(g + 1)**3
Let h(p) be the third derivative of p**11/498960 - p**9/30240 + p**8/15120 - p**5/30 - 23*p**2. Let l(a) be the third derivative of h(a). Factor l(f).
2*f**2*(f - 1)**2*(f + 2)/3
Let i(w) = 3*w**2 - 9*w. Let d(s) = 2*s**2 - 8*s. Let j(l) = -5*d(l) + 4*i(l). Solve j(v) = 0 for v.
-2, 0
Let o = 820 + -817. Let k(n) = -n + 6. Let y be k(6). Factor -t + y + 5/2*t**2 - 3/2*t**o.
-t*(t - 1)*(3*t - 2)/2
Let f = -7 + 5. Let z be 1*(f + 1)*-2. Factor -2*c**2 + 3*c**z - 18 - 5*c**2 + 2*c**2 + 12*c.
-2*(c - 3)**2
Factor 1/10*i**2 - 1/10*i**3 - 1/10*i**4 + 0 + 1/10*i.
-i*(i - 1)*(i + 1)**2/10
Factor -2/3*g**3 + 4/3*g**2 - 2/3*g + 0.
-2*g*(g - 1)**2/3
Suppose 4*b + 70 = 5*b. Let f be -6*4*(-5)/b. Determine j, given that -f*j - 3/7*j**3 - 11/7*j**2 - 4/7 = 0.
-2, -1, -2/3
Let z(f) be the first derivative of f**4/2 - 4*f**3 - 9*f**2 + 28*f - 136. Suppose z(o) = 0. What is o?
-2, 1, 7
Let u(o) be the first derivative of -10/17*o + 34 + 10/51*o**3 - 1/17*o**2 + 1/34*o**4. Solve u(g) = 0 for g.
-5, -1, 1
Let h be 10 + -3 + -3 + (-420)/112. Let n be 0 + 2 + (-2)/2. Factor -3*b - 3/2*b**3 - h*b**4 - 13/4*b**2 - n.
-(b + 1)**2*(b + 2)**2/4
Let o(p) be the second derivative of p**4/42 + 6*p**3/7 - 19*p**2/7 + 36*p. Factor o(h).
2*(h - 1)*(h + 19)/7
Factor -1/2*y**3 - 1/4 + 3/2*y**2 - 5/4*y**4 - 1/4*y + 3/4*y**5.
(y - 1)**3*(y + 1)*(3*y + 1)/4
Let p(l) be the first derivative of l**5/25 + 11*l**4/10 - 127*l**3/15 + 106*l**2/5 - 108*l/5 + 901. Factor p(m).
(m - 2)**2*(m - 1)*(m + 27)/5
Let c be -15*(2/(-6) + (-4)/6). Suppose c*o - 20*o = -15. Factor 2/5*s - 6/5*s**2 - 2/5*s**4 + 0 + 6/5*s**o.
-2*s*(s - 1)**3/5
Let m(q) be the first derivative of 6*q**5/5 - 51*q**4/4 + 19*q**3 + 21*q**2 - 50. Find i, given that m(i) = 0.
-1/2, 0, 2, 7
Let k(y) be the third derivative of -y**6/70 + 3*y**5/140 + y**4/14 - 3*y**3/14 + 125*y**2. Find b such that k(b) = 0.
-1, 3/4, 1
Let i(h) be the second derivative of -h**4/4 + 33*h**3/2 - 93*h**2 - 126*h - 3. Factor i(w).
-3*(w - 31)*(w - 2)
Let a be (1/15)/(1/((-11)/(-616))). Let q(v) be the third derivative of 1/160*v**6 - 1/80*v**5 - a*v**7 + 0*v**3 + 0 - 3*v**2 + 0*v + 1/96*v**4. Factor q(o).
-o*(o - 1)**3/4
Let v(o) be the third derivative of o**6/160 - o**5/48 - 11*o**4/96 - o**3/8 - 97*o**2. Factor v(t).
(t - 3)*(t + 1)*(3*t + 1)/4
Let s be (-3)/((-7)/((-42)/2)*-9)*2. Find b such that 7*b - 3/2*b**s - 4 = 0.
2/3, 4
Let u = 11309896407/580 + -19499827. Let n = -1/116 - u. Let 6/5*t**2 + n*t - 23/5*t**3 + 7/5*t**4 - 8/5 = 0. What is t?
-1, 2/7, 2
Let a(w) be the third derivative of 0*w**4 + 0 + 16*w**2 + 0*w**3 + 1/20*w**5 + 0*w - 1/40*w**6. Find n, given that a(n) = 0.
0, 1
Let 717*k**3 + 6*k**4 + 2*k**2 - 1439*k**3 - 2*k**5 + 716*k**3 = 0. Calculate k.
