1
Let l(v) be the third derivative of 0*v**3 + 1/105*v**5 + 0*v - 1/420*v**6 + 0 - 3*v**2 - 1/84*v**4. Factor l(b).
-2*b*(b - 1)**2/7
Suppose -14*z - 12*z**2 + 4*z**3 + 14*z - 8*z**3 = 0. Calculate z.
-3, 0
Let q be (-6)/(-9)*-3 - -2. Suppose y = -q*y + 2. Find s, given that -s**2 - 4*s**5 - 4*s**4 + y*s**5 + 5*s**2 + 2*s**3 = 0.
-2, -1, 0, 1
Let n(m) = m**2 + 19*m - 39. Let z be n(-21). Let s(p) be the first derivative of 3/20*p**4 - 1/10*p**6 - 3/25*p**5 + 2 + 0*p + 1/5*p**z + 0*p**2. Factor s(b).
-3*b**2*(b - 1)*(b + 1)**2/5
Let s(f) be the second derivative of f**7/336 + 7*f**6/240 + 19*f**5/160 + 25*f**4/96 + f**3/3 + f**2/4 - 2*f. Factor s(r).
(r + 1)**3*(r + 2)**2/8
Let u = 6 + -4. Determine z so that -z**3 - u*z**5 - 5*z**4 + 4*z**2 + 3*z**4 + 5*z**3 - 2 - 2*z = 0.
-1, 1
Factor -20/17*u - 2/17*u**2 - 50/17.
-2*(u + 5)**2/17
Let b(t) = 2*t**3 - 6*t**2 + 6*t - 7. Let u(i) = 3*i**2 - 2*i**2 + 0*i**2 + 3*i - 3 + i**3 - 4*i**2. Let l(g) = -2*b(g) + 5*u(g). Factor l(j).
(j - 1)**3
Let b(d) be the third derivative of -1/390*d**5 + 0*d - 1/780*d**6 - 5*d**2 + 0 + 1/156*d**4 + 0*d**3 + 1/1365*d**7. Factor b(x).
2*x*(x - 1)**2*(x + 1)/13
Let q(j) = -j**4 + j**3. Let s(t) = -t**5 - t**4 - 18*t**3 - 12*t**2 - 4*t. Let x be ((-4)/(-6))/((-10)/15). Let g(a) = x*s(a) - 5*q(a). What is z in g(z) = 0?
-2, -1, 0
Suppose -5*l = -20 - 0. Factor -7 - 3*p**l - 1 - 24*p + 18*p**2 + 17.
-3*(p - 1)**3*(p + 3)
Let z(o) be the third derivative of 0*o**3 + 0*o**4 + 3*o**2 + 0*o - 1/300*o**5 - 1/600*o**6 + 0. Determine f so that z(f) = 0.
-1, 0
Let z(p) be the first derivative of 5*p**4/4 + 5*p**3/3 - 5*p**2 + 23. Factor z(o).
5*o*(o - 1)*(o + 2)
Suppose 0 = q - 4, 4*v - 5*v + 3*q = 7. Let p be (-12)/(-75)*v/2. Suppose p*g + 0 - 4/5*g**2 + 2/5*g**3 = 0. What is g?
0, 1
Factor 2*d**2 - 2*d - 7*d**3 + 5*d**3 + 2*d**2.
-2*d*(d - 1)**2
Let f(c) be the third derivative of 1/72*c**4 + 0*c**3 + 0 + 0*c - 1/360*c**6 - 5*c**2 + 1/630*c**7 - 1/180*c**5. What is w in f(w) = 0?
-1, 0, 1
Suppose d - 24 = -4*d - 2*c, 5*c - 2 = 2*d. Let m = d - 2. Let 8*w**4 + m*w**2 - 2*w**4 - 4*w**3 + 10*w**3 + 2*w**5 = 0. What is w?
-1, 0
Let o(h) be the first derivative of -10*h**3/33 - 2*h**2/11 + 2. Suppose o(f) = 0. Calculate f.
-2/5, 0
Factor 4*f**2 + 3488 - 3488.
4*f**2
Let m(w) be the first derivative of 2*w**5/15 + w**4/2 + 2*w**3/9 - w**2 - 4*w/3 + 6. Find k such that m(k) = 0.
-2, -1, 1
Let r be ((-1)/2)/((-3)/18). Suppose s + 14 = r*f, -5*f + 1 = -3*s - 25. Let -3/4*v**2 + 0 - 3/4*v**3 - 1/4*v**f - 1/4*v = 0. Calculate v.
-1, 0
Let g be ((-4)/(-21))/((-30)/(-35)). Let c(a) = -a**3 - 10*a**2 - 10*a - 9. Let r be c(-9). Find i, given that r + 2/9*i + g*i**2 = 0.
