8*d**2 + 2/15*d**6 - 2*d**3. Factor f(l).
4*(l - 1)**2*(l + 1)*(l + 4)
Let p(g) be the third derivative of g**8/84 + 4*g**7/35 + 11*g**6/30 + 2*g**5/5 + g**2 + 162*g. Factor p(c).
4*c**2*(c + 1)*(c + 2)*(c + 3)
Let a(c) be the second derivative of 1/2*c**5 - 5/42*c**7 - 3*c - 5/2*c**2 - 5/6*c**3 + 0 - 1/6*c**6 + 5/6*c**4. What is d in a(d) = 0?
-1, 1
Let n(x) be the second derivative of x**5/4 + 55*x**4/4 + 105*x**3/2 + 155*x**2/2 - 254*x. What is q in n(q) = 0?
-31, -1
Factor 180 - 30*r + 5/4*r**2.
5*(r - 12)**2/4
Let t(v) = v + 1. Let m(c) = -625*c**2 + 617*c + 12. Let d(y) = -m(y) + 2*t(y). Let d(r) = 0. Calculate r.
-2/125, 1
Let m = -3291/55 + 421/5. Let a = m + -262/11. Factor 2/11*d**4 - 4/11 + 10/11*d - 2/11*d**3 - a*d**2.
2*(d - 1)**3*(d + 2)/11
Let a(x) be the second derivative of -3*x - 10*x**2 - 5/12*x**4 + 0 + 10/3*x**3. Factor a(j).
-5*(j - 2)**2
Let h(s) be the second derivative of -s**4/12 - 7*s**3/6 + 9*s**2 - 100*s. Factor h(l).
-(l - 2)*(l + 9)
Factor -233 + 233 + 90*f**2 + 35*f**3 - 45*f.
5*f*(f + 3)*(7*f - 3)
Let x = -2 - 19. Let t = -19 - x. Determine m, given that 3*m**4 - 3*m**t + 201 - 6*m - 3*m**5 - 201 + 9*m**3 = 0.
-1, 0, 1, 2
Suppose 27*k**2 + 12*k + 1 - 45*k + 5 = 0. Calculate k.
2/9, 1
Let b be 4/((-4 - -5) + 1). Let o = 3590/13 + -276. Factor 0 + 2/13*p**b + o*p.
2*p*(p + 1)/13
Suppose -5*m = -3*r - 244, -5*m - 460 = 14*r - 9*r. Let z = -83 - r. Factor -9/2*a**3 - 3/4*a + 0 - 3/4*a**z + 3*a**4 + 3*a**2.
-3*a*(a - 1)**4/4
Let w = -2979/2 - -8939/6. Suppose -1/3*i**3 + 0*i + w*i**2 + 0 = 0. Calculate i.
0, 1
Let q(k) be the third derivative of k**5/100 + 7*k**4/40 + k**3 + 716*k**2. Factor q(s).
3*(s + 2)*(s + 5)/5
Let o(d) be the first derivative of -1/22*d**4 - 8/33*d**3 - 9*d - 4/11*d**2 + 10. Let u(f) be the first derivative of o(f). Determine m so that u(m) = 0.
-2, -2/3
Let l = -7412 + 66716/9. Factor 0*f - l*f**2 + 0 - 2/9*f**3.
-2*f**2*(f + 4)/9
Suppose 108 = -1262*p + 1298*p. Determine r so that 0*r**2 + 2/11*r**p + 0 + 0*r = 0.
0
Factor 3/4*x - 1/4*x**2 + 5/2.
-(x - 5)*(x + 2)/4
Let p(k) be the second derivative of 8*k + 1/3*k**3 - 5/2*k**2 + 0 - 1/60*k**4. Factor p(r).
-(r - 5)**2/5
Let k(z) = -2*z**2 - 17*z. Let y be k(-8). Let x be (-4)/y*6*-2. Suppose -14*g - 4*g - 12*g**2 + x*g - 4*g**3 - 4 = 0. What is g?
-1
Let a be (0*(-3)/(-6))/2. Let b(q) be the second derivative of -1/30*q**4 + 2*q + 0*q**2 + a*q**3 + 0. Suppose b(g) = 0. Calculate g.
0
Suppose -5*j - 4*l + 2 = 0, -2*j + 5*j = -3*l. Solve -88*n**4 - 2*n + 0*n + 4*n**j - 30*n**3 + 4*n + 16*n**4 = 0 for n.
-1/3, 0, 1/4
Let a(u) be the second derivative of -u**8/336 - u**7/70 + u**5/15 - 15*u**2/2 + 8*u. Let s(z) be the first derivative of a(z). Solve s(r) = 0.
-2, 0, 1
Let a = 251/133 - -13/19. Suppose 21 = -4*i + 11*i. What is l in -12/7*l**i - 8/7*l**5 + 0 + 0*l + a*l**4 + 2/7*l**2 = 0?
