- 168*o**2 - o**5.
3*o*(o - 1)*(o + 1)*(o + 2)**2
Let p(t) be the second derivative of 0*t**2 - 11*t + 0*t**3 + 0 + 6/5*t**5 + 3/4*t**4 + 1/2*t**6. Factor p(f).
3*f**2*(f + 1)*(5*f + 3)
Let x(f) = -15*f**5 + 13*f**4 + 20*f**3 - 13*f**2 - 5*f + 9. Let o(s) = 2*s**5 - s**3 - s - 1. Let u(l) = 18*o(l) + 2*x(l). Suppose u(r) = 0. What is r?
-7/3, -2, -1, 0, 1
Let f(p) = p**3 + 4*p**2 + 3. Let x be f(-4). Suppose -12*h + 5*h - 16*h**5 + 36 - 320*h**x - 41*h - 124*h**4 - 296*h**2 = 0. What is h?
-3, -1, 1/4
Let y(o) be the third derivative of -o**5/480 - 3*o**4/64 + 398*o**2. Let y(t) = 0. What is t?
-9, 0
Let n(j) = 44*j - 6 - j**2 + 4*j**2 + 4*j**2 - 40*j. Let s = -9 + 2. Let l(m) = -10*m**2 - 6*m + 9. Let w(u) = s*n(u) - 5*l(u). Factor w(i).
(i - 1)*(i + 3)
Suppose -4*v - 20 = 2*w, -v = -3*w + 31 - 12. Factor -3*z + 0 + 0*z**2 + 9/4*z**3 - 3/4*z**w.
-3*z*(z - 2)**2*(z + 1)/4
Factor -2241*f**2 - 5*f**3 - 20*f - 2231*f**2 + 4452*f**2.
-5*f*(f + 2)**2
Let k(p) be the third derivative of 0 - 4/5*p**3 - 1/10*p**5 + 1/100*p**6 + 0*p + 2/5*p**4 + 15*p**2. What is m in k(m) = 0?
1, 2
Let v(n) be the first derivative of -56*n**3/51 + 25*n**2/17 + 6*n/17 - 98. Factor v(f).
-2*(f - 1)*(28*f + 3)/17
Let t(k) be the second derivative of -1/3*k**4 - 7/15*k**6 + 0*k**2 + 9/10*k**5 + 0 - 5*k + 0*k**3. Factor t(s).
-2*s**2*(s - 1)*(7*s - 2)
Suppose 35*f + 62*f = 0. Factor f - 4/3*a**2 + 4/3*a.
-4*a*(a - 1)/3
Factor 2/3*p**3 + 0*p + 2*p**2 + 0.
2*p**2*(p + 3)/3
Let a(p) be the first derivative of -3*p**4/8 + 4*p**3 + 15*p**2 + 286. Factor a(i).
-3*i*(i - 10)*(i + 2)/2
Let h(w) be the third derivative of -4/15*w**7 + 13*w**2 + 0*w + 1/8*w**4 + 0 + 17/120*w**6 + 1/3*w**5 + 1/21*w**8 + 0*w**3. Determine y, given that h(y) = 0.
-1/4, 0, 1, 3
Let y(z) be the third derivative of -z**7/15120 + z**6/4320 + 3*z**4/4 + 25*z**2. Let f(p) be the second derivative of y(p). Suppose f(a) = 0. Calculate a.
0, 1
Let a(l) be the third derivative of l**7/105 + l**6/60 - 13*l**5/30 - 25*l**4/12 - 4*l**3 - 812*l**2. Factor a(m).
2*(m - 4)*(m + 1)**2*(m + 3)
Let w be (0/13)/(8/8). Let j = 0 - 0. Factor w*y**2 + j*y - 10/7*y**4 - 4/7*y**3 + 0.
-2*y**3*(5*y + 2)/7
Let v(d) be the first derivative of 3*d**4/2 + d**3 - 12*d**2 - 12*d + 113. Solve v(x) = 0 for x.
-2, -1/2, 2
Let h(a) be the third derivative of 0*a + 1/12*a**4 + 5/3*a**3 + 37*a**2 + 1/600*a**5 + 0. Factor h(t).
(t + 10)**2/10
Let j(n) = 5*n - 45. Let b be j(9). Let k(l) be the second derivative of b + 0*l**3 + 1/12*l**4 - 2*l + 0*l**2. Determine q, given that k(q) = 0.
0
Let g(x) = -8*x**5 + 7*x**4 - 7*x**3 + 8*x**2. Let o(c) = c**5 - c**3. Let f(t) = 3*g(t) + 21*o(t). Solve f(q) = 0.
0, 1, 2, 4
Factor 10/3*k**3 + 4/3 + 2/3*k**4 + 6*k**2 + 14/3*k.
2*(k + 1)**3*(k + 2)/3
Determine g so that -5/4*g**3 + 0 - 55/4*g**2 - 25/2*g = 0.