-1, 0
Let i(v) be the first derivative of -4*v**5/95 - 9*v**4/38 - 2*v**3/19 + 4*v**2/19 - 11. Let i(c) = 0. Calculate c.
-4, -1, 0, 1/2
Let t(x) be the second derivative of x**4/48 - x**3/24 + x. Let t(b) = 0. What is b?
0, 1
Let r(k) be the first derivative of k**4/12 + k**3/3 + k**2/2 + k/3 - 3. Factor r(t).
(t + 1)**3/3
Let b be 208/(-36) - (-2)/(-9). Let a(o) = -7*o**2 + 3*o - 8. Let w(y) = -8*y**2 + 3*y - 9. Let u(x) = b*w(x) + 7*a(x). Suppose u(r) = 0. What is r?
1, 2
Let l be (-1 - -2)/((-2)/4). Let f(t) = -4*t**2 + 4*t + 4. Let a(d) = -d**3 + d**2 - d - 1. Let w(c) = l*a(c) - f(c). Factor w(y).
2*(y - 1)*(y + 1)**2
Solve -2/5 + 2/5*x**4 - 2/5*x**3 - 7/5*x - 8/5*x**2 + 1/5*x**5 = 0.
-1, 2
Let w(j) = 93*j**2 + 37*j**3 - 5*j + 31*j + 70*j + 9*j**4 + 41. Let x(t) = -14*t**4 - 56*t**3 - 140*t**2 - 144*t - 62. Let l(p) = 8*w(p) + 5*x(p). Factor l(q).
2*(q + 1)**2*(q + 3)**2
Let o(u) be the first derivative of -3 - 3/4*u**4 + 2*u**3 + 0*u - 3/2*u**2. Factor o(a).
-3*a*(a - 1)**2
Let z be ((-8)/36)/(4/(-6)). Suppose -3*c + 9 = -4*k - 7, -c = -5*k - 9. Factor -2/3*n**3 - 1/3*n**c - z*n**2 + 0*n + 0.
-n**2*(n + 1)**2/3
Suppose 5*z - 13 = -3. Suppose 0 = -z*j - 2 + 8. Determine w, given that 0*w**3 + w**3 - 4*w**3 + 4*w**j - 2*w**2 = 0.
0, 2
Let b be 0 + -2 + 3/60*43. Let k(f) be the second derivative of -b*f**5 + 0 - f**2 + 3*f + 1/6*f**3 + 1/3*f**4. Determine s so that k(s) = 0.
-2/3, 1
Let i(a) be the third derivative of 0*a + 0*a**4 - 1/150*a**5 + 1/15*a**3 + 0 + 5*a**2. Factor i(k).
-2*(k - 1)*(k + 1)/5
Let -239 + 15*c**2 + 239 + 5*c**3 = 0. What is c?
-3, 0
Let m(v) = -3*v**2 + 3*v - 9. Let b(s) = -s**2 + s - 4. Let p be 39/15 + 3/(-5). Let n(d) = p*m(d) - 5*b(d). Factor n(f).
-(f - 2)*(f + 1)
Let s(p) = p - 7. Let v be s(11). Let d(m) be the second derivative of 1/42*m**v - 3*m + 0*m**2 + 0 + 1/21*m**3. Determine f, given that d(f) = 0.
-1, 0
Let t(k) = -4*k**2 + 2. Let v(j) = j**3 - j**2 + 1. Let m(b) = t(b) - 2*v(b). Suppose m(q) = 0. What is q?
-1, 0
Let y be 18/7*(6 + 1). Suppose -3*l - 2 = 3*h - 5*h, -l - y = -5*h. Find s, given that 0 - 4 + 3*s**2 - 4*s**2 - h*s = 0.
-2
Factor 8 + 36*j - 5*j**4 + 2*j**2 + 25*j**4 + 4*j**5 + 56*j**3 + 4*j**4 + 62*j**2.
4*(j + 1)**4*(j + 2)
Let x be (-1 - -1)/(-4 - -5). Let h be x/((-3)/(6/(-4))). Let -n**5 - n**4 + 0 + h = 0. What is n?
-1, 0
Let a(c) be the second derivative of -c**5/110 - c**4/66 + c**3/33 + c**2/11 - 8*c. Suppose a(j) = 0. Calculate j.
-1, 1
Let u be (-3)/(-5)*80/24. Factor 108/5*a**3 + 54/5*a**4 + 16/5*a + 0 + 72/5*a**u.
2*a*(3*a + 2)**3/5
Let z be (-4)/18 - (-704)/(-72). Let p be (0 - -2) + z/5. Solve 2/3*l + l**2 + p = 0.
-2/3, 0
Let z(c) = c**3 - 6*c**2 + 2. Let s(a) = a**3 - 5*a**2 - 4*a - 6. Let i be s(6). Let o be z(i). Solve 3*h + 6*h**o - 4 - h - 4*h**2 = 0 for h.
