2
Suppose -k + 0*j - 5*j + 2 = -4*j, 14*j - 8*j = -4*k. Suppose -3*d + 2*d = -2. Factor 21 - k*q + 3/7*q**d.
3*(q - 7)**2/7
Suppose 0 = 4*q - 3*p + 33, -3*p - 4 = p. Let w be 435/(-51)*1 - q. Factor 2/17*z**2 + 10/17*z + w.
2*(z + 1)*(z + 4)/17
Find a, given that -36 + 479/2*a**2 - 6*a**4 + 103/2*a**3 + 81*a = 0.
-3, -2/3, 1/4, 12
Let w(z) = 7*z**3 - 49*z**2 + 37*z + 25. Let k(v) = -3*v**3 + 24*v**2 - 19*v - 10. Let y(m) = -15*k(m) - 6*w(m). Factor y(x).
3*x*(x - 21)*(x - 1)
Let o(j) be the first derivative of j**6/2 + 144*j**5/5 + 393*j**4 - 1298*j**3 - 1575*j**2/2 + 3750*j + 5805. Find l such that o(l) = 0.
-25, -1, 1, 2
Let k(m) be the first derivative of 1058*m + 44 + 46*m**2 + 2/3*m**3. Factor k(c).
2*(c + 23)**2
Let y(j) be the second derivative of 0*j**2 + 6 + 19*j - 1/54*j**4 + 43/27*j**3. Let y(c) = 0. Calculate c.
0, 43
Let s be (-25)/(-24) - (12 + -10)/(-6). Let g(o) = -40*o + 85. Let w be g(2). Suppose -1/4*z**3 + 0 + 0*z - 9/8*z**w + s*z**4 + 0*z**2 = 0. What is z?
0, 2/9, 1
Suppose 0 = 2*o - 3*v - 73 - 36, -o + v = -52. Suppose -o = 4*g - 59. Determine i so that 8*i**2 + 4*i + 0*i**4 + 0*i**4 - 2*i**4 - 6 + 31*i**g - 35*i**3 = 0.
-3, -1, 1
Let o(x) = 22*x**4 + 104*x**3 - 422*x**2 + 367*x + 864. Let m(w) = 16*w**4 + 70*w**3 - 282*w**2 + 245*w + 576. Let n(b) = 7*m(b) - 5*o(b). Factor n(c).
2*(c - 6)**2*(c - 4)*(c + 1)
Let m(x) be the third derivative of -x**6/540 - 7*x**5/90 - x**4/2 - 619*x**2. Find c, given that m(c) = 0.
-18, -3, 0
Let w be (-4)/6*(-276)/(-8). Let l = 25 + w. Let 241 + 2*i**l - 241 = 0. What is i?
0
Let o(a) be the third derivative of -a**6/80 - 261*a**5/40 - 519*a**4/16 - 259*a**3/4 + a**2 - 1251*a. Factor o(x).
-3*(x + 1)**2*(x + 259)/2
Determine q so that 2*q**4 + 46*q**3 - 10*q**2 + 229*q**5 - 84*q**5 - 31*q - 69*q**5 + 80 - 85*q - 78*q**5 = 0.
-4, -2, 1, 5
Let r(g) be the second derivative of -1/8*g**4 + 0 + 1/80*g**5 + 5/24*g**3 - 80*g + 0*g**2. Solve r(w) = 0.
0, 1, 5
Let b be (1/3)/(3/(-81)). Let s be 8/(-12)*(0 + b/2). Factor 93*u**3 - 46*u**3 - 44*u**s - 3*u**2 - 6*u.
3*u*(u - 2)*(u + 1)
Let o be (3 - 1) + -7 - 124/(-44). Let j = 212/77 + o. Suppose -1/7*b**3 - j*b**2 - 5/7*b - 2/7 = 0. What is b?
-2, -1
Let s(u) be the first derivative of -u**5/15 - 5*u**4/2 - 52*u**3/3 - 148*u**2/3 - 64*u - 4199. Factor s(y).
-(y + 2)**3*(y + 24)/3
Suppose -492/5 - 68/5*a**2 + 2/5*a**3 - 562/5*a = 0. What is a?
-6, -1, 41
Let d = -128052 + 128057. Let 0 - 8/11*n**3 - 2/11*n**d + 0*n**2 + 0*n + 8/11*n**4 = 0. Calculate n.
0, 2
Determine i, given that 14*i**2 - 272*i - 185*i - 4*i**4 - 108*i**3 + 4*i**5 + 161*i + 96 + 294*i**2 = 0.
-6, 1, 4
Factor -375*r**4 - 70*r**2 + 756*r**4 - 508*r**3 + 566*r**2 - 377*r**4 + 1008*r.