0, 1
Let j(c) = 3*c - 9. Let k = 5 - 0. Let f be j(k). Factor -28*t**3 + 4 - 2*t**5 - 18*t - t**2 + 33*t**2 + f*t**4 + 6*t**4.
-2*(t - 2)*(t - 1)**4
Let j(q) be the first derivative of -q**4/2 - 8*q**3 - 36*q**2 + 29. Factor j(z).
-2*z*(z + 6)**2
Suppose -8/19*k + 18/19*k**3 + 0*k**2 - 4/19*k**4 - 6/19*k**5 + 0 = 0. What is k?
-2, -2/3, 0, 1
Let o be (-1 + (-30)/(-14))/(11121/847 + -13). Factor -16/5 + 2*f**3 - o*f**2 + 56/5*f.
2*(f - 2)**2*(5*f - 2)/5
Suppose -4 = -n, -n - n = 5*k - 18. Let 8/5*c**k - 2/5*c**3 - 6/5*c + 0 = 0. Calculate c.
0, 1, 3
Let 0 + o - 10/3*o**2 + o**3 = 0. What is o?
0, 1/3, 3
Let n(m) be the second derivative of 2*m**6/15 - 4*m**5/5 - 7*m**4/3 + 20*m**3/3 + 96*m. Factor n(b).
4*b*(b - 5)*(b - 1)*(b + 2)
Let 0 - 1/6*p - 3/2*p**3 - 1/3*p**5 + 7/6*p**4 + 5/6*p**2 = 0. What is p?
0, 1/2, 1
Let 3/4*p - 3/4*p**4 + 0 - 3/4*p**3 + 3/4*p**2 = 0. Calculate p.
-1, 0, 1
Let b be (9/((-45)/10))/(30/(-1)). Let d(o) be the third derivative of 1/600*o**6 + 0 + b*o**3 + 0*o**5 - 1/40*o**4 + 0*o + 6*o**2. Factor d(y).
(y - 1)**2*(y + 2)/5
Let j(x) be the third derivative of x**7/1575 + 17*x**6/300 + 104*x**5/75 - 169*x**4/45 - 299*x**2. Determine a, given that j(a) = 0.
-26, 0, 1
Let x(q) be the first derivative of -q**5/20 + 13*q**4/16 + q**3/4 - 41*q**2/8 + 13*q/2 + 88. Let x(b) = 0. What is b?
-2, 1, 13
Let n(s) be the second derivative of 8*s**2 + 1/5*s**5 + 0 + 16/3*s**3 + 5/3*s**4 - 13*s. What is x in n(x) = 0?
-2, -1
Let o(p) be the second derivative of -2*p + 0 - 7/60*p**4 + 2/15*p**3 + 7/300*p**6 + 4*p**2 - 1/75*p**5. Let n(v) be the first derivative of o(v). Factor n(d).
2*(d - 1)*(d + 1)*(7*d - 2)/5
Let f(t) be the third derivative of t**8/2520 + t**7/315 + t**6/135 + 10*t**3/3 + 34*t**2. Let m(p) be the first derivative of f(p). What is v in m(v) = 0?
-2, 0
Let q(o) = 25*o**4 - 68*o**3 + 79*o**2 - 59*o + 13. Let x(d) = 26*d**4 - 68*d**3 + 78*d**2 - 62*d + 14. Let k(c) = -6*q(c) + 5*x(c). Factor k(p).
-4*(p - 1)**3*(5*p - 2)
Let c be 2/(-9) + 450/567. Let n be (-4)/(-38) + 72/38. Suppose 4/7*j - c*j**n + 8/7 = 0. Calculate j.
-1, 2
Let r = 242 + -241. Let a(i) be the first derivative of -4/3*i**3 + r + 4*i + 0*i**2. Let a(y) = 0. What is y?
-1, 1
Let y(h) = h**3 - 12*h**2 + 12*h - 8. Let p be y(11). Solve -f**4 + 150*f - 318*f**2 - 2*f**4 + 303*f**2 - 24*f**p = 0.
-5, 0, 2
Let 3*p**3 + 56*p**2 - 2 - 3*p**4 + 2 - 41*p**2 + 9*p = 0. What is p?
-1, 0, 3
Suppose 5*i + 27 = m, 2*m + 9 = -m - 3*i. Factor -4 + 10*b**2 - 4*b**2 - 5*b**m.
(b - 2)*(b + 2)
Let n(k) = 2*k + 27. Let u be n(-11). Let 59*a**2 + u*a**3 - 19*a**2 - 5*a**5 - 15*a**4 - 25*a**2 = 0. What is a?
-3, -1, 0, 1
Let r(q) be the first derivative of -5*q**6/6 - 22*q**5/5 + 15*q**4/4 + 62. Factor r(u).
