3
Factor -10/3*w**2 + 702 + 2/3*w**3 - 102*w.
2*(w - 9)**2*(w + 13)/3
Suppose -i**3 + 1/5*i**4 + 17/5*i + 12/5 - 1/5*i**2 = 0. Calculate i.
-1, 3, 4
Let j(k) be the first derivative of 1/20*k**4 - 4/5*k + 157 + 3/25*k**5 - 1/30*k**6 - 11/15*k**3 + 6/5*k**2. Solve j(z) = 0 for z.
-2, 1, 2
Determine q so that 605/4*q + 1/4*q**3 - 76*q**2 - 151/2 = 0.
1, 302
Let a(d) = -7*d**4 + 2*d**3 + 7*d**2 - 2*d - 2. Let p(r) = 37 + 45 - 81. Let t(c) = -a(c) - 2*p(c). Suppose t(i) = 0. What is i?
-1, 0, 2/7, 1
Let g(p) be the second derivative of -1/8*p**4 + 139*p - 19*p**3 - 1083*p**2 + 0. Factor g(l).
-3*(l + 38)**2/2
Suppose 187500/13*l + 0 - 28250/13*l**2 - 2/13*l**4 - 488/13*l**3 = 0. Calculate l.
-125, 0, 6
Let m(x) be the second derivative of 3 + 10/3*x**4 + x - 35/2*x**3 - 1/4*x**5 + 45*x**2. Determine r, given that m(r) = 0.
2, 3
Let x(u) = -u**3 + 21*u**2 - 3*u + 11. Let l be x(13). Let f = l + -6593/5. Find b such that 24/5*b**2 - 4/5*b - f*b**3 + 0 = 0.
0, 2/9, 2/3
Let m = -453811 + 453813. Factor -3*r**4 + 81/7*r**m + 0 - 3/7*r**5 - 27/7*r**3 + 162/7*r.
-3*r*(r - 2)*(r + 3)**3/7
Let v(k) = -31*k**2 + 9*k + 40. Let z(b) = -88*b**2 + 25*b + 120. Let x(i) = -17*v(i) + 6*z(i). Suppose x(h) = 0. What is h?
-8, 5
Let l(n) = 8*n + 256. Let j be l(-30). Suppose j*f + 19*f = 34*f. Factor -2/7*g**3 + f - 8/7*g + 10/7*g**2.
-2*g*(g - 4)*(g - 1)/7
Let g = -94244 + 94248. Factor 1/3*q**3 - 9/4*q**2 + 1/12*q**g - 4/3 + 19/6*q.
(q - 2)*(q - 1)**2*(q + 8)/12
Suppose 2*z = 12*z + 4*i - 42, -3*i = -5*z + 6. Let a(m) be the first derivative of -5*m**z + 10*m**4 + 4*m**5 - 35/2*m**2 - 10*m + 32. Factor a(s).
5*(s - 1)*(s + 2)*(2*s + 1)**2
Let i be -6 - (113/226)/(2/(-44)). What is n in 4*n - 7/2*n**i + 0 + 13*n**3 - 18*n**2 + 9/2*n**4 = 0?
-2, 0, 2/7, 1, 2
Let n(z) = 2*z**3 + 47*z**2 - 257*z + 277. Let d be -5 + (0 + 5 - 0) - -1. Let a(u) = u**3 + u**2 - u + 1. Let x(b) = d*n(b) + 3*a(b). Factor x(c).
5*(c - 2)**2*(c + 14)
Let m(o) be the third derivative of o**8/336 + 17*o**7/210 + 29*o**6/60 - 29*o**5/10 - 153*o**4/8 - 81*o**3/2 - 4*o**2 + 5*o. Factor m(h).
(h - 3)*(h + 1)**2*(h + 9)**2
Let l(p) be the third derivative of -5*p**8/336 - 4*p**7/21 - 17*p**6/24 - 5*p**5/6 + 1297*p**2. Let l(q) = 0. Calculate q.
-5, -2, -1, 0
Let j be 45/(-26 + -46 + 87). Factor 2/11*s**j - 12/11 - 2/11*s + 12/11*s**2.
2*(s - 1)*(s + 1)*(s + 6)/11
Factor 2/13*j**3 - 40/13*j**2 + 128/13*j + 0.
2*j*(j - 16)*(j - 4)/13
Let 83*z**4 + 150*z**3 - 21*z**5 + 142*z**4 + 40*z + 524*z**2 - 1424*z**2 - 304*z = 0. What is z?
-2, -2/7, 0, 2, 11
Factor -2/21*s**2 + 384/7*s + 1154/21.
-2*(s - 577)*(s + 1)/21
Let g(c) be the first derivative of 36 + 1/3*c**3 + 2/3*c - 5/6*c**2. Find q, given that g(q) = 0.
