 -1/3*a**3 + 0 + 0*a**2 - a - 1/12*a**j. Determine w so that g(w) = 0.
-2, 0
Let g(t) = -t**5 + t**4 + t**2. Let n(c) = -7*c**5 + 21*c**4 - 26*c**3 + 16*c**2 - c - 1. Let l(q) = -6*g(q) + 3*n(q). Factor l(i).
-3*(i - 1)**4*(5*i + 1)
Factor -8/3*f**3 - 32/9*f**2 + 0 - 4/3*f + 4/9*f**5 + 0*f**4.
4*f*(f - 3)*(f + 1)**3/9
Let u be 11/3 + (-12)/18. Factor -z**2 + 5*z + 4*z**2 - u*z**4 - 2*z - 3*z**3.
-3*z*(z - 1)*(z + 1)**2
Factor 2*q - 403*q**5 - 10*q**3 + 408*q**5 + 3*q.
5*q*(q - 1)**2*(q + 1)**2
Let q be 0 + 1 - (-5 - -2). Suppose q*d - 15 = d. What is j in -6*j**5 + 3*j**5 + j**d + 2*j**3 = 0?
-1, 0, 1
Let w(x) be the third derivative of -x**7/70 - x**6/20 + x**4/4 + x**3/2 - 3*x**2. Let w(l) = 0. Calculate l.
-1, 1
Let j(g) be the second derivative of -g**4/9 - 4*g**3/9 - 2*g**2/3 + 22*g. Factor j(r).
-4*(r + 1)**2/3
Let z(i) be the second derivative of -i**9/30240 - i**8/13440 + i**7/5040 + i**6/1440 + i**4/6 + 3*i. Let y(v) be the third derivative of z(v). Factor y(k).
-k*(k - 1)*(k + 1)**2/2
Suppose -5*p = 5*b + 1 - 11, -6 = -3*b. Factor 1/6*d**2 + p*d - 1/6.
(d - 1)*(d + 1)/6
Let f = 10 + -7. Factor 0 + 0*v + 0*v**f + 2/9*v**4 - 2/9*v**2.
2*v**2*(v - 1)*(v + 1)/9
Let w(m) = m**3 - m**2 + 4*m - 3. Let f be w(2). Suppose -3 = -4*z + l, -3*z + 5*l - 10 - f = 0. Determine q so that 2*q**5 - q**4 + z*q**4 - q**5 = 0.
-1, 0
Find t, given that -8/5 + 2/5*t**2 - 2/5*t**3 + 8/5*t = 0.
-2, 1, 2
Let d(g) be the second derivative of -g**7/2520 + g**6/360 - g**5/120 + g**4/4 - 3*g. Let a(q) be the third derivative of d(q). Factor a(t).
-(t - 1)**2
Let h(v) be the second derivative of v**6/60 + v**5/40 - v**4/4 - v**3/3 + 2*v**2 - 22*v. Factor h(t).
(t - 2)*(t - 1)*(t + 2)**2/2
Let f(b) be the first derivative of -b**6/180 - b**5/60 + b**3 + 4. Let u(k) be the third derivative of f(k). Solve u(z) = 0.
-1, 0
Let k(u) be the third derivative of u**7/12600 + u**6/900 + u**5/150 + u**4/8 - 3*u**2. Let b(m) be the second derivative of k(m). Factor b(q).
(q + 2)**2/5
Let x(g) = -2*g**3 + 10*g - 4. Let p(c) be the second derivative of -c**5/20 + c**4/12 + 5*c**3/3 - 2*c**2 + 7*c. Let v(b) = 2*p(b) - 3*x(b). Factor v(t).
2*(t - 1)*(t + 2)*(2*t - 1)
Let l(t) = t**3 + 5*t**2 - 8*t. Let h(z) = -z**3 - 33*z + 4*z**3 - 10*z**2 + 31*z**2. Let w(i) = 2*h(i) - 9*l(i). Factor w(o).
-3*o*(o - 1)*(o + 2)
Let y(x) be the third derivative of x**5/100 - 3*x**4/40 + x**3/5 + x**2. Factor y(k).
3*(k - 2)*(k - 1)/5
Let b(c) = -c**3 - 6*c**2 - 4*c + 8. Let t be b(-5). Let h(i) be the first derivative of -4/3*i**t - 4*i - 5*i**2 + 1. What is w in h(w) = 0?
-2, -1/2
Let j be (8/192)/(50/8). Let d(n) be the third derivative of 0 + 0*n**4 + j*n**5 + 0*n**3 + 0*n - 2*n**2. Factor d(b).
2*b**2/5
Factor -24/7*y**4 - 72/7*y**2 - 27/7*y + 0 - 3/7*y**5 - 66/7*y**3.
-3*y*(y + 1)**2*(y + 3)**2/7
Suppose 1/8*f + 1/8*f**2 - 1/8*f**3 - 1/8 = 0. What is f?
