)/13
Find k such that -981*k + 997*k + 206 - 158 - 4*k**2 = 0.
-2, 6
Let s(j) be the third derivative of 1/18*j**4 - 1/30*j**5 + 1/180*j**6 + 0*j**3 + 127*j**2 + 0 + 0*j. Factor s(h).
2*h*(h - 2)*(h - 1)/3
Let n(d) be the third derivative of -11/96*d**4 + 1/12*d**3 + 1/48*d**5 - 9*d + d**2 + 0. Factor n(v).
(v - 2)*(5*v - 1)/4
Let q(i) = -i**4 + i**3 + i. Suppose -4*d = 3*l + 2*l - 1, -d - 3*l = -2. Let k(s) = -16*s**4 - 4*s**2 + 24*s + 8. Let r(j) = d*k(j) + 12*q(j). Factor r(g).
4*(g - 1)*(g + 1)**2*(g + 2)
Suppose 264 = -12*u - 2220. Let b = u + 210. Determine g, given that 108/7*g + 10/7*g**5 - 54*g**2 + 0 - 94/7*g**4 + 306/7*g**b = 0.
0, 2/5, 3
Let q(u) be the second derivative of -u**7/504 - 7*u**6/48 - 5*u**5/6 + 75*u**4/4 + 192*u. Let t(l) be the third derivative of q(l). Factor t(g).
-5*(g + 1)*(g + 20)
Let i(n) be the first derivative of -4*n**6/3 - 44*n**5/5 + 106*n**4 - 220*n**3 - 4489. Determine r so that i(r) = 0.
-11, 0, 5/2, 3
Let z(t) be the third derivative of -t**5/20 - 65*t**4/4 - 4225*t**3/2 - 1476*t**2 - 1. Find h such that z(h) = 0.
-65
Let b(q) be the second derivative of 490*q**2 - 6*q + 70/3*q**3 + 5/12*q**4 - 14. Factor b(i).
5*(i + 14)**2
Let w be 2*10/4 + ((-27)/78 - 66/429). Determine a, given that -21/4*a + 0*a**2 + w + 3/4*a**3 = 0.
-3, 1, 2
Let s(r) = 3*r**2 - 3*r + 4. Let n be 2/(-6)*((0 - 0) + -18). Let t(k) = -8*k**2 + 7*k - 9. Let w(f) = n*t(f) + 15*s(f). Factor w(g).
-3*(g - 1)*(g + 2)
Let p(j) = 34*j - 129. Let y be p(16). Let o = -413 + y. Determine k so that 4*k**3 + 0*k - 2/3*k**4 + 0 + 14/3*k**o = 0.
-1, 0, 7
Let f(o) be the first derivative of o**7/140 - 3*o**6/40 + 11*o**5/40 - 3*o**4/8 + o**2/2 - 233*o - 26. Let g(h) be the second derivative of f(h). Factor g(a).
3*a*(a - 3)*(a - 2)*(a - 1)/2
Let z(p) be the second derivative of -128/3*p**2 + 5/3*p**4 + 6*p - 32/3*p**3 + 1 - 1/15*p**5. Let z(d) = 0. What is d?
-1, 8
Suppose -17*d + 227 = -18*d + 2*f, -3*d = -f + 691. Let u be 45186/330 - 63/d. Factor 16/5 + 588/5*s**2 + u*s**3 + 168/5*s.
2*(7*s + 2)**3/5
Determine v so that 67*v**2 - 1021*v**3 - 1024*v**3 + 3069*v**3 + 53*v + 13*v - 1023*v**3 = 0.
-66, -1, 0
Let j(i) be the third derivative of -i**6/660 - 184*i**5/55 - 101199*i**4/44 + 611618*i**3/33 + 20*i**2 + 99*i. Determine h, given that j(h) = 0.
-553, 2
Factor -2766/7*m**3 - 2/7*m**4 - 136818*m**2 - 954962/7*m + 0.
-2*m*(m + 1)*(m + 691)**2/7
Let k(o) = 150*o - 312. Let n(t) = -t**2 - t. Let w(z) = -2*k(z) + 4*n(z). Find b such that w(b) = 0.
-78, 2
Let m(l) be the third derivative of l**8/108 - l**7/35 - 11*l**6/108 + l**5/18 + 41*l**4/108 + 4*l**3/9 + 169*l**2. Find d such that m(d) = 0.
-1, -4/7, -1/2, 1, 3
Suppose 692*o = 189*o - 685*o + 3564. Suppose 9/2*h**2 - 4 - 1/2*h**4 - h + h**o = 0. Calculate h.