2/3, 1
Factor 158*g**2 + 276*g + 5*g**3 + 1332 + 359*g + 289*g - g**3 + 14*g**2.
4*(g + 3)**2*(g + 37)
Let 13/3*q - 25/3 - 1/12*q**2 = 0. What is q?
2, 50
Let v(o) be the third derivative of -o**9/15120 + o**8/5040 + o**7/630 - o**5/60 + 25*o**3/6 + o**2 - 79. Let f(i) be the third derivative of v(i). Factor f(q).
-4*q*(q - 2)*(q + 1)
Let b(u) = 11*u**4 - 60*u**3 + 64*u**2 - 5*u - 5. Let i(c) = -18*c**4 + 90*c**3 - 96*c**2 + 8*c + 8. Let f(w) = 8*b(w) + 5*i(w). Factor f(s).
-2*s**2*(s - 1)*(s + 16)
Suppose -4*l + 4*g + 68 = 64, -l = g - 5. Determine o so that 7/2*o**2 + 9/2 + 1/2*o**l + 15/2*o = 0.
-3, -1
Let k(b) = -3*b**2 + 4*b. Let y(z) = 2*z**2 - 2*z. Suppose 0 = -a - 5*t + 13, 4*t = 4*a - 5*a + 11. Let h = -11 - -16. Let j(i) = a*k(i) + h*y(i). Factor j(x).
x*(x + 2)
Find l such that 0 - 570/7*l - 2/7*l**3 + 572/7*l**2 = 0.
0, 1, 285
Let a(o) be the first derivative of -63/2*o**2 - 105 + 66*o - o**3. Suppose a(r) = 0. What is r?
-22, 1
Let g(i) be the first derivative of i**6/1080 - i**4/24 - 45*i**2/2 - 71. Let c(j) be the second derivative of g(j). Factor c(u).
u*(u - 3)*(u + 3)/9
Factor -32*f - 98/3*f**2 - 2/3*f**3 + 0.
-2*f*(f + 1)*(f + 48)/3
Let b(c) be the second derivative of -c**4/84 + 38*c**3/21 - 74*c**2/7 + 276*c - 2. Solve b(z) = 0 for z.
2, 74
Solve 230/17 - 1378/17*l - 12/17*l**2 = 0.
-115, 1/6
Let j(s) be the first derivative of -s**4/14 - 10*s**3/7 - 47*s**2/7 + 18*s - 3126. Find o such that j(o) = 0.
-9, -7, 1
Let n(r) be the first derivative of r**3/3 - 1490*r**2 + 2220100*r - 2637. Factor n(o).
(o - 1490)**2
Let k = -85 - -90. Let d be 9/(-30)*(-10)/k. Factor -7/5*u + u**2 - 1/5*u**3 + d.
-(u - 3)*(u - 1)**2/5
Let b(a) be the second derivative of -5/42*a**7 - 8 - 35/6*a**4 + 10*a + 0*a**2 + 2/3*a**6 + 3/4*a**5 + 20/3*a**3. Solve b(q) = 0 for q.
-2, 0, 1, 4
Determine a, given that 114*a**2 + 387/7 + 1041/7*a + 18/7*a**3 - 3/7*a**5 - 129/7*a**4 = 0.
-43, -1, 3
Suppose -18 = 5*y + 6*y - 73. Let j(m) be the first derivative of -2/5*m**2 + 0*m + 2/25*m**y + 16 + 1/5*m**4 - 2/15*m**3. Factor j(l).
2*l*(l - 1)*(l + 1)*(l + 2)/5
Let o(j) be the second derivative of -j**6/6 + 3*j**5/4 + 25*j**4 - 920*j**3/3 + 1440*j**2 - 93*j + 1. Factor o(i).
-5*(i - 4)**3*(i + 9)
Factor -201*c**3 - 105/2 - 93/2*c**4 - 417/2*c - 309*c**2 + 3/2*c**5.
3*(c - 35)*(c + 1)**4/2
Let t = 1 + 5. Factor -y**3 - 3*y**3 - 16*y**2 + t*y**3 + 14*y + 0*y**3.
2*y*(y - 7)*(y - 1)
Let n(p) be the first derivative of 8 + 15/11*p**4 + 70/33*p**3 + 16/55*p**5 + 15/11*p**2 + 4/11*p. Find r, given that n(r) = 0.
-2, -1, -1/2, -1/4
Factor -1145*u - 766*u**2 - 240273 + 240483 + 109*u**2 - 28*u**2 - 30*u**3.
-5*(u + 2)*(u + 21)*(6*u - 1)
Suppose -4/9*b**5 + 4/3*b**2 + 0 + 20/9*b**4 + 0*b - 28/9*b**3 = 0. Calculate b.
