e x, given that r(x) = 0.
0, 3, 16
Let b(f) be the first derivative of -800*f**5 + 4020*f**4 - 81602*f**3/15 + 804*f**2/5 - 8*f/5 - 1566. Factor b(j).
-2*(j - 2)**2*(100*j - 1)**2/5
Suppose 5*p - 65 = -4*b, -b - 5 = -4*p + 26. Suppose 0 = -2*i - 3*i - p*i. Find m, given that 3/4*m**2 - 9/2*m + i = 0.
0, 6
Let m(h) be the second derivative of -h**7/63 - 13*h**6/45 - 3*h**5/10 + 37*h**4/18 + 10*h**3/9 - 8*h**2 - 1543*h. Suppose m(o) = 0. What is o?
-12, -2, -1, 1
Suppose v - 25 - 7 = 0. Factor 8*o - 42*o**3 + v*o + 46*o**3 - 52*o**2 + 96.
4*(o - 12)*(o - 2)*(o + 1)
Factor -198 - 24*l + 3/2*l**2.
3*(l - 22)*(l + 6)/2
Let z(x) be the first derivative of 5440/3*x**3 + 0*x - 1904/5*x**5 - 108 + 400*x**2 + 49/3*x**6 + 2172*x**4. Factor z(j).
2*j*(j - 10)**2*(7*j + 2)**2
Suppose 5*l - y = 20, 4*l + 2*y = 8 + 8. Find p, given that 3*p + 292*p**2 - l*p - 296*p**2 = 0.
-1/4, 0
Let f(v) be the second derivative of -3*v**5/20 + v**3/2 + 2*v + 169. Suppose f(a) = 0. What is a?
-1, 0, 1
Let z be 4 - (6 + 3) - -6. Let r(g) = -6*g**2 + 59*g - 99. Let l(s) = -s**2 - s + 1. Let n(j) = z*r(j) - l(j). Factor n(t).
-5*(t - 10)*(t - 2)
Let w be -1 + 25/2 - (-5)/(-10). Suppose -7*x + w*x - 12 = 0. Factor -8*c**2 + 16*c**x + c + 3*c + 19*c**3 - 31*c**3.
4*c*(c - 1)**2
Suppose 35 + 1 = -2*q. Let m be 4*5/(-10) - q/2. Let -6*h**2 + 6*h**3 - 12 + m - 2*h**4 + 5 + 2*h = 0. Calculate h.
0, 1
Let p(i) be the first derivative of 117*i**4/8 - 35*i**3 - 21*i**2 + 36*i + 795. Suppose p(k) = 0. Calculate k.
-2/3, 6/13, 2
Factor 160/9 + 6424/3*u**2 - 1172/3*u + 484/9*u**3.
4*(u + 40)*(11*u - 1)**2/9
Let k be (-3)/((-51)/(-2))*1020/(-2340)*13. Suppose -1/3*t**2 + 1/3*t + k = 0. Calculate t.
-1, 2
Suppose -6*h = h - 2*h. Suppose s - 4*z + 18 = h, 3*z - z = -4*s + 18. Determine b so that -2*b**2 - 6*b**4 + 2 - 10*b**2 + 3*b + 3*b**s + 1 - 15*b**3 = 0.
-1, 1/2
Let v be ((-18)/(-12) - 1)*6. What is p in p**2 + v*p**4 - p**2 + 6*p**3 - 6*p - 6*p**2 + 3*p**2 = 0?
-2, -1, 0, 1
Let l(t) be the second derivative of -t**4/108 + t**3/2 + 14*t**2/9 - 3160*t. Let l(a) = 0. What is a?
-1, 28
Let y be 27/8 - (1 - 10/16). Determine h so that -340*h**5 + 6*h**4 - h**3 - 6*h**2 - h**y + 344*h**5 - 2*h = 0.
-1, -1/2, 0, 1
Let y(b) = -b**5 + b**3 + b + 1. Let m = 16 - 13. Let p(f) = -8*f**m - f**4 + 8*f**5 - 1 - 2 - 5*f + 3*f**4 - 2*f**2 - 2. Let s(v) = p(v) + 5*y(v). Factor s(c).
c**2*(c - 1)*(c + 1)*(3*c + 2)
Let s(y) = y**2 + 399*y - 402. Let h(b) = -4*b**2 - 1596*b + 1609. Let j(u) = 4*h(u) + 18*s(u). Determine a so that j(a) = 0.
-400, 1
Let n(m) be the third derivative of m**8/420 + m**7/105 + m**6/90 + 7*m**3 - 27*m**2. Let f(d) be the first derivative of n(d). Find a such that f(a) = 0.