-2, -1, 1, 4
Let n(u) be the second derivative of 93*u - 9/8*u**4 + 0 - 405/8*u**3 - 1/56*u**7 - 1/40*u**6 + 2025/8*u**2 + 57/40*u**5. Factor n(k).
-3*(k - 3)**3*(k + 5)**2/4
Let j(i) = -10*i**2 + 2140*i + 10. Let n(v) = -9*v**2 + 4278*v + 22. Let x(w) = 11*j(w) - 5*n(w). Determine y, given that x(y) = 0.
0, 430/13
Suppose 2/7*o**2 + 942/7*o - 944/7 = 0. Calculate o.
-472, 1
Let p(h) = 6*h**3 - 231*h**2 + 225*h + 30. Let w(c) = c**3 - 33*c**2 + 32*c + 4. Let a(g) = 2*p(g) - 15*w(g). Find r, given that a(r) = 0.
0, 1, 10
Let w be (-21)/(84/16)*2/(-16). Let x(c) be the first derivative of -1/5*c**3 + 11 + 1/25*c**5 - w*c**2 + 1/20*c**4 - 2/5*c. Suppose x(r) = 0. What is r?
-1, 2
Let s(f) be the second derivative of f**5/10 + 1255*f**4/12 - 314*f**3/3 + 5038*f. Factor s(r).
r*(r + 628)*(2*r - 1)
What is r in 44/7*r**2 + 0 + 1/7*r**5 + 10/7*r**4 + 33/7*r**3 + 20/7*r = 0?
-5, -2, -1, 0
Let p(z) be the first derivative of -2*z**3 - 1/12*z**6 + 3*z - 1/4*z**2 + 1/4*z**4 + 3/5*z**5 + 92. Let p(f) = 0. What is f?
-1, 1, 6
Let 0 - 3/5*x**4 - 27*x**2 + 810*x - 72/5*x**3 = 0. Calculate x.
-15, 0, 6
Let w(b) be the third derivative of b**6/480 + 849*b**5/80 + 720801*b**4/32 + 203986683*b**3/8 + 16*b**2 + 2. Factor w(i).
(i + 849)**3/4
Suppose h - 293 = -4*h + 2*o, h - 56 = 3*o. Let n = h + -55. Solve -5 - 30*v + 26*v + 29 - n*v**2 = 0 for v.
-3, 2
Let l(j) = -3*j + 26. Let t be l(8). Factor -139*p**2 + 141*p**t + 19 - 2*p**3 + 32*p + 21.
-2*(p - 5)*(p + 2)**2
Suppose 5*n - 127 + 717 = 4*c, 3*n + 586 = 4*c. Suppose -38168 - 113*z**2 - 2*z**3 + 0*z**3 - c*z**2 - 108063 - 12783 - 11094*z = 0. Calculate z.
-43
Factor 2312/13 - 586/13*n + 2/13*n**2.
2*(n - 289)*(n - 4)/13
Let x be ((-2900)/10)/29 - -13. Determine z, given that -12/7 + 100/7*z**x + 4/7*z**5 + 76/7*z - 33/7*z**4 - 135/7*z**2 = 0.
1/4, 1, 2, 3
Let f(g) be the first derivative of g**5/35 - 39*g**4/28 + 232*g**3/21 - 120*g**2/7 - 512*g/7 - 2684. Factor f(h).
(h - 32)*(h - 4)**2*(h + 1)/7
Let t(m) be the third derivative of m**6/24 + 13*m**5/6 + 140*m**4/3 + 1600*m**3/3 - 7*m**2 - 46*m. Factor t(d).
5*(d + 8)**2*(d + 10)
Let s(q) be the second derivative of q**5/5 - 4*q**4/3 - 26*q**3 - 108*q**2 - 4*q + 242. Factor s(w).
4*(w - 9)*(w + 2)*(w + 3)
Let l be 0/((6/(-21))/((-2)/(-14))). Find b such that 47 + 2*b**3 + l*b + 12*b - 10*b**2 + 45 - 92 = 0.
0, 2, 3
Let a(q) be the second derivative of q**4/24 + q**3/3 - 24*q**2 - 584*q. Solve a(c) = 0 for c.
-12, 8
Suppose -20*h = -19*h - 3. Factor 252*i + 60*i**2 + 13*i**3 + 4*i**3 + 196 - 13*i**h.
4*(i + 1)*(i + 7)**2
Let h = 2864/3675 + -138/1225. Determine v, given that 0 - 6*v - h*v**2 = 0.
-9, 0
Let a(i) be the second derivative of i**7/210 + i**6/120 - 45*i**2/2 - 24*i. Let b(w) be the first derivative of a(w). Factor b(p).
p**3*(p + 1)
Determine m, given that -1/5*m**4 + 19/5*m**3 + 48/5 - 47/5*m**2 - 19/5*m = 0.