0, 1/4, 1
Let x be (-1)/(-3 - (1 + -3)). Let v be x*(1 + -2)*-2. Factor s**4 + s**2 + 4*s**2 - 8*s**2 + 1 + s**v.
(s - 1)**2*(s + 1)**2
Let d(g) be the first derivative of -12/5*g**5 + 0*g**2 - 16*g - 32 + 28/3*g**3 - g**4 + 2/3*g**6. Suppose d(l) = 0. Calculate l.
-1, 1, 2
Solve 101750*r**4 + 1 + 55*r**3 - 101635*r**4 + 10*r**5 - 1 = 0.
-11, -1/2, 0
Let r(x) be the first derivative of x**5/30 - x**4/3 + x**3 - 4*x**2/3 + 5*x/6 + 219. Factor r(p).
(p - 5)*(p - 1)**3/6
Let l(a) be the second derivative of a**7/210 - a**6/75 + a**4/30 - a**3/30 + 11*a. Factor l(h).
h*(h - 1)**3*(h + 1)/5
Let b = -5 + 3. Let m(y) = -3*y - 3. Let l be m(b). Factor -4*f**2 + 3*f**2 + 2*f + l*f**2 - 1 - 3*f**2.
-(f - 1)**2
Let y(r) be the third derivative of 1/30*r**4 + 2/3*r**3 - 2/75*r**5 + 0 + 0*r - 3*r**2 + 7/1800*r**6. Let d(g) be the first derivative of y(g). Factor d(m).
(m - 2)*(7*m - 2)/5
Find p such that -p**2 - 8*p + 76 + 3*p - 62 = 0.
-7, 2
Let t be 66/11 + 177/(-30). Let y(o) be the second derivative of -t*o**5 - 2/7*o**2 - 11/21*o**3 - 8/21*o**4 + 0 + 4*o. Factor y(w).
-2*(w + 1)**2*(7*w + 2)/7
Let h(u) be the first derivative of 1/2*u**4 + 8 + 4*u**3 + 9*u**2 + 8*u. Factor h(o).
2*(o + 1)**2*(o + 4)
Let k(n) be the second derivative of n**5/110 - n**4/6 - n**3/33 + n**2 + 4*n + 58. Determine a, given that k(a) = 0.
-1, 1, 11
Find b, given that 4/3*b + 0*b**2 - 4/3*b**3 + 0 = 0.
-1, 0, 1
Factor -24*y**3 - 2*y**4 - 14*y**3 + 23 - 55 - 98*y - 102*y**2.
-2*(y + 1)**3*(y + 16)
Let n be (6/(-27))/((-14)/72). Factor 4/7*r**5 + 32/7*r**2 - 4*r - 8/7*r**4 + 8/7 - n*r**3.
4*(r - 1)**4*(r + 2)/7
Let w(g) = 10*g + 20. Let k be w(16). Factor -d**2 + 0*d**2 + 60*d - k - 4*d**2.
-5*(d - 6)**2
Let n(k) be the second derivative of 0 + k**2 + 5/12*k**4 - 7/6*k**3 + 5*k. Factor n(v).
(v - 1)*(5*v - 2)
Let t(l) be the third derivative of 1/12*l**6 - 1/42*l**7 - 5/336*l**8 - l**2 - 5/6*l**3 + 0 - 5/24*l**4 + 1/6*l**5 + 0*l. Suppose t(p) = 0. Calculate p.
-1, 1
Let s(i) = 155*i**3 - 4860*i**2 + 3165*i - 55. Let r(g) = 11*g**3 - 347*g**2 + 226*g - 4. Let y(m) = -55*r(m) + 4*s(m). Suppose y(t) = 0. What is t?
0, 2/3, 23
Suppose 1 + 3 = 2*w, i = -5*w + 24. Factor 25*a + 4*a**2 - 20*a - i*a**2 + 5*a**3.
5*a*(a - 1)**2
Let q(b) = 3*b**3 - b**2 + 2*b - 1. Let f be q(1). Factor -6*s - 3*s**f + 9*s**2 - 3*s**3 + 3*s**3.
-3*s*(s - 2)*(s - 1)
Let c = 14 + -20. Let q be (2 + 8/c)*9. Factor -2*i + 2*i**2 - 3*i**2 - q + 3 + 2.
-(i + 1)**2
Let t(u) = 15*u**3 + 20*u**2 - 15*u - 20. Let l(m) = -22*m**3 - 30*m**2 + 22*m + 30. Let x = 12 + -5. Let r(f) = x*t(f) + 5*l(f). Factor r(d).