-1, 1
Solve h**2 - 3*h**2 + 4 + 4*h + h**2 - 3*h**3 - 4*h**2 = 0 for h.
-2, -2/3, 1
Solve -7*l + 0*l + 2 - 9*l**2 + 5*l**2 - 5*l**2 = 0 for l.
-1, 2/9
Let x be 1494/189 + -8 - (-6)/14. Solve -x*u - 1/3*u**2 + 1/3*u**3 + 1/3 = 0.
-1, 1
Let y(h) = h**3 + 5*h**2 - 8*h + 1. Let w be y(-6). Factor -a**4 - w*a - a**4 + 6*a**4 + 12*a**3 - 3*a.
4*a*(a - 1)*(a + 2)**2
Let q(k) be the third derivative of 0*k**5 + 0*k**3 + 1/315*k**7 + 0*k - 1/540*k**6 + 0 + 0*k**4 + k**2. Let q(z) = 0. What is z?
0, 1/3
Let d(i) be the second derivative of 1/3*i**4 + 0 + 1/2*i**2 - 2*i + 5/6*i**3. Solve d(n) = 0.
-1, -1/4
Let w(p) = -4*p - 3. Let l be w(-2). Solve -2 + u**2 - 2*u - 2 + l + 4*u = 0.
-1
Let u be (-2)/(-3)*2616/64. Let i = u + -27. Factor 0 + 0*z - i*z**2.
-z**2/4
Let f(y) = -y**3 - 8*y**2 - 8*y - 4. Let p be f(-7). Suppose -5*k + 29 = 3*u, 0 = -u - p*u - 3*k + 24. Factor 0*v**2 + 1/5 - 2/5*v**u - 1/5*v**4 + 2/5*v.
-(v - 1)*(v + 1)**3/5
Let o(k) be the third derivative of k**7/70 - k**6/20 + k**5/20 + 7*k**2. Factor o(h).
3*h**2*(h - 1)**2
Let z be (-1)/(-14) - (-121)/242. Factor z - 2/7*r**2 - 2/7*r.
-2*(r - 1)*(r + 2)/7
Let 16*j**5 + 4 - 40*j**2 + 39*j**4 + 80*j**3 - 46*j**4 - 53*j**4 = 0. What is j?
-1/4, 1
Let j(m) be the third derivative of -m**6/8 + 11*m**5/60 - m**4/12 + 5*m**2. Solve j(o) = 0 for o.
0, 1/3, 2/5
Let d(n) = 28*n + 142. Let r be d(-5). Factor -2*l - 1/2*l**2 - r.
-(l + 2)**2/2
Let p = -58097/1135 + -3/227. Let o = 52 + p. Factor 4/5*w**2 + o + 2*w.
2*(w + 2)*(2*w + 1)/5
Find k, given that 6*k + 3*k**3 - 69/5*k**2 + 24/5 = 0.
-2/5, 1, 4
Let z be 956/2920 - (-1)/5. Let j = -2/73 + z. Factor -3/2*h + j*h**2 + 1.
(h - 2)*(h - 1)/2
Let k be (-10)/(-4)*(-28)/(-5). Let r be (-2)/k*35/(-15). Factor 0 + 1/3*s + 2/3*s**2 + r*s**3.
s*(s + 1)**2/3
Let g = -3 + 3. Suppose -3*l = 3*u - 8 - 1, 2*l - u + 3 = g. Find b such that -2*b**4 + 2/9*b**2 - 2/3*b**3 - 10/9*b**5 + 0*b + l = 0.
-1, 0, 1/5
Let p be (3/2)/((-18)/(-24)). Suppose -p*l - 2 = -8. Factor 8/7*o**2 + 4/7 - 2/7*o**l - 10/7*o.
-2*(o - 2)*(o - 1)**2/7
Let c = -8 + 14. Let v(o) = o**4 + o. Let x(u) = 2*u**5 + 6*u**4 - 2*u**3 + 6*u. Let t(r) = c*v(r) - x(r). Factor t(y).
-2*y**3*(y - 1)*(y + 1)
Let p be (15/2)/(1*28/8). Factor p*a**2 - 3/7*a**3 - 24/7*a + 12/7.
-3*(a - 2)**2*(a - 1)/7
Suppose 0 = -11*s + 93 - 60. Suppose 0 + 2/3*g - 1/3*g**2 - 1/3*g**s = 0. What is g?
-2, 0, 1
Factor -2*d**2 + 10 - 13 + 5.
-2*(d - 1)*(d + 1)
Let o(z) be the third derivative of z**7/210 - z**6/120 - z**5/60 + z**4/24 + 10*z**2. Factor o(k).
k*(k - 1)**2*(k + 1)
Let q be (70/(-10))/((-1)/6). Let u be -4 - (0 + q/(-9)). What is p in -u + 1/3*p**2 + p - p**3 + 1/3*p**4 = 0?
