. Let v(r) = -d(r) - 9*g(r). Suppose v(z) = 0. What is z?
-1, 3, 10
Let g(t) be the second derivative of -7*t**6/30 + 113*t**5/10 - 1345*t**4/12 - 191*t**3 + 216*t**2 - 698*t. What is v in g(v) = 0?
-1, 2/7, 9, 24
Let k(m) be the first derivative of -8*m**7/105 - 3*m**6/10 - 2*m**5/5 - m**4/6 - 55*m**2/2 - 36. Let x(o) be the second derivative of k(o). Factor x(y).
-4*y*(y + 1)**2*(4*y + 1)
Let f(s) be the third derivative of -s**5/90 - 797*s**4/6 - 635209*s**3 - 3458*s**2 + 2. Suppose f(v) = 0. Calculate v.
-2391
Let m = 90 + -99. Let b be (-8)/(24/(-29)) + m. What is o in 0 - b*o + 1/3*o**2 + 1/3*o**3 = 0?
-2, 0, 1
Let f = -373 + 409. Factor -f*q**3 + 76 + 40*q**3 + 116*q**2 + 53*q - 32*q**2 + 103*q.
4*(q + 1)**2*(q + 19)
What is m in -1/3*m**2 - 103/3 + 104/3*m = 0?
1, 103
Suppose -11*y + 1453 + 1924 = 0. Let k = y + -307. Factor k + 0*n**3 + 0*n + 1/10*n**4 - 1/10*n**2.
n**2*(n - 1)*(n + 1)/10
Let x be 16/10 + (-4)/(-10). Let f be 1/1 - (0 - 1). Let 4*p**2 + 5*p**f - 16*p + 12 + 0*p**2 - 5*p**x = 0. Calculate p.
1, 3
Let q = -720117 + 720119. Factor -5/2*d - 7 + 1/2*d**q.
(d - 7)*(d + 2)/2
Suppose -22*g + 2/5*g**2 + 212/5 = 0. Calculate g.
2, 53
Suppose 4*g - 105 + 381 = 0. Let y = 74 + g. Determine v so that 186*v**3 + 10*v**4 - 106*v**3 + 4*v - 10*v**2 - 108*v**3 + 24*v**y = 0.
-1, -2/3, 0, 1/4, 1
Let i(k) = k**2 - 7*k - 15. Let c be i(9). Let j(b) be the first derivative of -4*b - 2*b**2 + b**4 + 7 + 4/3*b**c. Determine r so that j(r) = 0.
-1, 1
Let 0 - 232/3*s**3 + 146/9*s**4 - 2/9*s**5 - 544/9*s + 1096/9*s**2 = 0. Calculate s.
0, 1, 2, 68
Let j(r) be the third derivative of 0 + 1/180*r**6 + 0*r**3 - 1/504*r**8 + 212*r**2 + 2/45*r**5 - 4/315*r**7 + 0*r + 0*r**4. Suppose j(m) = 0. What is m?
-4, -1, 0, 1
Let v(w) = -6*w + 7. Let g be v(9). Let i = g - -51. Suppose -6*d**2 - 3 - 29*d**3 + 47*d**3 - 15*d - 3*d**i - 3*d**5 + 12 = 0. Calculate d.
-3, -1, 1
Let x(j) = 29*j**2 + 3374*j + 6272. Let p(b) = -4*b**2 - 480*b - 896. Let f(h) = 30*p(h) + 4*x(h). Solve f(o) = 0 for o.
-224, -2
Let t(x) be the third derivative of -1/15*x**5 + 0*x**3 + 0 - 5/6*x**4 + x**2 + 2/105*x**7 + 1/6*x**6 - 4*x. Factor t(k).
4*k*(k - 1)*(k + 1)*(k + 5)
Suppose 528*z = 529*z - 42. Find r such that 147 + 2*r**2 - z*r - 13*r**2 + 3*r**2 + 2*r**2 + 9*r**2 = 0.
7
Suppose 0 = 11*k - 8*k - 9. Let y = -45402 + 45405. What is h in 3/4*h + 9/4*h**k + 0 - y*h**2 = 0?
0, 1/3, 1
Factor -30883 + 55053*q - 54051*q - 52784 - 3*q**2.
-3*(q - 167)**2
Let z(v) = -v + 12. Suppose -4*s + 16 = 2*q, 2*q + 4*s - 16 = -2*q. Let t be z(q). What is f in t - 17*f - 11*f + 39*f + 3*f**2 - 23*f = 0?
2
Factor 14*c**3 - 62*c**3 + 64*c**3 + 60*c**2 - 800*c - 2*c**4 + 1750.
-2*(c - 5)**3*(c + 7)
Factor 36 + 3*r**2 + 5*r**2 + 0*r**2 - 15*r**2 + 5*r**2 - 34*r.
