201540. Factor x*i**2 - 1/4*i + 0.
i*(i - 1)/4
Let -2/11*r**4 + 158/11 + 472/11*r + 152/11*r**3 + 468/11*r**2 = 0. Calculate r.
-1, 79
Let x = 152630 + -152628. What is t in 2/15*t**x + 8/15 - 2/3*t = 0?
1, 4
Let i(v) be the second derivative of -v**7/2100 - 3*v**6/100 - 81*v**5/100 + 5*v**4/2 + 45*v. Let q(c) be the third derivative of i(c). Factor q(o).
-6*(o + 9)**2/5
Let q be 490/140*(-24)/(-14). Suppose 0 = -3401*v + 3403*v - q. Find w such that 0 + v*w**2 + 3/4*w**3 + 3*w = 0.
-2, 0
Let y(z) be the second derivative of 68*z - 8/3*z**3 + 1/3*z**4 + 6*z**2 - 2. Factor y(s).
4*(s - 3)*(s - 1)
Let s(k) = -76 - 28 + 146 - 13*k. Let m be s(3). Determine f so that 0 - 2/7*f**m - 2/7*f**2 + 0*f = 0.
-1, 0
Let s(d) be the third derivative of 1/12*d**4 - 34*d**2 - 1/150*d**5 + 0 - 4/15*d**3 + 0*d. Let s(v) = 0. What is v?
1, 4
Let d(r) be the first derivative of -2*r**3 + 5936*r**2 + 3958*r - 6721. Factor d(q).
-2*(q - 1979)*(3*q + 1)
Suppose y - 4*y = -354. Factor -y*q + 6 - 7 - 35 - 36*q - 10*q**2 - 24.
-2*(q + 15)*(5*q + 2)
Let h = 474/155 - 171/62. Determine f so that 1/10*f**4 + 7/10*f**2 + 1/2*f**3 + 0 + h*f = 0.
-3, -1, 0
Factor 8*w - 4/7*w**2 + 288/7.
-4*(w - 18)*(w + 4)/7
Suppose -2 = l - 3*q - 3, -3*q + 29 = 2*l. Suppose 0 = -l*k + 5*k + 15. Find c, given that 4*c**k - 6 + 15*c**2 + 5*c - 13*c - 21*c**2 + 16*c**2 = 0.
-3, -1/2, 1
Let y(q) = -4*q + 22. Let w be y(5). Let w*z**3 + 80 + 3*z**2 - 45*z + 2*z**3 - 19*z + z**2 = 0. Calculate z.
-5, 2
Let v(a) = 17*a + 529. Let z be v(-31). Let h(s) be the third derivative of 8*s**z + 1/15*s**5 + 0*s - 8/3*s**3 + 0 - 1/2*s**4. Factor h(q).
4*(q - 4)*(q + 1)
Let c(a) be the third derivative of a**6/360 - a**5/30 + a**4/8 - 2*a**3/9 + 517*a**2 - 3*a + 2. Factor c(k).
(k - 4)*(k - 1)**2/3
Let a(w) be the third derivative of -1/3*w**4 - 2*w**2 + 0 - 1/15*w**5 + 2*w**3 + 11*w. Factor a(v).
-4*(v - 1)*(v + 3)
Let u(q) be the second derivative of -q**8/2240 + q**7/210 - q**6/240 - 3*q**5/20 - 20*q**4/3 - 54*q. Let w(p) be the third derivative of u(p). Factor w(x).
-3*(x - 3)*(x - 2)*(x + 1)
Find h, given that 20*h**2 + 9248/5 - 1666/5*h - 2/5*h**3 = 0.
16, 17
Let d(y) be the third derivative of 252*y**2 + 7/120*y**5 + 0*y + 0 + 1/480*y**6 + 3/32*y**4 - 27/2*y**3. Suppose d(t) = 0. What is t?
-9, 4
What is k in 49/4*k**2 - 93/4*k**3 - 1/4*k**5 + 23/4*k**4 + 47/2*k - 18 = 0?
-1, 1, 4, 18
Let n(o) be the second derivative of -1/30*o**6 + 0 + 0*o**2 + 1/10*o**5 - 1/3*o**3 + 10*o + 1/12*o**4. Factor n(a).
-a*(a - 2)*(a - 1)*(a + 1)
Let y(u) be the third derivative of 0 - 1/12*u**4 - 48*u**2 + 5/112*u**8 + 11/60*u**5 - 11/210*u**7 + 0*u + 0*u**3 - 13/120*u**6. Solve y(d) = 0.
-1, 0, 1/3, 2/5, 1
Let r(f) be the second derivative of -f**8/168 + 4*f**7/105 - f**6/12 + f**5/15 - 13*f**2 + 31*f. Let c(y) be the first derivative of r(y). Factor c(v).