-5*(d - 1)*(d + 1)*(d + 2)
Suppose 0 = -4*v - 3*r - 6, 2*v + 5*r + 10 = 3*v. Suppose -8*l + 4*l + 488 = v. Let 1 - 1 - 4*u**3 + l*u**4 - 118*u**4 - 8*u**2 = 0. What is u?
-1, 0, 2
Let v(t) = 35*t**2 + 90*t. Let i(n) = n**2 + n + 3. Let p(c) = -5*i(c) + v(c). What is g in p(g) = 0?
-3, 1/6
Let g(w) be the third derivative of w**7/1155 + w**6/110 + 4*w**5/165 - w**4/22 - 3*w**3/11 + 252*w**2. Determine f so that g(f) = 0.
-3, -1, 1
Let d(w) = -w**3 + 12*w**2 - 12*w + 17. Let b be d(11). Let u be 3/(-10)*((-11)/b + 1). Determine f, given that 1/4*f**2 - u + 1/4*f**3 - 1/4*f = 0.
-1, 1
Let i = 16811/75636 - 1/25212. Solve -2/9*d**3 - i*d**4 + 2/3*d**2 + 10/9*d + 4/9 = 0 for d.
-1, 2
Let u = 2/1049 + 1037/6294. Solve u*y**3 + 1/3*y**2 + 0 + 1/6*y = 0 for y.
-1, 0
Suppose 3*u = -l + 12, 0 = -0*l + 5*l + 2*u - 8. Let z(q) be the first derivative of q**3 - 3/2*q**2 + 4 + l*q + 3/4*q**4 - 3/5*q**5. Factor z(k).
-3*k*(k - 1)**2*(k + 1)
Solve -23*m**3 + 22*m**3 - 9*m**3 - 2*m**4 - 3*m**4 = 0 for m.
-2, 0
Let l = -617 - -621. Solve 6/11*f - 6/11*f**3 + 4/11 - 2/11*f**l - 2/11*f**2 = 0 for f.
-2, -1, 1
Let d(y) be the first derivative of 0*y - 18 - 4/13*y**2 + 2/39*y**3. Suppose d(g) = 0. Calculate g.
0, 4
Let y = 479/220 - -4/55. Let q(d) be the first derivative of 0*d - 3*d**2 - 5*d**3 + 2 - y*d**4. Factor q(f).
-3*f*(f + 1)*(3*f + 2)
Suppose -2*r + 5*t - 3*t - 4 = 0, 0 = -5*r - 2*t + 4. Suppose 5*c - 16 = 4. Suppose -6*d**2 + 8*d**2 + r*d**2 + c*d = 0. What is d?
-2, 0
Suppose -u = 11*u - 300. Let r be 1*4 + (-65)/u. Let 9/5*b**3 + 2/5*b**2 + 0*b + 0 + r*b**4 = 0. What is b?
-1, -2/7, 0
Find w, given that -3/2*w + 0 - 63/8*w**3 - 15/2*w**2 + 3/4*w**4 + 21/8*w**5 = 0.
-1, -2/7, 0, 2
Factor -4/5 + 1/5*r**2 + 3/5*r.
(r - 1)*(r + 4)/5
Suppose 13*r + 39*r + 0 + 215*r**2 + 0 - 213*r**2 = 0. What is r?
-26, 0
Let s(d) = -3*d**2 + 7*d. Let l be s(2). Suppose 2*g + 4*x + 6 = l, -4*x = 5*g + 4. Let 0 + 1/3*p**4 + 0*p - 1/3*p**2 + g*p**3 = 0. Calculate p.
-1, 0, 1
Let m(j) be the first derivative of j**2 + 27 + 12*j - 2/3*j**3. Factor m(p).
-2*(p - 3)*(p + 2)
Let v be 7/((-21)/12) + 2 + 3. Let z(u) be the first derivative of 4/7*u + 2/21*u**3 + 3/7*u**2 + v. Factor z(j).
2*(j + 1)*(j + 2)/7
Suppose -4*g + 2*w + 172 = 0, 4*w + 6 + 133 = 3*g. Suppose -g = -6*i + 3*i + x, 0 = i - 2*x - 22. Solve 9*z**4 + 4*z**2 - 7*z**5 + 3*z**4 + 3*z**5 - i*z**3 = 0.
0, 1
Let f(a) be the second derivative of a**6/135 - a**5/18 - 4*a**4/27 + 16*a**3/9 - 23*a. What is y in f(y) = 0?
-3, 0, 4
Let p(z) be the third derivative of z**8/50400 + z**7/12600 + z**5/12 + 11*z**2. Let u(y) be the third derivative of p(y). Suppose u(w) = 0. Calculate w.
-1, 0
Let y = -222 + 225. Suppose y*n = 8*n - 15. Factor 0 - 1/2*c - 3/2*c**2 - 3/2*c**n - 1/2*c**4.
-c*(c + 1)**3/2
Let x(p