-10, -1, 0
Factor -4*c**2 + 46*c + 2*c**2 - 7*c**2 + 104*c + 51.
-3*(c - 17)*(3*c + 1)
Suppose 0 - 1/3*u**3 + 31/3*u**2 + 0*u = 0. What is u?
0, 31
Let l = 277586 - 14433905/52. Let p = l + -43/4. Factor 56/13*r - 16/13 - 16/13*r**4 + p*r**5 + 50/13*r**3 - 76/13*r**2.
2*(r - 2)**3*(r - 1)**2/13
Let h(o) = 3*o**4 - 2*o**2 - 4*o**3 - 11 + 28*o**3 + 5*o**2 - 24*o. Let q(c) = -4*c**4 - 36*c**3 - 4*c**2 + 36*c + 16. Let w(v) = -8*h(v) - 5*q(v). Factor w(g).
-4*(g - 1)*(g + 1)**2*(g + 2)
Factor 7/6*o**3 - 47*o**2 + 480*o - 400/3.
(o - 20)**2*(7*o - 2)/6
Let k be (-15)/18*30/(-50). What is u in 3/2 + 5/2*u**2 - 7/2*u - k*u**3 = 0?
1, 3
Let v(x) be the third derivative of -7*x**6/48 - 167*x**5/40 + 73*x**4/24 - 775*x**2. Find l, given that v(l) = 0.
-73/5, 0, 2/7
Factor 430 - 390*a - 460 - 350*a**4 - 365*a - 2308*a**2 - 4020*a**3 + 250*a**5 + 301*a.
2*(a - 5)*(a + 3)*(5*a + 1)**3
Let c be 9 + -8 + -5 + (-38)/(-8). Factor 9/8*b + c*b**2 - 3/4.
3*(b + 2)*(2*b - 1)/8
Let k(q) be the third derivative of -1/20*q**4 + 0 + 1/100*q**5 - 22*q**2 + 0*q - 3/10*q**3. Factor k(b).
3*(b - 3)*(b + 1)/5
Let v(t) be the first derivative of -22/9*t**3 - 4*t**2 + 32 + 14/15*t**5 + 8/3*t + 2*t**4. Suppose v(k) = 0. What is k?
-2, -1, 2/7, 1
Let k(p) be the third derivative of -2*p**2 + 0*p + 1/60*p**6 + 0 - 1/20*p**5 + 1/210*p**7 + 2/3*p**3 - 1/6*p**4. Find n such that k(n) = 0.
-2, 1
Solve -352/3*d + 14/3*d**5 - 622/3*d**2 - 235/3*d**4 + 1067/3*d**3 + 128/3 = 0.
-1/2, 2/7, 1, 8
Suppose 3*z = r + 1, -2*z + 1 + 1 = 0. Factor -392*c**2 - 9*c**3 - 11*c**3 + 356*c**r + c**4 - 28*c - 5*c**4 - 8.
-4*(c + 1)**3*(c + 2)
Let b(l) be the third derivative of -l**5/35 - l**4/6 + l**2 - 70. Factor b(g).
-4*g*(3*g + 7)/7
Let m = -3/1870 - -50511/13090. Factor -3/7*i**4 + 0 + m*i - 45/7*i**2 + 3*i**3.
-3*i*(i - 3)**2*(i - 1)/7
Let f(g) be the first derivative of -1/2*g**3 + 13/20*g**2 + 1/5*g - 55. Solve f(u) = 0.
-2/15, 1
Suppose -6 + 4/3*n + 2/9*n**2 = 0. Calculate n.
-9, 3
Let y(i) be the second derivative of 0 - 3*i + 32/39*i**3 - 16/13*i**2 - 4/13*i**4 - 1/195*i**6 + 4/65*i**5. Find b, given that y(b) = 0.
2
Determine k so that 1/4*k**2 + 529 + 23*k = 0.
-46
Let y(q) = q**3 + 9*q**2 + 14*q + 2. Let k be y(-7). Factor -12*o**3 + 3 + 158*o**2 - 158*o**k + 9*o.
-3*(o - 1)*(2*o + 1)**2
Let 9/2 + 9*u**3 + 33/2*u + 21*u**2 - 3/2*u**4 - 3/2*u**5 = 0. Calculate u.
-1, 3
Let u(w) be the second derivative of -w**5/100 + w**4/40 + w**3/5 + 2*w**2 + 33*w. Let y(t) be the first derivative of u(t). Solve y(g) = 0.
-1, 2
Suppose -643*z = -656*z. Let v(q) be the second derivative of -3*q - 2/3*q**3 - 4*q**2 + 1/3*q**4 + z. Factor v(a).