0, 1, 3
Let z(d) be the second derivative of d**5/120 + 5*d**4/8 + 68*d**3/9 + 19*d**2 - 61*d + 12. Let z(u) = 0. What is u?
-38, -6, -1
Let x(v) be the second derivative of v**5/100 + v**4/6 - 7*v**3/30 - 98*v**2/5 + 43*v - 1. Find y, given that x(y) = 0.
-7, 4
Suppose 4*z - j - 56 = -5*j, -z + 3*j = -2. Solve 10*k + z*k**2 - 5957*k**3 + 0*k + 5958*k**3 = 0.
-10, -1, 0
Let q(l) = l**3 + 17*l**2 + 17*l + 19. Suppose -47 = i - 31. Let p be q(i). Factor d + p*d**5 - 574*d**4 + 2*d + 574*d**4 - 6*d**3.
3*d*(d - 1)**2*(d + 1)**2
Let k(j) be the first derivative of -j**4/8 - 63*j**3 - 11907*j**2 - 1000188*j + 1472. Factor k(h).
-(h + 126)**3/2
Find i such that -2395/4*i**2 - 915/4*i**3 + 2115/4*i + 25/4*i**4 + 585/2 = 0.
-3, -2/5, 1, 39
Let s(n) = 47*n**3 + 2734*n**2 + 54015*n + 15162. Let p(w) = 2*w**3 - w**2 - 8. Let r(z) = 6*p(z) - s(z). Suppose r(v) = 0. What is v?
-39, -2/7
Let h = -63 - -88. Factor 21 + 190*t + h + 26 - 72 - 5*t**2.
-5*t*(t - 38)
Let c be 1/(-3) + (5 - 76/(-3)). Suppose 0 = -c*h + 27*h + 9. Factor 51*s**h + 3 - 3 - 4*s**2 - 47*s**3 - 4*s**5 + 4*s**4.
-4*s**2*(s - 1)**2*(s + 1)
Let f = -67339/280 - -13479/56. Find x, given that 1/5*x + 6/5 - f*x**2 = 0.
-2, 3
Suppose 89*b + 581*b - 20531200 = 198*b - 330*b. Determine d so that -2/5*d**3 - 1920*d - b - 48*d**2 = 0.
-40
Suppose v = 3*w + 15, v - 26 = -4*w + 17. Let j = v - 25. Factor -4*y**3 - 24*y**j - 4 + 55*y**2 + 7*y**3 - 26*y**2 - 4*y.
(y - 1)*(y + 2)*(3*y + 2)
Let k(p) = p**2 - 19*p + 24. Let s be k(18). Let f be (-1290)/(-900) - s/10. Find x such that -3/2*x**3 + 7/6*x**5 + 1/3*x - f*x**4 + 0 + 5/6*x**2 = 0.
-1, -2/7, 0, 1
Factor -65*a - 6663*a**2 + 990 + 410*a + 6668*a**2.
5*(a + 3)*(a + 66)
Let l(k) be the first derivative of k**4/2 - 5840*k**3 + 25579200*k**2 - 49794176000*k - 4379. Factor l(i).
2*(i - 2920)**3
Let w(p) be the first derivative of -5*p**4/4 - 100*p**3/3 + 5*p**2/2 + 100*p + 922. Determine f so that w(f) = 0.
-20, -1, 1
Let h = -5531 + 5534. Let n(v) be the first derivative of 0*v + 8/27*v**h + 10 + 1/18*v**4 - 5/9*v**2. Find l, given that n(l) = 0.
-5, 0, 1
Suppose 0 + 4/5*s**3 - 32/5*s - 8/5*s**2 = 0. What is s?
-2, 0, 4
Let q(j) = -j**5 + j**3 + j**2 - j - 1. Let f = 55 + -51. Let v(r) = r**5 + 2*r**4 - 4*r**3 - 4*r**2 + 4*r + 4. Let c(i) = f*q(i) + v(i). Factor c(d).
-d**4*(3*d - 2)
Let b = -3/957136 - -957145/2871408. Determine f so that -20/3*f + f**2 + 2*f**3 + 4 - b*f**4 = 0.
-2, 1, 6
Let f be 35 + 2414/(-85) + ((-12)/2 - -1). Suppose -3*t = o + 3, -4*o = 5*t - 2 + 14. Let -f*c**3 + t - 4/5*c - 2*c**2 - 2/5*c**4 = 0. What is c?
-2, -1, 0
Let s(q) be the second derivative of 2*q - 147/4*q**2 - 3 - 1/8*q**4 + 7/2*q**3. Factor s(n).
-3*(n - 7)**2/2
Let l(y) be the third derivative of -9/2*y**3 - 91*y**2 + 0 + 1/