-2*(r - 1)*(r + 18)
Let k(h) be the third derivative of 166*h**6/45 - 5*h**5/2 - h**4/3 - 29*h**3/3 - 2*h**2 - 111. Let b(x) be the first derivative of k(x). Factor b(r).
4*(4*r - 1)*(83*r + 2)
Let w(a) = 84*a**3 + 3510*a**2 + 844*a + 98. Let i(s) = 2*s**3 - s**2 + s - 2. Let b(t) = 44*i(t) + 2*w(t). Let b(g) = 0. What is g?
-27, -1/8
Let g = -10/537 + 577/2148. Suppose 8 = -7*d + 11*d. Let 1/2*c + 0 + g*c**d = 0. Calculate c.
-2, 0
Find v such that -24879*v - 26633*v - 15897612 - 3*v**2 + 65324*v = 0.
2302
Let p(s) be the third derivative of -31*s**5/15 + 35*s**4/6 - 8*s**3/3 + s**2 + 57. Factor p(g).
-4*(g - 1)*(31*g - 4)
Let u(y) be the second derivative of -y**5/45 + 95*y**4/9 + 572*y**3/27 + 4210*y. Factor u(w).
-4*w*(w - 286)*(w + 1)/9
Let s(x) = x**3 - 12*x**2 + 12*x - 8. Let z be s(11). Factor -3*a**5 - 85*a**2 - 56*a + 100*a**4 + 43*a**5 + 10*a**z - 1360 + 1350 + a.
5*(a - 1)*(a + 2)*(2*a + 1)**3
Suppose -1/3*c**2 + 9*c - 9*c**3 + 1/3*c**4 + 0 = 0. Calculate c.
-1, 0, 1, 27
Let c = -2575/2 + 1289. Let a(s) be the first derivative of c*s**2 + 2*s - 2/3*s**3 + 16. Factor a(q).
-(q - 2)*(2*q + 1)
Suppose 2*b + 3*j = 8, b + 9*j - 4 = 6*j. Suppose -2*p - 6 = 0, -b*p = -4*s + 8*s - 4. Factor 20*u**3 + 4*u**2 + 4*u**2 - 22*u**3 - 10*u + s + 0.
-2*(u - 2)*(u - 1)**2
Let v(d) be the third derivative of d**6/420 + 2*d**5/21 - 69*d**4/28 - 162*d**3/7 + d**2 + 175*d + 2. Suppose v(c) = 0. What is c?
-27, -2, 9
Let b(d) be the second derivative of -85*d - 1/18*d**4 + 0 + 1/10*d**5 - 11/9*d**3 - 7/3*d**2. Determine r so that b(r) = 0.
-1, 7/3
Suppose -11*i + 15*i - 112 = 0. Suppose 2*y = 2*a - i, -2*a + 3*y = -13 - 19. Factor a*c**3 - 10*c**4 + 2*c**3 - c**5 - 2*c**4 + 5*c**5 - 4*c**2.
4*c**2*(c - 1)**3
Factor -556*k**2 - 3*k**3 - 112 + 2217*k + 324*k**2 - 872*k**2 - 998.
-3*(k - 1)**2*(k + 370)
Let y(p) be the first derivative of -p**5/60 + 120*p + 75. Let x(t) be the first derivative of y(t). Factor x(z).
-z**3/3
Let -17*v**3 - 34*v**2 + 6*v**5 + 2*v**5 + 102*v**2 - 50*v**4 + 18*v**2 + 69*v**3 - 24*v = 0. Calculate v.
-1, 0, 1/4, 3, 4
Suppose -2*j - 4*c - 9 = -1, -7*j - c = -24. Let f = 893 - 11593/13. Let f*r**3 + 38/13*r**2 - 8/13 - 30/13*r**j - 24/13*r + 8/13*r**5 = 0. Calculate r.
-1, -1/4, 1, 2
Let w(m) be the third derivative of 7*m**6/180 + 13*m**5/45 + 31*m**4/36 + 4*m**3/3 + m**2 - 122. Factor w(y).
2*(y + 1)**2*(7*y + 12)/3
Let 288 - 3542*v**2 + 1171*v**2 + 1656 + 9*v**3 + 1093*v**2 + 960*v**2 + 2700*v = 0. What is v?
-2/3, 18
Let v(y) be the second derivative of y**5/70 + 61*y**4/3 + 181472*y**3/21 - 366368*y**2/7 + 4598*y. Suppose v(c) = 0. What is c?
-428, 2
Let x(n) be the first derivative of 3*n**3 + 13*n**2/2 + 22*n + 1. Let u(z) = z**2. Let q(l) = 24*u(l) - 3*x(l). Factor q(f).
