j - 3)*(j - 1)/5
Find k, given that -512/17 + 2/17*k**3 - 48/17*k**2 + 288/17*k = 0.
4, 16
Let v(t) = t**3 - 57*t**2 - 59*t + 60. Let z be v(58). Find q such that 2/3*q**z + 2*q + 0 = 0.
-3, 0
Let r = -46 + 50. Let h be (-6)/(-27)*21 - r. Find p such that 7/2*p**2 + h + 1/3*p**3 - 7/6*p**4 - 10/3*p = 0.
-2, 2/7, 1
Let g(d) be the second derivative of -2*d**6/15 - 7*d**5/5 + d**4/3 + 14*d**3/3 - 40*d + 3. Determine a so that g(a) = 0.
-7, -1, 0, 1
Let i = -15 - -12. Let k be (-27)/(-15) + i/(-15). Let -6*v**4 - 2*v**5 - 6*v**3 - 6 - 7 + 13 - 2*v**k = 0. Calculate v.
-1, 0
Let i(o) = -13*o**2 + 143*o - 5. Let j(h) = 5*h**2 - 72*h + 2. Let c(f) = 6*i(f) + 15*j(f). Factor c(v).
-3*v*(v + 74)
Let q(x) be the first derivative of 3/5*x**5 + 3/2*x**4 - 33 - 4*x**3 - 3*x**2 + 9*x. Factor q(j).
3*(j - 1)**2*(j + 1)*(j + 3)
Let s(b) = -b**3 - b**2 + b - 1. Let z(t) = -5*t**4 - 20*t**3 - 40*t**2 - 40*t - 5. Let c(o) = 5*s(o) + z(o). Factor c(n).
-5*(n + 1)**3*(n + 2)
Let j(z) be the third derivative of 0*z**3 + 0*z**5 + 2/525*z**7 - 1/300*z**6 - 1/840*z**8 + 0*z**4 + 0 + 0*z - 6*z**2. Factor j(a).
-2*a**3*(a - 1)**2/5
Let t(w) be the second derivative of -w**6/600 - 41*w**2/2 - 36*w. Let d(u) be the first derivative of t(u). Factor d(v).
-v**3/5
Let n be 0 + (-4 + -1 + 4)*0. Suppose -3*h = -0*h - 2*v, n = 5*h - v - 7. Factor 0 + 4/3*i - 2*i**5 - 2*i**h + 14/3*i**4 - 2*i**3.
-2*i*(i - 1)**3*(3*i + 2)/3
Let g(u) = -3*u**4 + 15*u**3 - 24*u**2 + 6*u + 6. Let x(n) = -6*n**4 + 30*n**3 - 48*n**2 + 11*n + 13. Let z(a) = -13*g(a) + 6*x(a). Factor z(r).
3*r*(r - 2)**2*(r - 1)
Factor -7/5*g**2 + 1/5*g**3 - 9/5 + 3*g.
(g - 3)**2*(g - 1)/5
Let h(o) = -o**3 - 8*o**2 - 2*o - 7. Let i be h(-8). Factor -4*c - 6*c**3 + i*c**3 + 0*c**2 + 8*c**2 - 7*c**3.
-4*c*(c - 1)**2
Let z(m) = -5*m**2 + 10*m - 13. Let a(x) = 14*x**2 - 29*x - 17 + 17 + 38. Let c(i) = -4*a(i) - 11*z(i). Solve c(n) = 0.
3
Let u = 15576 - 15574. Factor 0 + 2/3*m + 4/3*m**u + 2/3*m**3.
2*m*(m + 1)**2/3
Factor 2*d**2 - 1/4*d**3 + 3/2 - 13/4*d.
-(d - 6)*(d - 1)**2/4
Let d = -6884 - -41141/6. Let z = -27 - d. Factor 1/3*g**4 + 0 + 0*g**2 + 0*g + z*g**3 + 1/6*g**5.
g**3*(g + 1)**2/6
Let r(c) be the second derivative of 0*c**3 - 1/3*c**4 + 0 - 15*c - 4/5*c**5 + 0*c**2. Let r(q) = 0. What is q?
-1/4, 0
Let a(x) be the third derivative of -2/3*x**4 + 4/105*x**7 + 2*x**2 - 2/3*x**5 - 1/84*x**8 + 0*x + 1/6*x**6 + 16/3*x**3 + 0. Find n, given that a(n) = 0.
-2, -1, 1, 2
Let v be (20/(-57))/((-8)/132). Let u be 11 - (-3 + 11 + -1). Determine l, given that 50/19*l**u + v*l**3 - 12/19*l**2 + 16/19 - 56/19*l = 0.
-2, -1, 2/5
Suppose h - 794 = -795. Let t(m) = -m + 3*m**2 + 0 - 1 - 2*m**2. Let b(j) = -3*j**3 - 4*j**2 + 7*j + 4. Let o(r) = h*b(r) - 4*t(r). Solve o(k) = 0 for k.