-u**3*(u + 5)*(5*u - 3)
Let g(l) be the third derivative of l**8/6720 + l**7/840 - l**6/180 + 5*l**4/8 - 17*l**2. Let f(x) be the second derivative of g(x). Find q such that f(q) = 0.
-4, 0, 1
Factor 3*x**3 + 8*x + 120456*x**4 - x**5 - 120460*x**4 + 0*x**3 + 0*x**2 + 14*x**2.
-x*(x - 2)*(x + 1)**2*(x + 4)
Determine f so that -7/2*f**5 + 117/2*f**4 - 168*f + 1039/2*f**2 - 98 - 617/2*f**3 = 0.
-2/7, 1, 2, 7
Let t(w) be the first derivative of 4*w**5/5 + 6*w**4 - 304*w**3/3 + 372*w**2 - 468*w + 462. Determine z so that t(z) = 0.
-13, 1, 3
Let h(s) = -s**3 + 10*s**2 + 11*s - 1. Let x be h(11). Let a be x*1 + 5 + 0. Factor 2*c**3 - 5*c**a - 2*c**4 + 5*c**2 - 2*c + 3*c**2 - c**4.
-2*c*(c - 1)*(c + 1)*(4*c - 1)
Let m = -9773 - -9773. Solve 88/9*c**2 + m + 8/9*c + 38*c**3 + 280/9*c**5 + 542/9*c**4 = 0.
-1, -2/5, -2/7, -1/4, 0
Let b(i) be the second derivative of i**9/3780 - i**7/210 - i**6/90 + 5*i**4/4 + 9*i. Let y(t) be the third derivative of b(t). Factor y(z).
4*z*(z - 2)*(z + 1)**2
Let p be (2 + 8)/(-2*(1 + -2)). Let t be (-2 + 0 + 2)*p/(-10). Determine a, given that 3*a**5 + 24/5*a**4 - 6/5*a**2 + 3/5*a**3 + 0 + t*a = 0.
-1, 0, 2/5
Let v(w) be the third derivative of -w**7/315 - 11*w**6/360 + 17*w**5/45 + 41*w**4/72 - 2*w**3 - 11*w**2 + 2*w. What is i in v(i) = 0?
-9, -1, 1/2, 4
Let j be (3024/(-720))/((-7)/6). Factor -2/5 - j*a**2 - 2*a - 14/5*a**3 - 4/5*a**4.
-2*(a + 1)**3*(2*a + 1)/5
Let w(l) be the second derivative of -7*l**6/15 - 47*l**5/10 - 14*l**4/3 + 4*l**3 + 2*l - 5. Factor w(y).
-2*y*(y + 1)*(y + 6)*(7*y - 2)
Suppose 0 = -6*i - 2328 + 144. Let r = -4728/13 - i. Find m such that r*m**2 + 2/13*m + 2/13*m**3 + 0 = 0.
-1, 0
Determine c so that 1 + 5/3*c**4 - 8/3*c**2 + 1/6*c + 1/3*c**3 - 1/2*c**5 = 0.
-1, -2/3, 1, 3
Suppose 5*i - 25 = -4*v, -27 = -74*v + 71*v - i. Let k(b) be the first derivative of 2/9*b**3 + 0*b**2 - 2/3*b + v. Factor k(r).
2*(r - 1)*(r + 1)/3
Let p(o) be the third derivative of o**6/200 + o**5/300 - o**4/60 + 54*o**2 - 2*o. Determine x, given that p(x) = 0.
-1, 0, 2/3
Let n(s) = 2*s**3 - 6*s**2 - 8*s + 2. Let f be n(4). Factor 0*j**2 - j**3 + f*j + 0*j**3 - 3*j**2 - 4*j.
-j*(j + 1)*(j + 2)
Let f be (-6)/1*((-3798)/540 - -7). Factor -1/5*a**3 + f*a**2 + 0 + 1/5*a - 1/5*a**4.
-a*(a - 1)*(a + 1)**2/5
Let g be 0 + 2*(5 - 2). Suppose -g*m = -m - 30. Factor 10*u**2 - 3*u**3 + m*u**2 - 17*u**2 + 4*u**2.
-3*u**2*(u - 1)
Factor 16/5*s + 2*s**2 - 2/5*s**3 - 24/5.
-2*(s - 6)*(s - 1)*(s + 2)/5
Suppose 55 = -5*a - 2*d + 479, 0 = 5*a + d - 427. Factor -3*f**4 + 48 - 30*f**3 + 149*f**2 - 108*f**2 - a*f**2 + 24*f + 6*f**3.
-3*(f - 1)*(f + 1)*(f + 4)**2
Let x(y) be the second derivative of -17*y**4/12 + 4*y**3 - 25*y**2/2 - 5*y. Let n(h) = 19*h**2 - 23*h + 25. Let w(i) = -6*n(i) - 7*x