**2 - 923 - 7*w**2 - 386 - 1891 = 0. Calculate w.
40
Factor -51/2*i**3 + 0 - 165/2*i + 1/2*i**4 - 217/2*i**2.
i*(i - 55)*(i + 1)*(i + 3)/2
Let a(i) be the second derivative of i**6/45 - 23*i**5/18 + 361*i**4/54 - 389*i**3/27 + 140*i**2/9 + 3*i + 918. Solve a(n) = 0.
1, 4/3, 35
Let d = 3865 - 5442. Let t = d + 11047/7. Suppose t*s + 0 - 1/7*s**2 = 0. What is s?
0, 8
Let h be 1771/(-1210) - 3/((-45)/24). Let a(v) be the first derivative of 20/33*v**3 + 4/11*v - 9/11*v**2 - h*v**4 - 14. Find z, given that a(z) = 0.
1/3, 1, 2
Let t(k) be the first derivative of -k**3/5 - 177*k**2/10 + 36*k - 431. Factor t(u).
-3*(u - 1)*(u + 60)/5
Let 183/4*z**2 - 44*z - 77/4*z**3 + 1/4*z**5 + 15 + 9/4*z**4 = 0. Calculate z.
-15, 1, 2
Let q(u) be the third derivative of -u**6/840 - 23*u**5/210 - 15*u**4/56 + 158*u**2 + 4. Suppose q(o) = 0. What is o?
-45, -1, 0
Determine a so that 6456*a - 7814988 - 4/3*a**2 = 0.
2421
Factor -13*x + 6*x + 35*x**2 - 14*x + 54 - 38*x**2.
-3*(x - 2)*(x + 9)
Let z(h) be the second derivative of -2/105*h**7 - 32/25*h**5 - 2/15*h**4 + 22/5*h**3 - 64*h - 32/5*h**2 + 0 + 12/25*h**6. Suppose z(s) = 0. Calculate s.
-1, 1, 16
Let 39*z + 507/2 + 3/2*z**2 = 0. What is z?
-13
Let s(x) = -65*x + 13392. Let h be s(206). Factor -3/4*p**h + 0 + 12*p.
-3*p*(p - 16)/4
Let z(m) = 7*m**2 - 3*m - 72. Let b(a) = 111*a**2 - 48*a - 1149. Let v(r) = -4*b(r) + 63*z(r). Solve v(c) = 0.
-4, 5
Let u(j) be the second derivative of -43/18*j**2 - 1/36*j**4 + 148*j + 0 - 65/27*j**3. Factor u(c).
-(c + 43)*(3*c + 1)/9
Determine s so that -5/2*s**4 + 1007/2*s + 361 + 193/2*s**3 - 1917/2*s**2 = 0.
-2/5, 1, 19
Let i(o) be the third derivative of -o**5/40 + 5*o**4/16 + 1254*o**2. Solve i(k) = 0 for k.
0, 5
Factor -67/5*o - 1/5*o**2 + 0.
-o*(o + 67)/5
Let t(f) be the first derivative of 166 + 1/15*f**3 + 1/5*f - 1/5*f**2. Factor t(w).
(w - 1)**2/5
Suppose 27*y - 2504 = -6959. Let g be (-6)/(-11)*y/(-20). Find c, given that -3/2*c**2 - g*c - 3 = 0.
-2, -1
Let r(i) = 84*i + 1011. Let k be r(-12). Let g(z) be the second derivative of 1/40*z**5 + 1/6*z**k + 0*z**2 + 1/8*z**4 + 18*z + 0. Find n such that g(n) = 0.
-2, -1, 0
Suppose 0 = -4*t - 2*k + 66, k = -3*k - 4. Factor -t*h**2 + 5*h**4 + h**5 + 15*h**3 + 5 + 7*h**2 + 0*h - 17*h**3 + h.
(h - 1)**2*(h + 1)**2*(h + 5)
Let v be 8/24 + (-1496)/(-1632). Determine m, given that -25/4*m**3 + 45/4*m**2 - 15/4*m - v = 0.
-1/5, 1
Let a(m) be the third derivative of -m**6/80 + 465*m**5/8 - 1801875*m**4/16 + 465484375*m**3/4 + 59*m**2. Find b such that a(b) = 0.
775
Let i = -139484/11 + 1042234/77. Let l = -852 + i. Determine b, given that 0*b + 32/7*b**4 + 2*b**5 + 4/7*b**2 + l*b**3 + 0 = 0.
-1, -2/7, 0
What is z in 67/3*z 