-1, 0, 1
Let u = 455 - 2274/5. Let c(j) be the first derivative of -1 - u*j**4 + 4/15*j**3 + 0*j**2 + 0*j. Factor c(x).
-4*x**2*(x - 1)/5
Let r be -33*(-7)/(-147)*(-12)/66. Let -2/7*h - r*h**3 + 4/7*h**2 + 0 = 0. Calculate h.
0, 1
Let t(k) be the third derivative of k**6/1980 - k**5/660 - 17*k**3/6 + 21*k**2. Let q(n) be the first derivative of t(n). Find r, given that q(r) = 0.
0, 1
Let x = -102 - -105. Suppose -5*n**2 - n**2 + 2*n**x - 2*n**2 - 4 + 10*n = 0. What is n?
1, 2
Suppose 4 + 1 = n. Factor 2*t**5 - 5*t**3 - 3*t**n + 6*t**5.
5*t**3*(t - 1)*(t + 1)
Factor -5329/5 - 1/5*i**2 + 146/5*i.
-(i - 73)**2/5
Let j(g) be the third derivative of g**8/30240 + g**7/1260 + g**6/120 + g**5/20 - g**4/4 + 3*g**2. Let p(b) be the second derivative of j(b). Factor p(x).
2*(x + 3)**3/9
Suppose 5*l - 13 = 2. Suppose 4*s = 2*n + n - l, 5*s - 10 = n. Determine k, given that 19*k + 36*k**3 + 32*k**2 - 20*k**5 + 0*k**n - 32*k**4 - 35*k = 0.
-2, -1, 0, 2/5, 1
Let b(j) be the first derivative of 3*j**5/5 - 3*j**4/4 - 17*j**3 - 45*j**2/2 + 237. Find v such that b(v) = 0.
-3, -1, 0, 5
Find l such that 13*l + 4/5*l**3 + 16/5 + 68/5*l**2 = 0.
-16, -1/2
Let n be (2/21)/(-3 - (-692)/228). Let v = n - 16/7. Factor v + 2/7*d**2 + d.
(d + 3)*(2*d + 1)/7
Let h(j) = 6*j**3 - j**2 + 4*j - 1. Let x be h(3). Let u = x - 1146/7. Factor 0 + 4/7*d**2 + 2/7*d**3 + u*d.
2*d*(d + 1)**2/7
Let f(u) be the second derivative of -u**8/6720 + u**6/720 + u**4/3 + 17*u. Let j(h) be the third derivative of f(h). Factor j(r).
-r*(r - 1)*(r + 1)
Factor -3/2*l**3 - 1/2 + 3/2*l + l**4 - 1/2*l**2.
(l - 1)**2*(l + 1)*(2*l - 1)/2
Suppose 0*j - 3*i = -2*j + 10, -2 = -5*j - 4*i. Suppose -j*o - 15 = -5*p + 3*o, -5*p + 15 = -o. Suppose 1/5*b**4 + 0*b + 0*b**2 + 0 + 0*b**p = 0. What is b?
0
Let x(t) be the third derivative of -t**7/1470 + t**6/210 - t**5/105 - 108*t**2 + 3*t. Solve x(d) = 0 for d.
0, 2
Determine g, given that 4*g - 11/2*g**2 + 7/4*g**3 + 0 = 0.
0, 8/7, 2
Suppose z = -2*y + 5*z + 6, 3*y - 9 = -4*z. Let m be y/6 + (-1)/2. Factor -2/13*x**5 + 6/13*x**3 + 0 + m*x - 4/13*x**2 + 0*x**4.
-2*x**2*(x - 1)**2*(x + 2)/13
Let m(c) = -21*c**4 + 230*c**3 - 12*c**2 - 226*c + 45. Let i(s) = s**4 + 2*s**2 + s. Let x(p) = -4*i(p) + m(p). Find q, given that x(q) = 0.
-1, 1/5, 1, 9
Let m(t) be the second derivative of -3*t**5/40 + 2*t**4 - 137*t**3/36 + 5*t**2/2 + 205*t. Solve m(o) = 0 for o.
1/3, 2/3, 15
Let d(u) = -11*u**2 + 4*u. Let p be (3/3)/((-2)/(-26)). Let h(q) = 5*q**2 - 2*q. Let n(y) = p*h(y) + 6*d(y). Factor n(r).
-r*(r + 2)
Let o = 34 - 95. Let k = -57 - o. What is j in 0*j + 0*j**3 + 1/3*j**2 - 1/3*j**k + 0 = 0?
-1, 0, 1
Let y(p) = 17*p**2 + 25*p - 80. Let c(t) = -81*t**2 - 126*t + 399. Let k(q) = 5*c(q) + 24*y(q). Let k(a) = 0. What is a?