4*(a - 2)*(a + 1)
Let j(l) = 11*l**2 + 5*l - 11. Let w(u) be the third derivative of -u**5/12 - u**4/12 + 5*u**3/6 + 17*u**2. Let v(y) = 2*j(y) + 5*w(y). Let v(f) = 0. What is f?
-1, 1
Let g be -6 + (10 - 4) + 36/12. Let 0 + 15/2*b**2 + 9/2*b - 3*b**g = 0. What is b?
-1/2, 0, 3
Factor -4*m**3 + 6*m**4 + 18*m**3 + m**5 + 7*m**2 + 9*m - 4 - 15*m**2 + 24*m**2 + 6.
(m + 1)**4*(m + 2)
Suppose -14/3*z**4 + 2078/15*z**3 + 1576/15*z - 224*z**2 - 224/15 = 0. Calculate z.
2/7, 2/5, 1, 28
Let w be (4 + (-36)/8)*0. Let u(h) be the first derivative of w*h + 1/12*h**4 - 2/15*h**5 + 0*h**3 - 5 + 0*h**2 + 1/18*h**6. Factor u(z).
z**3*(z - 1)**2/3
Let u(z) be the second derivative of -z**4/48 - z**3/24 - 2*z + 24. Let u(h) = 0. What is h?
-1, 0
Let c(r) be the first derivative of r**4/20 + 14*r**3/15 + 43*r**2/10 + 6*r + 655. Suppose c(s) = 0. What is s?
-10, -3, -1
Suppose 0 = -u - 3 + 5. Let n = 5 - u. What is c in -3*c + 2*c**n + 3*c**3 - 2*c**3 = 0?
-1, 0, 1
Let f(m) be the first derivative of -m**4/16 - 2*m**3/3 + 256. Factor f(l).
-l**2*(l + 8)/4
Let -4 + 225/2*q**4 - 545/2*q**3 + 91*q**2 + 10*q = 0. Calculate q.
-1/5, 2/9, 2/5, 2
Let i = -4292 - -4294. Factor 0*h**i + 2/11*h**5 - 6/11*h**4 + 0 + 0*h + 4/11*h**3.
2*h**3*(h - 2)*(h - 1)/11
Let x(s) be the second derivative of -8/9*s**4 - 8/9*s**3 + 0 - 1/3*s**5 + s - 2/45*s**6 + 0*s**2. Determine h so that x(h) = 0.
-2, -1, 0
Let s(y) = 4*y + 4. Let u be s(-2). Let w be (-3 + -1)*(-5 - u). Factor 3*l**w - 48*l**3 + 26*l**3 + 3 - 6*l**2 + 22*l**3.
3*(l - 1)**2*(l + 1)**2
Let o = -6602 + 6604. Suppose -18/13*n**5 - 38/13*n**3 + 60/13*n**4 - 44/13*n**o + 56/13*n - 16/13 = 0. Calculate n.
-1, 2/3, 1, 2
Solve -304/7*m**2 + 52/7*m**4 - 152/7*m**3 - 4/7*m**5 + 1056/7*m + 1152/7 = 0 for m.
-2, -1, 4, 6
Let c(k) = k**2 - 5*k + 9. Let h be c(5). Suppose 2*t - 24 = 4*n, -5*t = -8*t - 3*n + h. Factor -t*y**2 - 8/3*y**4 + 22/3*y**3 + 2/3*y + 2/3.
-2*(y - 1)**3*(4*y + 1)/3
Factor 4418/5 + 2/5*n**2 + 188/5*n.
2*(n + 47)**2/5
Suppose -53*w - 1006 + 1112 = 0. What is n in -16 - 1/4*n**w - 4*n = 0?
-8
Let -238/5*a**3 + 0*a + 0 - 4/5*a**2 = 0. What is a?
-2/119, 0
Let d(j) be the first derivative of 1431644*j**4/11 + 40328*j**3/11 + 426*j**2/11 + 2*j/11 - 788. Factor d(z).
2*(142*z + 1)**3/11
Let x(t) be the third derivative of -t**5/240 + t**4/96 + 5*t**3/6 - 4*t**2 + 18*t. Let x(d) = 0. Calculate d.
-4, 5
Suppose j = 8*x - 9*x + 672, 2*x = 4*j + 1356. Let c = -4710/7 + x. Factor -8/7*m**3 - 4/7 + c*m**2 + 4/7*m + 4/7*m**5 - 4/7*m**4.
4*(m - 1)**3*(m + 1)**2/7
Suppose -76*f - 47*f + 288 = 21*f. Find z, given that 2*z**3 - 8/7 - 2/7*z**f - 16/7*z + 10/7*z**4 + 2/7*z**5 = 0.
-2, -1, 1
Let i(v) = 17*v**3 - 13*v**2 + 3*v + 3. Let q(f) = -14*f**3 + 12*f**2 - 2*f - 4. Let m(u) = -4*i(u) - 5*q(u). Facto