-2*v**2*(v - 2)*(v - 1)**2
Suppose -10 = -4*h - 10. Suppose h = -6*j - 0 - 0. Factor 3*a**2 + 4*a**3 - 2*a**4 + 2*a**2 + 8 + a**2 - 16*a + j*a**2.
-2*(a - 2)*(a - 1)**2*(a + 2)
Let c = 778 + -770. Let n(p) be the first derivative of 1/9*p**3 + 1/2*p**2 + 0*p + c. Factor n(s).
s*(s + 3)/3
Let q(j) be the third derivative of j**6/36 - j**5/8 + 5*j**4/24 - 83*j**3/6 + j**2 - 44*j. Let d(l) be the first derivative of q(l). Factor d(w).
5*(w - 1)*(2*w - 1)
Let y(u) = u**2 + 37*u + 178. Let s be y(-31). Let h be 5*119/70 + s. Factor -1/4 - 1/4*o**2 + h*o.
-(o - 1)**2/4
Factor 6050/3*o + 0 - 218/3*o**3 + 2/3*o**4 + 5830/3*o**2.
2*o*(o - 55)**2*(o + 1)/3
Find o, given that -198025/4 - 915/4*o**2 - 5/4*o**3 - 44055/4*o = 0.
-89, -5
Factor 4/3*d**4 + 2288*d**2 + 73984/3 + 41344/3*d + 304/3*d**3.
4*(d + 4)**2*(d + 34)**2/3
Let f(n) be the first derivative of 4*n**3/15 + 64*n**2/5 + 448*n/5 + 513. Solve f(d) = 0.
-28, -4
Let k(v) = -5*v**3 - 21*v**2 + 170*v - 136. Let b(c) = -c**3 + 2*c**2 + c. Let w(p) = -4*b(p) + k(p). Determine q, given that w(q) = 0.
-34, 1, 4
Factor -1216/5 - 604/5*a + 2/5*a**2.
2*(a - 304)*(a + 2)/5
Suppose 31*d + 5 = 98. Determine h, given that 875*h**5 + 247*h**d + 13 - 442*h**5 + 3 + 144*h + 383*h**2 - 449*h**5 - 24*h**4 = 0.
-4, -1, -1/4, 4
Factor 2/5*u**3 + 4160*u - 43264/5 + 412/5*u**2.
2*(u - 2)*(u + 104)**2/5
Let l be (-2222)/(-1045) - (51/(-15) - -5). Suppose 4*o - 8 = 3*p - 0*p, -3*p = 0. Factor -l + 8/19*d + 2/19*d**o.
2*(d - 1)*(d + 5)/19
Let v be ((-5)/10 - 0)/1*-6. Factor 4*b**4 + 8640*b + 451*b**2 - 3780*b**v - 249*b**4 + 1264*b**2 - 15175*b**2 - 1280.
-5*(b + 8)**2*(7*b - 2)**2
Let -247*f**2 + 88*f - 134*f + 249*f**2 = 0. What is f?
0, 23
Let l(r) be the first derivative of -9*r**4 + 44*r**3 - 121*r**2/2 - 5545. Factor l(w).
-w*(6*w - 11)**2
Let m(a) be the second derivative of -a**5/40 + 283*a**4/24 - 4970*a**3/3 - 5041*a**2 + 8*a + 34. Solve m(x) = 0.
-1, 142
Let c = 539583/53081 - 170/7583. Find z such that 6/7*z - 37/7*z**2 + 0 - 40/7*z**4 + c*z**3 = 0.
0, 3/8, 2/5, 1
Suppose -1510 = -3*u + 713. Let f = 5188/7 - u. Suppose -2/7*t**3 + 0*t**2 + 1/7*t**5 + 0 + f*t**4 + 0*t = 0. Calculate t.
-2, 0, 1
Let c(o) = 4*o**3 + 21*o**2 + 5*o - 12. Let z(i) = i**2 + i. Suppose 0 = 14*h - 10*h - 40. Let d(f) = h*z(f) + 2*c(f). Factor d(j).
4*(j + 1)*(j + 6)*(2*j - 1)
Suppose -69*i**2 - 85*i**5 - 60 + 54*i**2 - 516*i + 75*i**4 + 605*i**3 - 4*i = 0. What is i?
-2, -1, -2/17, 1, 3
Let v(y) be the second derivative of -y**7/5460 - y**6/1170 + 2*y**5/195 + y**3/6 + 7*y - 8. Let p(q) be the second derivative of v(q). Factor p(c).
-2*c*(c - 2)*(c + 4)/13
Let n(d) = -24*d**4 + d**2 + d - 1. Let c(p) = 4*p**5 - 85*p**4 + 115*p**3 + 36*p**2 - 118*p + 25. Let v(m) = 5*c(m) - 5*n(m). Suppose v(q) = 0. Calculate q.