-1, 1, 3, 16
Let s(d) = -d**3 + 80*d**2 + 83*d - 190. Let x(w) = w**2 + w + 2. Let f(t) = -s(t) - 7*x(t). Find y, given that f(y) = 0.
-2, 1, 88
Let j = 3285 - 3281. Let f(g) be the second derivative of -11/2*g**3 - 13/4*g**j - 3/5*g**5 + 0 + 14*g - 3*g**2. Factor f(u).
-3*(u + 1)*(u + 2)*(4*u + 1)
Let i be -1*0/(-4) - (-4 + -1). Suppose -3*z - 2*x + x + 19 = 0, -z - i*x = -11. Factor -z*k**3 + 0 - 3/2*k**4 - 15/2*k**2 - 3*k.
-3*k*(k + 1)**2*(k + 2)/2
Suppose 33*g - 92 + 26 = 0. Let t(n) = -n**3 + 2*n**2 + 5*n - 2. Let c(x) = -2*x**3 - 2*x**2 + x - 1. Let h(p) = g*c(p) - t(p). Let h(d) = 0. What is d?
-1, 0
Suppose 6 + 6 - 40 = -14*p. Let m(c) be the third derivative of 0*c + 15*c**4 + 3/2*c**6 + 40/3*c**3 + 0 + 97/12*c**5 + 2/21*c**7 - 5*c**p. Factor m(i).
5*(i + 4)**2*(2*i + 1)**2
Let u(g) be the second derivative of g**4/30 - 676*g**3/15 + 114244*g**2/5 + 2075*g. Let u(p) = 0. Calculate p.
338
Let -86*g**4 - 636056/3*g**2 + 1/3*g**5 + 0 + 7396*g**3 + 0*g = 0. Calculate g.
0, 86
Let g(y) = -y**3 + 11*y**2 + 26*y + 6. Let t be g(13). Find p such that -2*p**5 + p**5 - 12*p**3 - t*p**3 - 3*p**4 + 5*p**4 + 17*p**3 = 0.
0, 1
Suppose -47 + 15 = -4*c. Factor 4*s**5 - c*s - 4*s**4 - 2*s**5 - 6*s**3 - 294*s**2 + 310*s**2.
2*s*(s - 2)*(s - 1)**2*(s + 2)
Let j(h) be the third derivative of h**8/84 + 6*h**7/35 - 13*h**6/15 - 14*h**5/5 + 25*h**4/6 + 22*h**3 + h**2 - 669*h. Let j(r) = 0. Calculate r.
-11, -1, 1, 3
Let u be (-18)/90*25/(-140)*4/6. Let r(c) be the second derivative of 16*c + u*c**4 + 1/21*c**3 + 0 - 2/7*c**2. Factor r(w).
2*(w - 1)*(w + 2)/7
Let a = -195 + 199. Find t such that 143*t**4 - 9*t - 6*t + 5*t**2 + 15*t**3 - 10 - 138*t**a = 0.
-2, -1, 1
Let q(i) be the second derivative of -3*i**7/56 + i**6/2 + 9*i**5/80 - 17*i**4/2 - 9*i**3/2 + 30*i**2 + 2*i + 1351. Determine w, given that q(w) = 0.
-2, -1, 2/3, 4, 5
Let z = -13 + 37. Factor 3*v**3 - 80 + z*v + 15*v**2 + 58 + 34.
3*(v + 1)*(v + 2)**2
Factor -4913*w**2 - 8 + 152*w + 5036*w**2 + 90*w.
(w + 2)*(123*w - 4)
Suppose -3*h - 31 + 28 = -2*r, 0 = -5*r - 5*h - 5. Let g(q) be the second derivative of 0*q**2 - 5/12*q**4 + r - 5/6*q**3 - 18*q. Find a such that g(a) = 0.
-1, 0
Let d(b) = b**3 + 9*b**2 - 32*b - 6. Let o be d(-9). Let z = o - 555/2. Suppose 3/2*a**3 + 0 + 0*a - z*a**2 = 0. Calculate a.
0, 3
Suppose 0 = -4*u - 323 + 323. Let y(r) be the third derivative of 2/3*r**3 + 0*r + u + 1/120*r**5 - 5/24*r**4 + 1/240*r**6 - 24*r**2. Let y(a) = 0. What is a?
-4, 1, 2
Let v = -132375/4 - -33095. Suppose -v*t**3 - 1/2 - 4*t**2 - 13/4*t = 0. What is t?
-2, -1, -1/5
Let p = 23001/35 +