-3*(f + 2)*(f + 11)
Let v(i) be the first derivative of -176/3*i**3 + 14/3*i**6 + 24*i**2 - 109 - i**4 + 0*i + 104/5*i**5. Determine q so that v(q) = 0.
-3, -2, 0, 2/7, 1
Factor -3/4*w**2 + 1/4*w**4 - 1/2*w**3 - 1 + 2*w.
(w - 2)*(w - 1)**2*(w + 2)/4
Let c(p) = 10*p**2 - 171*p - 359. Let b be c(19). Let r(m) be the first derivative of -2*m + 1/12*m**3 + 1/4*m**b - 17. Find q, given that r(q) = 0.
-4, 2
Let d be 6*(9/(-2))/(-3). Let 8*h + d*h - h + 4*h**2 = 0. What is h?
-4, 0
Let p(t) = 12*t**5 - 16*t**4 - 4*t**3 + 16*t**2 - 32*t + 8. Let n(d) = -d**5 + 2*d**3 + 2*d - 1. Let m(a) = 8*n(a) + p(a). Let m(f) = 0. Calculate f.
-1, 0, 1, 2
Suppose 4*f + 4*k - 20 = 0, f + 4*k - 2 = 12. Factor -14*j + f*j**2 - 1 + 8*j + 5*j.
(j - 1)*(2*j + 1)
Suppose 92*y - 1605 = -443*y. Suppose 8/7*i + 0 - 1/7*i**y - i**2 = 0. What is i?
-8, 0, 1
Let o(w) be the first derivative of -1/51*w**6 - 338/51*w**3 + 0*w**2 + 0*w + 10/17*w**5 + 37 - 143/34*w**4. Factor o(q).
-2*q**2*(q - 13)**2*(q + 1)/17
Let m(s) be the third derivative of 5*s**5/12 - 290*s**4/3 + 26912*s**3/3 - 63*s**2. Find j, given that m(j) = 0.
232/5
Let j = -9663894/7 + 1384290. What is n in 574992/7 + 396/7*n**2 + j*n + 2/7*n**3 = 0?
-66
Let z(j) = -3*j**2 + 57*j - 90. Let h(c) = c**3 + 8*c**2 - 171*c + 270. Let y(g) = -3*h(g) - 8*z(g). Factor y(l).
-3*(l - 3)*(l - 2)*(l + 5)
Let a(y) be the first derivative of y**4/20 - 96*y**3/5 - 579*y**2/10 - 58*y - 1649. Solve a(t) = 0 for t.
-1, 290
Factor -105*v**3 - 500*v - 295*v**2 - 232*v**2 + 12*v**2 - 17*v**2 - 68*v**2 - 5*v**4.
-5*v*(v + 1)*(v + 10)**2
Let q(i) be the first derivative of 2*i**3/3 + 750*i**2 + 281250*i - 981. Find c such that q(c) = 0.
-375
Let h = 6506 + -6504. Let a(d) = -2*d**2 + 18*d - 16. Let u be a(8). Let 2/7*w**3 + u - 6/7*w**4 - 4/7*w + 6/7*w**h + 2/7*w**5 = 0. What is w?
-1, 0, 1, 2
Factor -1/4*z**4 + 27*z - 216 - 1/4*z**3 + 18*z**2.
-(z - 8)*(z - 3)*(z + 6)**2/4
Let h be 198/275*(-1 + 2)*(-1770)/(-531). Let 0 + 3/5*m**4 - 12/5*m + 3/5*m**3 - h*m**2 = 0. Calculate m.
-2, -1, 0, 2
Let y(v) be the second derivative of 10*v**7/21 - 236*v**6/35 - 349*v**5/35 + 4*v**4 + 88*v**3/21 - 13*v + 256. Suppose y(n) = 0. Calculate n.
-1, -2/7, 0, 2/5, 11
Let -76/5*g**2 - 16*g + 78/5 + 16*g**3 - 2/5*g**4 = 0. Calculate g.
-1, 1, 39
Factor -100*u**4 + 7961*u**2 + 3*u - 395*u**3 - 3*u - 7941*u**2.
-5*u**2*(u + 4)*(20*u - 1)
Let u(w) = -4103*w + 110783. Let a be u(27). Factor 60/7*g**a - 3/7*g**4 + 0 + 72/7*g + 6/7*g**3.
-3*g*(g - 6)*(g + 2)**2/7
Let a(p) be the second derivative of -p**8/840 + p**7/210 + 2*p**6/45 + p**3/6 + 9*p**2/2 - 73*p + 1. Let u(h) be the second derivative of a(h). Factor u(v).
-2*v**2*(v - 4)*(v + 2)
Let d(r) = r**3 + 12*r**2 -