5
Let s(t) be the second derivative of 7/3*t**3 - 4*t + 7/12*t**4 + 3/2*t**2 - 1/5*t**5 + 0. Find o such that s(o) = 0.
-1, -1/4, 3
Let j(c) be the first derivative of -2*c**5/5 - 6*c**4 - 92*c**3/3 - 60*c**2 - 50*c + 34. Suppose j(h) = 0. What is h?
-5, -1
Let z(u) be the third derivative of 1/6*u**4 + 1/120*u**6 + 0 - 15*u**2 - 1/140*u**7 + 1/10*u**5 + 0*u**3 - 1/672*u**8 + 0*u. Solve z(w) = 0 for w.
-2, -1, 0, 2
Solve 16/11*j - 10/11*j**2 - 8/11 + 2/11*j**3 = 0.
1, 2
Let y(o) = -8*o + 128. Let q be y(16). Suppose q + 1/3*h**3 - 1/3*h**2 - 2/3*h = 0. What is h?
-1, 0, 2
Determine g so that -6 - 795*g + 4*g**3 + 1618*g + 28*g**2 - 767*g + 38 = 0.
-4, -2, -1
Factor -5*u + 3178*u**4 - 20*u**2 + 4*u**5 - 12*u**3 - 3*u - 3174*u**4.
4*u*(u - 2)*(u + 1)**3
Let n(a) = -a + 2. Let g be n(2). Let f = -1/10928 + 16393/10928. Solve g*x - f*x**2 + 3/2 = 0.
-1, 1
Let x = -14908 - -14910. Find j such that x*j + 4/3 - 10/3*j**2 = 0.
-2/5, 1
Let x = -4542/35 - -651/5. Determine s, given that x*s**2 - 3/7*s + 0 = 0.
0, 1
Let d(p) be the first derivative of -5*p**3/3 - 725*p**2 - 105125*p - 524. Solve d(u) = 0.
-145
Let s(b) = 2*b**2 - 8*b + 6. Suppose 5*m + 0*m + k = 12, 4*k + 24 = 4*m. Let x be s(m). Factor 2/15*j + x - 2/15*j**2.
-2*j*(j - 1)/15
Let g(j) = -j**3 + 3*j**2 + 2. Let s be g(3). Factor 3*o**s - o**2 + 4*o**3 - 4*o**2 - 2*o**2.
4*o**2*(o - 1)
Suppose -150*o + 146*o = 0. Suppose 4*h + 2*m - 18 = o, 0 = 5*h - 6*h - 5*m + 9. Find t such that 8/3*t**2 + 2*t**h + 0*t - 1/3*t**5 - 4*t**3 + 0 = 0.
0, 2
Let m(c) be the third derivative of -c**5/360 + 7*c**4/144 + 2*c**3/9 - 15*c**2 - 3. Suppose m(b) = 0. What is b?
-1, 8
Let x = 85 + -82. Let u(o) be the second derivative of 3/2*o**2 + x*o - 3/20*o**5 - 3/2*o**3 + 3/4*o**4 + 0. Factor u(y).
-3*(y - 1)**3
Let q = 4692799/122421 + 2/40807. What is i in 140*i - q*i**2 + 60 + 25/3*i**4 - 30*i**3 = 0?
-2, -2/5, 3
Suppose -5*z + 183 = -222. Let p = z + -77. Factor -4/5*s + 2/5*s**2 + 4/5*s**3 + 0 - 2/5*s**p.
-2*s*(s - 2)*(s - 1)*(s + 1)/5
Let k(y) be the second derivative of 11*y**5/10 - 23*y**4/6 + 2*y**3/3 + 186*y. Factor k(m).
2*m*(m - 2)*(11*m - 1)
Let k(f) be the second derivative of f**6/105 + 3*f**5/35 - 13*f**4/42 - 22*f**3/7 + 72*f**2/7 - 201*f - 1. Solve k(c) = 0 for c.
-6, -4, 1, 3
Let x be 3/63*198 + -6. Solve 6*b**3 + 0 - 12/7*b**4 - x*b - 24/7*b**2 = 0.
-1/2, 0, 2
Let o(m) = -22*m - 59*m**2 + 0*m - 4*m - 14*m**3 - 21*m + 9. Let k(n) = -14*n**3 - 58*n**2 - 46*n + 10. Let d(t) = -7*k(t) + 6*o(t). Factor d(w).
2*(w + 2)**2*(7*w - 2)
Let n = 223 - 217. Let u(y) be the first derivative of -y**2 - y + n - 1/3*y**3. Factor u(h).
-(h + 1)**2
Let i be 2/10 - (-4017)/65. Factor 72*f**2 - 4*f**4 - 5 - f**4 - i*f**2.
-5*(