-1, 0
Let g = 127 - 91. Suppose 17*b = 14*b + g. Let -4 + 5*d**5 - 10*d - 15*d**2 + 4*d**3 + d + 6 - b*d**4 + 25*d**2 = 0. Calculate d.
-1, 2/5, 1
Suppose 2*f - 4*p = 8022 - 2022, -p + 6005 = 2*f. Determine j so that -204*j - 5799*j**2 + 5802*j**2 + f + 466 = 0.
34
Let t be ((-159)/2385)/((-62)/20 - (5 - 8)). Find o such that t*o**4 + 0*o**2 + 4/3*o - 2/3 - 4/3*o**3 = 0.
-1, 1
Let g(c) be the third derivative of c**5/15 - 13*c**4 - 158*c**3/3 + 587*c**2. Factor g(s).
4*(s - 79)*(s + 1)
Let t be (646/(-14212) - 10/22)/((-2)/1 - 0). Factor -15*u - 5/2*u**3 - 37/4*u**2 - 9 - t*u**4.
-(u + 2)**2*(u + 3)**2/4
Let 45*p - 43836*p**2 - 216*p + 43835*p**2 = 0. Calculate p.
-171, 0
Let z(o) = 4*o**3 - 4*o**2 - 946*o + 826. Let x(d) = -5*d**3 + 25*d**2 + 945*d - 825. Let y(b) = -6*x(b) - 7*z(b). Suppose y(f) = 0. Calculate f.
1, 8, 52
Solve -1/3*h**4 + 11*h**2 - 28/3*h - 20 + 0*h**3 = 0 for h.
-6, -1, 2, 5
Let r(k) = -2*k - 5*k**2 + 10*k + 4*k**3 - 7*k - 3*k + 7. Let l(h) = -h**3 + 2*h**2 + h - 2. Let q(c) = 7*l(c) + 2*r(c). Factor q(m).
m*(m + 1)*(m + 3)
Let h(t) = 13*t - 15*t**3 - 15*t**2 + 7*t**3 + 9*t**3 + 16. Let f be h(14). Factor 4*r**2 - 5*r**2 - 2*r - 2*r**f + 2 - r**2.
-2*(r + 1)*(2*r - 1)
Let w(p) = -6*p**2 - 55*p + 11. Let o(y) = y**2 + y - 12. Let j(k) = -15*o(k) - 3*w(k). Factor j(v).
3*(v + 1)*(v + 49)
Let r(w) be the second derivative of -w**7/280 + 9*w**5/40 + 14*w**3/3 + 13*w - 1. Let v(q) be the second derivative of r(q). Factor v(i).
-3*i*(i - 3)*(i + 3)
Let x(i) = -i**2 - 331*i + 3062. Let h be x(9). Let 0 - 24/5*n**3 + 12/5*n - h*n**4 - 2/5*n**2 = 0. Calculate n.
-2, -1, 0, 3/5
Let w(t) be the third derivative of -t**7/105 - 3*t**6/10 - 31*t**5/10 - 47*t**4/3 - 44*t**3 + 9907*t**2. Solve w(p) = 0 for p.
-11, -3, -2
Let s(i) be the second derivative of -1/32*i**4 + 25/8*i**3 + 8 + 4*i - 1875/16*i**2. Factor s(h).
-3*(h - 25)**2/8
Let y(v) be the first derivative of -5*v**3 + 6*v**2 + 36 + 3/4*v**4 + 0*v. Factor y(r).
3*r*(r - 4)*(r - 1)
Suppose 4*s + 3*s - 196 = 0. Suppose 4*u - 4*a = s, -4*a = -a - 15. Factor -2*x**5 + 3377*x**2 - u*x**4 - 3401*x**2 - 5*x - 26*x**3 - 3*x.
-2*x*(x + 1)**2*(x + 2)**2
Suppose -312 - 178*h**2 + 77*h - 193 + 177*h**2 + 283 = 0. What is h?
3, 74
Factor -442/7*u - 152/7*u**2 - 292/7 - 2/7*u**3.
-2*(u + 1)*(u + 2)*(u + 73)/7
Suppose 928 + 20 = -2*w. Let h = w + 477. Factor 0*x - 3/5*x**2 + 3/5*x**h + 0.
3*x**2*(x - 1)/5
Let r(o) be the first derivative of -44*o**3/15 + 212*o**2/5 + 32*o - 790. Let r(j) = 0. What is j?
-4/11, 10
Let n(l) = -l**3 - 156*l**2 - 24*l - 4. Let g(q) = 4*q**3 + 624*q**2 + 108*q + 18. Let k(t) = 4*g(t) + 18*n(t). Factor k(v).
-2*v**2*(v + 156)
Let o(j) be the first derivative of -20/9*j**3 + 1/24*j**4 - 141 + 147*j + 119/4*j**2. Factor o(t).