4*r*(r - 126)*(r - 2)*(r + 1)
Let u(c) be the first derivative of -1/150*c**5 + 15 + 0*c - 3/5*c**3 - 1/10*c**4 - 5*c**2. Let t(a) be the second derivative of u(a). Factor t(z).
-2*(z + 3)**2/5
Let g(z) = 67*z**3 + 32*z**2 - 63*z - 26. Let y(u) = 370*u**3 + 160*u**2 - 316*u - 131. Let o(k) = 33*g(k) - 6*y(k). Factor o(p).
-3*(p - 8)*(p - 3)*(3*p + 1)
Factor 1411344/7 + 4/7*s**2 - 4752/7*s.
4*(s - 594)**2/7
Let d(r) be the first derivative of r**6/18 - 8*r**5/15 - r**4/2 + 40*r**3/9 + 61*r**2/6 + 8*r - 4208. Factor d(f).
(f - 8)*(f - 3)*(f + 1)**3/3
Suppose -13*t - 26*t + 62634 = 0. Let a = t + -1603. Factor -4/7*h**a + 88/7*h**2 - 484/7*h + 0.
-4*h*(h - 11)**2/7
Find k such that -44*k**5 + 35*k**2 - 15*k**4 - 23*k**3 - 189*k + 49*k**5 + 99*k + 120*k + 8*k**3 = 0.
-1, 0, 2, 3
Suppose -2*r = 5*r + 42. Let d(t) = -t**2 - 1. Let u(g) be the first derivative of 4*g**3/3 - 5*g**2 + 28*g + 1. Let m(l) = r*d(l) - 2*u(l). Factor m(f).
-2*(f - 5)**2
Let p = 242 - 239. Suppose 6*x**3 + x**4 - 8 + 27*x**3 - 2*x**2 - 30*x**p - 12*x = 0. Calculate x.
-2, -1, 2
Let a(l) be the second derivative of 0*l**2 - 15/2*l**4 + 25/3*l**3 + 61/40*l**5 + 0 + 3/10*l**6 + 1/84*l**7 - 146*l. Suppose a(q) = 0. Calculate q.
-10, 0, 1
Let f(h) be the second derivative of -5/3*h**4 - h**3 + 71*h + 0 - 8/45*h**6 - 14/15*h**5 + 0*h**2. Solve f(q) = 0 for q.
-3/2, -1/2, 0
Let r = -539517 + 3237103/6. Factor -r*y**3 + 49/2 - 91/6*y + 17/6*y**2.
-(y - 7)**2*(y - 3)/6
Let z be 18/15*5/2. Factor 20 - 5*j**z + 15*j - 6*j + 10*j**2 + 11*j - 15*j**2.
-5*(j - 2)*(j + 1)*(j + 2)
Let s(v) be the second derivative of v**5/50 + 2*v**4 + 336*v**3/5 + 3136*v**2/5 - 33*v - 10. Solve s(u) = 0 for u.
-28, -4
Let j be (2 - (-832)/(-12))*123/10. Let k = j - -829. Factor t - k - 1/5*t**2.
-(t - 4)*(t - 1)/5
Factor -11*f - 1833221*f**2 - f**4 + 1833078*f**2 - 29*f**3 - 44*f**3 - 60*f.
-f*(f + 1)**2*(f + 71)
Let y be (-143)/22*(2 - 4). Suppose -2 = y*t - 14*t. Let -4 + t*l**2 - 2*l**3 + 0*l + 2*l - 2*l**4 + 4*l**2 = 0. Calculate l.
-2, -1, 1
Let s = 6/1237 + 1093/29688. Let k(z) be the third derivative of 1/30*z**5 + 0*z + 0*z**3 + s*z**4 + 1/120*z**6 + 11*z**2 + 0. Factor k(c).
c*(c + 1)**2
Solve 249/2 - 57/2*x**2 - 2364*x = 0 for x.
-83, 1/19
Let b(y) be the second derivative of 1/4*y**5 + 30*y + 1186380*y**2 + 15210*y**3 + 2 + 195/2*y**4. Factor b(j).
5*(j + 78)**3
Let o = 34327 + -34322. Let p(q) be the third derivative of -5/192*q**4 + 0*q + 1/8*q**3 - 19*q**2 + 0 - 1/480*q**o. Factor p(r).
-(r - 1)*(r + 6)/8
Suppose 58/7*l**3 + 34*l**2 + 24/7 + 256/7*l = 0. Calculate l.
-2, -3/29
Let z(v) be the first derivative of -v**4 + 1516*v**3/3 - 71440*v**2 - 144400*v - 2077. Find j, given that z(j) = 0.
-1, 190
Let w(g) be the first derivative of -3*g**3/4 - 93*g**2/2 + 63*g - 337. Let w(c) = 0. What is c?