-2, 1
Let c(v) be the first derivative of 0*v**3 + 0*v**2 - 3 + 1/20*v**5 + 0*v - 1/16*v**4. Factor c(h).
h**3*(h - 1)/4
Let l be 144/81*((-12)/(-16) - 0). Let 0*t + 3*t**4 + 7/3*t**5 + 0 - l*t**2 - 4*t**3 = 0. Calculate t.
-2, -2/7, 0, 1
Let j(s) be the second derivative of s**7/105 - 4*s**6/75 + 3*s**5/25 - 2*s**4/15 + s**3/15 + 9*s. Factor j(h).
2*h*(h - 1)**4/5
Let h(d) be the first derivative of -2/7*d**2 - 7 - 2/7*d - 2/21*d**3. Factor h(v).
-2*(v + 1)**2/7
Let r be 1/(-2 - (-14)/6). Determine f so that -2*f**2 - r*f - f**2 - 2 - 4*f = 0.
-2, -1/3
Factor 5*w**4 - 44*w**3 - 4*w**4 + 43*w**3.
w**3*(w - 1)
Let a(v) be the second derivative of -v**5/40 - 11*v**4/24 - 2*v**3 + 9*v**2 + 4*v. Suppose a(q) = 0. Calculate q.
-6, 1
Suppose -m + 4*m = 9. Factor -2*h - h**4 + 6*h**3 - 3*h**m - 2*h**5 + h**5 + h**2 + 0*h**2.
-h*(h - 1)**2*(h + 1)*(h + 2)
Let a(u) be the first derivative of 2/27*u**3 - 1/9*u**2 + 3 + 0*u. Determine s so that a(s) = 0.
0, 1
Suppose 0 = -29*w + 17*w. Suppose -2*t**2 + 10/3*t**3 - 4/3*t + w = 0. What is t?
-2/5, 0, 1
Let l(x) be the third derivative of x**5/180 - x**4/12 + x**3/2 - x**2. Factor l(r).
(r - 3)**2/3
Let g be ((-2)/(-3))/(385/660). What is r in 8/7*r - 18/7*r**4 + 22/7*r**2 - g - 12/7*r**3 = 0?
-1, 2/3
Factor 4/3*i**2 - 2/3*i**5 + 2*i**3 + 0*i + 0 + 0*i**4.
-2*i**2*(i - 2)*(i + 1)**2/3
Factor -2/7*y**4 + 0*y + 0*y**2 - 2/7*y**3 + 0.
-2*y**3*(y + 1)/7
Let l(u) be the third derivative of -u**6/30 - u**5/5 - u**4/2 - 2*u**3/3 + 4*u**2. Solve l(p) = 0 for p.
-1
Let p(j) be the second derivative of 3*j + 0*j**2 + 1/3*j**3 + 0 + 1/10*j**5 - 1/3*j**4. Find h such that p(h) = 0.
0, 1
Let q(f) be the third derivative of f**10/12600 + f**9/1890 + f**8/840 - f**6/180 - f**5/12 - f**2. Let s(x) be the third derivative of q(x). Factor s(d).
4*(d + 1)**3*(3*d - 1)
Let y(k) = -8*k**3 + 4*k**2 + 4*k - 6. Let n(i) = -i**3 + i**2 - i. Let o(z) = -12*n(z) + 2*y(z). Factor o(t).
-4*(t - 1)**2*(t + 3)
Let g(u) = -3*u**5 - 16*u**4 - 34*u**3 - 26*u**2 + 2. Let f(k) = -k**4 - k**3 + k**2 - 1. Let w(a) = -2*f(a) - g(a). Factor w(s).
3*s**2*(s + 2)**3
Solve -6*w**2 + w**5 - w**2 - 3*w**3 + 9*w**2 = 0 for w.
-2, 0, 1
Let r(f) be the first derivative of 0*f + 3 - 1/14*f**4 + 0*f**3 + 1/7*f**2. Factor r(t).
-2*t*(t - 1)*(t + 1)/7
Let c be 52/(-3) - (-9)/27. Let f = 17 + c. Factor -2/9*x**2 + 2/9*x**5 + 0*x - 2/9*x**3 + 2/9*x**4 + f.
2*x**2*(x - 1)*(x + 1)**2/9
Solve 8/3*m - 2/3*m**5 - 16/3*m**2 + 4/3*m**4 + 2*m**3 + 0 = 0 for m.
-2, 0, 1, 2
Let x be (-980)/(-105) + (-1 - 7). Let -4/3 + x*t**2 - 2*t**3 + 2*t = 0. What is t?
-1, 2/3, 1
Factor 4/15*c + 2/5*c**2 + 0 + 2/15*c**3.
2*c*(c + 1)*(c + 2)/15
Let f(m) be the second derivative of -m**5/90 + 2*m**2 - 2*m. Let u(d) be the first de