-1, 1, 2
Let k(u) be the first derivative of 0*u + 3/5*u**5 + 3/2*u**4 - 3*u**2 - u**3 + 5. Let k(a) = 0. Calculate a.
-2, -1, 0, 1
Let h = -303 - -305. Factor -1/5*k**3 - 2/5*k + 0 + 3/5*k**h.
-k*(k - 2)*(k - 1)/5
Let d = 10 + -10. Let z(g) be the third derivative of d - 1/24*g**3 + 0*g**4 + 0*g - g**2 + 1/240*g**5. Factor z(y).
(y - 1)*(y + 1)/4
Let q(g) be the first derivative of 13*g**4/2 + 8*g**2 - 1. Let x(c) = 2*c + c - 2*c**3 + 7*c**3. Let d(j) = -3*q(j) + 16*x(j). Factor d(v).
2*v**3
Determine y, given that -9 - 2*y - y + 5*y**2 - y**2 + y**2 - y**3 = 0.
-1, 3
What is c in 16*c**4 - 6*c**3 - 18*c**2 - 3 - 18*c**4 - 1 - 14*c - 4*c**3 = 0?
-2, -1
Suppose -3*w + 5*w = 0. Solve w*u**2 - 5 - 2*u**2 - 4*u + 3 = 0 for u.
-1
Factor 3/5*s**4 + 0 + 1/5*s**2 - 1/5*s + s**3.
s*(s + 1)**2*(3*s - 1)/5
Let b(h) be the third derivative of h**7/490 + h**6/280 - 3*h**5/140 - h**4/56 + h**3/7 + 8*h**2. Suppose b(j) = 0. What is j?
-2, -1, 1
Let s = 10108/9 + -1122. Let v = -7/9 + s. Factor 0*u - v*u**2 + 0.
-u**2/3
Let n(w) be the second derivative of -w**6/150 + 3*w**4/20 + 2*w**3/15 - 6*w**2/5 - 55*w. Factor n(u).
-(u - 3)*(u - 1)*(u + 2)**2/5
Let o be (-2)/7 + 23/7. Suppose -12*b + 3*b**2 + 4*b - 11*b**2 - 2*b**o = 0. What is b?
-2, 0
Suppose -28*y = -5*q - 31*y + 9, -4*q + 2*y + 16 = 0. Factor 3/5*u + 0 + 3/5*u**q - 6/5*u**2.
3*u*(u - 1)**2/5
Factor 33*r + 32*r**2 + 4 + 71*r + 14*r**3 - 82*r.
2*(r + 1)**2*(7*r + 2)
Let w(o) = -o**3 + o**2 + 3. Let j be w(0). Let 0*t**j - t**3 + 2*t - 6*t + 4*t**2 = 0. Calculate t.
0, 2
Solve -9*l**3 + 19*l**2 + 20*l - l**3 - 65*l**2 + 0*l**3 = 0 for l.
-5, 0, 2/5
Let l(g) be the first derivative of 10*g**6/3 - 12*g**5 + 65*g**4/4 - 10*g**3 + 5*g**2/2 - 7. Solve l(r) = 0.
0, 1/2, 1
Let n = 5 + -12. Let h be (-2)/n + (-9)/(-42). Find b such that 0 + h*b**3 + 0*b + b**2 = 0.
-2, 0
Let q be 1 - (-10)/(-54)*5. Let m(z) be the first derivative of -1 + 0*z - 1/9*z**2 + q*z**3. Suppose m(x) = 0. Calculate x.
0, 1
Let v(f) = -336*f**2 - 424*f - 116. Let t(o) = -61*o**2 - 77*o - 21. Let z(x) = 28*t(x) - 5*v(x). Suppose z(b) = 0. What is b?
-1, -2/7
Let v(x) be the second derivative of 5/6*x**4 + 2*x + 9/5*x**2 + 0 - 2*x**3. Factor v(l).
2*(5*l - 3)**2/5
Let b(n) be the second derivative of 7*n - 1/12*n**3 - 1/24*n**4 + 0 + 1/2*n**2. Find j such that b(j) = 0.
-2, 1
Find d, given that -2/7*d**4 + 0*d - 2/7*d**3 + 0 + 0*d**2 = 0.
-1, 0
Suppose 9/5*m**4 + 0*m - 3/5*m**2 + 0 - 6/5*m**5 + 0*m**3 = 0. What is m?
-1/2, 0, 1
Factor 2/3*q**2 + 2*q + 4/3.
2*(q + 1)*(q + 2)/3
Let l = -469/234 - -55/26. Factor -1/9*n**5 + l*n**3 + 0*n**2 + 0*n + 0*n**4 + 0.
-n**3*(n - 1)*(n + 1)/9
Let l(z) be the third derivative of z**6/780 - z**