-1, 1/4, 1, 2, 13
Factor 171 + 149*t + 925*t - 373*t**2 + 135*t**2 + 181*t**2.
-3*(t - 19)*(19*t + 3)
Let g(p) be the first derivative of 20/3*p**3 + p**5 + 0*p**2 + 0*p + 81 - 25/4*p**4. Factor g(m).
5*m**2*(m - 4)*(m - 1)
Suppose -3*h - 801 = -3*p, 25 = -3*p - 2*h + 816. Suppose -258*f + p*f = 0. Factor 0 + 0*l**2 + 1/5*l**3 + f*l.
l**3/5
Let v be 0/(6*2/6). Factor -3*l**4 + v*l**4 - 10*l**2 + 2*l**4 + 4*l + 8*l**3 - l**4.
-2*l*(l - 2)*(l - 1)**2
Suppose 0*m - 58 = -8*m - 34. Factor -2/9*q**m + 4/9 - 4/9*q**2 + 2/9*q.
-2*(q - 1)*(q + 1)*(q + 2)/9
Let 14*s**2 + 15*s**3 - 16*s**3 + 10*s**2 + 60*s - 2*s**3 = 0. What is s?
-2, 0, 10
Let u be 80*(-10)/(-85)*1241/292. Determine g, given that -u + 14/5*g**5 + 1102/5*g**2 + 746/5*g**3 + 178/5*g**4 + 64*g = 0.
-5, -2, -1, 2/7
Let g = 199466 + -398931/2. Factor 1/2*z**3 + 1/2*z**4 + 0*z - g*z**5 + 0 - 1/2*z**2.
-z**2*(z - 1)**2*(z + 1)/2
Let m be ((-12)/(-105))/(8 - (-663)/(-85)). Factor m*g + 8/7 - 4/7*g**2.
-4*(g - 2)*(g + 1)/7
Let i = 207 + -203. Suppose 0 = -p - g + 5, -i*p + 2*g - 1 + 3 = 0. Find y, given that 0*y + 0 - 2/11*y**5 + 2/11*y**4 + 2/11*y**3 - 2/11*y**p = 0.
-1, 0, 1
Let c(m) be the first derivative of m**3/3 + 129*m**2/8 + 8*m + 4643. Find r, given that c(r) = 0.
-32, -1/4
Let h(u) be the first derivative of u**3/18 + 527*u**2/2 + 833187*u/2 - 7876. Factor h(s).
(s + 1581)**2/6
Suppose -22*r**4 - 91*r + 17*r + 4*r**5 - 800 - 166*r + 236*r**3 - 50*r**4 + 872*r**2 = 0. What is r?
-2, -1, 1, 10
Factor 5268187*h**3 - 63 - 5268193*h**3 - 495 + 1718*h - 130*h**2.
-2*(h - 9)*(h + 31)*(3*h - 1)
Let s = -55 + 60. Suppose -d = d - h - 115, -s*d + 4*h + 286 = 0. Factor -d + 6*t**2 + 55 - 3*t**2.
3*(t - 1)*(t + 1)
Let k = -162419 - -162424. Find f, given that 0*f + 0*f**2 + 0 + 2*f**3 - 2/3*f**k - 4/3*f**4 = 0.
-3, 0, 1
Let c(p) be the second derivative of 8/3*p**3 - 11/120*p**6 - 5/2*p**2 + 1/168*p**7 + 43/80*p**5 - 99*p - 77/48*p**4 + 0. Suppose c(n) = 0. What is n?
1, 2, 5
Let a = 20287/2 - 10143. Factor a + 19/4*x**3 - 19/4*x - 1/2*x**2.
(x - 1)*(x + 1)*(19*x - 2)/4
Let b(o) be the third derivative of -o**6/180 - 4*o**5/45 + 71*o**4/36 + 26*o**3/3 + 591*o**2. Determine v, given that b(v) = 0.
-13, -1, 6
Let z be 2 + (-126)/(-15) - 12/30. Let -3*b**3 - 660 + 665 - 5*b**4 - z*b + 13*b**3 = 0. What is b?
-1, 1
Let j = 1821 + -1815. Let c be ((-7)/j)/(889/(-1143)). Factor -3/2*f**2 + 6 + 6*f - c*f**3.
-3*(f - 2)*(f + 1)*(f + 2)/2
Suppose 4*y - 504 = -488. Let i(g) be the third derivative of 1/20*g**5 + 0 - 7*g**2 + 1/8*g**y + 0*g - g**3. Suppose i(j) = 0. Calculate j.
-2, 1
Let s(b) = -b**2 - 9*b - 