(t - 21)**2*(t + 2)/6
Factor -1851*a**3 + 19 + 1865*a**3 - 19 + 24*a**2 + 2*a**4.
2*a**2*(a + 3)*(a + 4)
Let d(g) be the second derivative of -g**5/10 - 5*g**4/12 - g**3/3 + 5*g**2/2 + 50*g. Let n(o) = -o**3 - 2*o**2 + 3. Let c(j) = 3*d(j) - 5*n(j). Factor c(s).
-s*(s + 2)*(s + 3)
Suppose -3*k - 4*p - 1 = 0, -4*k - p + 8 = 2*p. Let 2*s**3 + 10*s**3 + 8*s**5 - 4*s**5 - s**k + 12*s**4 = 0. What is s?
-2, 0
Let t(x) be the second derivative of x**6/75 + 151*x**5/150 + 2381*x**4/90 + 3787*x**3/15 + 1176*x**2/5 - 2816*x. Determine g, given that t(g) = 0.
-21, -8, -1/3
Suppose 4/3*w**2 + 312 + 476/3*w = 0. Calculate w.
-117, -2
Factor 1042*w**2 - 24*w + 0*w**3 + w**3 + 3*w**3 - 1022*w**2.
4*w*(w - 1)*(w + 6)
Let v(j) be the second derivative of 2*j**6/15 - 773*j**5/5 + 199691*j**4/4 - 298378*j**3/3 + 74498*j**2 + 6*j + 22. Factor v(z).
(z - 386)**2*(2*z - 1)**2
Let g(u) be the first derivative of 14*u**3 - 24*u**2 + 18*u**4 - 27/5*u**5 - 91 + 9*u. What is c in g(c) = 0?
-1, 1/3, 3
Let p(t) = -34*t**3 - 40*t**2 + 42*t + 168. Let i = 88 - 93. Let q(f) = 14*f**3 + 16*f**2 - 17*f - 67. Let d(w) = i*p(w) - 12*q(w). Factor d(o).
2*(o - 2)*(o + 3)**2
Let n(d) be the first derivative of 12*d**2 + 18/7*d + 48 + 56/3*d**3. Determine r so that n(r) = 0.
-3/14
Let m(u) be the first derivative of 49*u**4/20 - 3899*u**3/15 + 1108*u**2/5 - 316*u/5 + 1551. Factor m(h).
(h - 79)*(7*h - 2)**2/5
Let i(g) be the third derivative of g**6/120 + g**5/15 + 5*g**4/24 + g**3/3 + 1475*g**2 - g. Factor i(q).
(q + 1)**2*(q + 2)
Let x(n) be the third derivative of -34*n**7/175 - 271*n**6/200 + 18*n**5/25 + 271*n**4/40 - 2*n**3/5 + 962*n**2. Find b, given that x(b) = 0.
-4, -1, 1/68, 1
Let v = 43005 - 43002. Let 0*t + 0 + 2/15*t**v - 2/15*t**2 = 0. What is t?
0, 1
Let i be 4*-1 + (-52)/(-8) - 21/42. Let y(x) = x + 6. Let k be y(-3). Factor 1/6*r - 1/6*r**k + 1/3*r**i - 1/3.
-(r - 2)*(r - 1)*(r + 1)/6
What is c in 998*c**4 - 389*c**2 + 382*c**4 + 194*c**2 + 8 - 281*c**2 - 941*c**3 + 916*c - 887*c**3 = 0?
-2/3, -1/115, 1
Let i(y) = y**4 - 30*y**3 + 60*y**2 - 40*y + 4. Let b(l) = l**4 - 1. Let v be 27/(-45) + (60/(-25) - -2). Let x(m) = v*i(m) - 4*b(m). Find d such that x(d) = 0.
0, 2
Let w(i) be the first derivative of -i**6/720 - 13*i**5/120 - 169*i**4/48 - i**3 - 24*i + 69. Let f(s) be the third derivative of w(s). Factor f(k).
-(k + 13)**2/2
Let a = 1314294/77 + -119480/7. Let g = 10 - 6. Determine h, given that -4/11*h**3 + 0 + 2/11*h**2 - a*h**g + 4/11*h = 0.
-2, -1, 0, 1
Let w = 8832 - 8832. Let z = 5 - -2. Factor -z*o**2 + w*o**2 + 3*o**3 + 5*o - 3*o**2 + 2*o**3.
5*o*(o - 1)**2
Let l(i) be the first derivative of -i**6/75 + i**5/50 + i**4/30 - i**3/15 + 58*i + 49. Let m(h) be the first derivative of l(h). Let m(g) = 0. What is g?
-1, 0, 1