-42, 2/3
Let n be (0/(4/(-4)))/1. Suppose n = -s + 2*a + a - 1, -3 = -4*s + 5*a. Factor -5*g**2 + 0*g**s - 3 + 2*g**3 - 2*g**3 - 7*g - g**3.
-(g + 1)**2*(g + 3)
Let v(d) be the third derivative of 0*d - 1/20*d**5 - 5/32*d**4 - 1/160*d**6 + 0 + 2*d**2 - 1/4*d**3. Factor v(c).
-3*(c + 1)**2*(c + 2)/4
Let q be (-17)/(-5) + 6/10. Suppose 0 = -49*x + 29*x + 40. Determine b so that -6*b**x - 12*b**4 + 2*b + 0*b**2 + 6*b**3 + 10*b**q = 0.
0, 1
Let i be (14/(-98))/((-4)/(-8)) - (-250)/140. Solve -i*x**2 - 3/2*x + 3/2*x**4 + 0 + 3/2*x**3 = 0 for x.
-1, 0, 1
Solve 160/3 - 1/3*s**2 - 9*s = 0 for s.
-32, 5
Let u = -213669 - -2350387/11. Solve -u*k**2 + 0*k + 0 + 2/11*k**3 = 0 for k.
0, 14
Let f be (-16)/1 - 63140/(-3936). Let o(p) be the third derivative of 1/60*p**5 + f*p**4 + 29*p**2 + 0 - p**3 + 0*p. Factor o(d).
(d - 2)*(d + 3)
Let p = -5907 - -41350/7. Let o(v) be the first derivative of -4/21*v**3 - 17 + 0*v + p*v**2. Determine k so that o(k) = 0.
0, 1/2
Factor 0*r + 766/3*r**4 - 14/3*r**5 + 0*r**2 + 220/3*r**3 + 0.
-2*r**3*(r - 55)*(7*r + 2)/3
Suppose -13*p - 92 = -17*p. Factor 3*u**2 + 30 - p - 31 + 21*u.
3*(u - 1)*(u + 8)
Suppose m + 110 = -2*l + 154, -4*l + 202 = 5*m. Solve 100/3 + 2/3*y**4 + 26/3*y**3 + 190/3*y + m*y**2 = 0.
-5, -2, -1
Suppose -314*m**2 - 1680 + 582*m**2 - 272*m**2 - 304*m = 0. What is m?
-70, -6
Let t(b) = b**2 - 19*b + 17. Let n be t(18). Let q = 8 - n. Factor -6 + 10*z + 3 - q - 2*z**2.
-2*(z - 3)*(z - 2)
Let r(p) = 4*p**3 - 4*p**2 - 2*p + 2. Let q be r(1). Factor 8/9*x**3 - 8/9*x**2 + q + 0*x - 2/9*x**4.
-2*x**2*(x - 2)**2/9
Suppose 390224000/11 - 2018400/11*c + 3480/11*c**2 - 2/11*c**3 = 0. What is c?
580
Let r(k) be the second derivative of -k**6/6 - 5*k**5/4 + 25*k**4/4 + 25*k**3/6 - 35*k**2 - 301*k. Find d, given that r(d) = 0.
-7, -1, 1, 2
Let f be 8 + 2052/(-266) + 1/((-126)/8). Let o(y) be the first derivative of -1/4*y**2 - 1/3*y + 1/8*y**4 + f*y**3 + 13 - 1/15*y**5. Let o(b) = 0. What is b?
-1, -1/2, 1, 2
Let d(h) be the first derivative of -1/22*h**4 + 4/11*h**3 - 4/11*h - 4/55*h**5 - 1/11*h**2 + 49. Let d(i) = 0. What is i?
-2, -1/2, 1
Let j(l) be the third derivative of l**8/336 - 11*l**7/42 + 217*l**6/40 + 3463*l**5/60 - 1769*l**4/3 + 1682*l**3 + 4763*l**2. Find w, given that j(w) = 0.
-6, 1, 2, 29
Let d(k) be the third derivative of -k**6/450 + 2*k**5/75 - k**4/10 - 77*k**3/6 - 47*k**2. Let z(o) be the first derivative of d(o). Factor z(g).
-4*(g - 3)*(g - 1)/5
Suppose 28*q - 210 = 7*q. Determine f, given that 5*f**4 - 3*f**4 - 287*f + 0*f**3 + 297*f - 12 - 10*f**3 + q*f**2 = 0.
-1, 1, 2, 3
Let l(p) be the third derivative of -p**7/210 + 7*p**6/120 - 4*p**5/15 + p**4/2 + 4*p**2 - 68*p. Factor l(o).
-o*(o - 3)*(o - 2)**2
Le