 the third derivative of t**6/360 + t**5/90 - t**2. Factor b(y).
y**2*(y + 2)/3
Determine s, given that 0*s + 0 + 2/3*s**3 + 2/9*s**4 + 4/9*s**2 = 0.
-2, -1, 0
Let c(i) be the second derivative of -2*i**7/147 + 3*i**5/35 + 2*i**4/21 + 24*i. Suppose c(u) = 0. What is u?
-1, 0, 2
Let o be (-246)/21 + 2/(-7). Let m be (2 + o/9)*3. Determine j, given that -m*j**3 + 2 - 2 - 2*j**2 = 0.
-1, 0
Suppose 0 = -3*q - q - 16. Let j be (-3)/(-1 - -4) - q. Find s such that 4*s**j - 2*s**2 + 4*s**3 + 2 - 4*s - 4*s**3 = 0.
-1, 1/2, 1
Suppose 1/6*o**4 + 0 + 1/6*o - 1/6*o**3 - 1/6*o**2 = 0. What is o?
-1, 0, 1
Solve -6/5*u**2 - 3/5*u + 6/5*u**4 + 0*u**3 + 3/5*u**5 + 0 = 0.
-1, 0, 1
Let m be 2/9 - (-4)/(-18). Let q(y) be the first derivative of 9/4*y**4 + 4*y**3 + m*y + 2*y**2 - 1. Factor q(d).
d*(3*d + 2)**2
Let i = -9 + 4. Let k = i + 7. Factor 2/3*c**5 + 4/3*c**k - 4/3*c**4 + 0*c**3 + 0 - 2/3*c.
2*c*(c - 1)**3*(c + 1)/3
Factor 1/6*i - 1/6 + 1/6*i**2 - 1/6*i**3.
-(i - 1)**2*(i + 1)/6
Let a = -54 - -57. Let p(m) be the second derivative of -3*m + 3/20*m**5 + 3/4*m**4 + 0 + 0*m**2 + m**a. Find i such that p(i) = 0.
-2, -1, 0
Let b(m) = -m**3 - 4*m**2 - 3*m - 8. Let r be b(-4). Let j(v) be the second derivative of -1/7*v**2 - 1/42*v**r + 0 - 2*v - 2/21*v**3. Factor j(t).
-2*(t + 1)**2/7
Let v(x) be the third derivative of -5*x**8/1512 + x**7/315 + 17*x**6/540 + x**5/270 - x**4/9 - 4*x**3/27 + 12*x**2. Solve v(b) = 0 for b.
-1, -2/5, 1, 2
Let y(q) be the third derivative of q**5/36 + 4*q**2. Suppose y(f) = 0. What is f?
0
Let r be (27/(-2))/((-36)/48). Factor -4*x**2 + 20*x**3 - 2*x - r*x**3 + 2*x.
2*x**2*(x - 2)
Let r(a) be the second derivative of -1/42*a**4 + 0*a**2 - 3*a + 0*a**3 - 1/35*a**6 + 0 + 3/70*a**5 + 1/147*a**7. Find i, given that r(i) = 0.
0, 1
Factor -3*j - 9*j**2 - 6 + 9*j**2 + 8*j**2 + 9*j**3 + 4*j**2.
3*(j + 1)**2*(3*j - 2)
Let t(j) = 5*j**2 - 6*j - 3. Let w(u) = 5*u**2 - 7*u - 2. Let k(i) = -4*t(i) + 5*w(i). Suppose k(n) = 0. Calculate n.
1/5, 2
Suppose 0 = 3*x - l + 2*l - 17, -4*x + 5*l = 9. Factor 1/4*c**x + 0 + 0*c**3 - 1/4*c**2 + 0*c.
c**2*(c - 1)*(c + 1)/4
Let d = -11 + 11. Suppose 5*r - 10 = -d*r. Factor -1/3*y**5 + 0*y + 2/3*y**4 - 1/3*y**3 + 0 + 0*y**r.
-y**3*(y - 1)**2/3
Let p(w) be the first derivative of 1/84*w**4 - 1 + 0*w**3 + w**2 + 0*w - 1/210*w**5. Let b(n) be the second derivative of p(n). Factor b(i).
-2*i*(i - 1)/7
Let a(f) = f**2 + 3*f + 2. Let u be a(-3). Factor -2*v**2 + v**2 + 2 + 5*v**2 - 4*v - u*v**2.
2*(v - 1)**2
Let y = 8 - 6. Let n(j) be the first derivative of -y - 3/5*j**2 - 2/15*j**3 - 4/5*j. Factor n(k).
-2*(k + 1)*(k + 2)/5
Let r(p) = -p**4 - p**3 + p**2 + p + 1. Let q(i) = i**4 + 8*i**3 - 13*i + 7. Let d(v) = -q(v) + 3*r(v). Determine b, given that d(b) = 0.
-2, 1/4, 1
Let a = 3148/1887 - 1/629. Determine z so that -3*z**3 - z**2 - a*z**4 + 1/3*z + 0 = 0.
-1, 0, 1/5
Let o = 19 - 27. Let k be 12/(-10)*4/o. Factor k*t + 1/5*t**2 + 2/5.
(t + 1)*(t + 2)/5
Let j(x) be the second derivative of 1/6*x**3 + 1/2*x**2 - 1/12*x**4 + 0 - 3*x - 1/20*x**5. Factor j(p).
-(p - 1)*(p + 1)**2
Let r(q) be the first derivative of -q**3 + 3*q + 4. Solve r(f) = 0.
-1, 1
Let m(n) be the third derivative of 0*n - 5/12*n**6 - 9*n**2 + 0 - n**5 - 1/4*n**4 + 2/3*n**3. Factor m(a).
-2*(a + 1)*(5*a - 1)*(5*a + 2)
Let t(r) be the first derivative of -r**3/24 - 3*r**2/16 - r/4 - 16. What is f in t(f) = 0?
-2, -1
Suppose -3*b = b - 12. Solve -16/9*d + 2/9*d**5 + 10/9*d**4 - 8/9*d**2 + 0 + 4/3*d**b = 0.
-2, 0, 1
Factor -4/5*w - 3/5 - 1/5*w**2.
-(w + 1)*(w + 3)/5
Let d be (-518)/(-330) + 4/10. Let q = d + -18/11. Factor -q*b**4 - b**3 + b + 2/3 - 1/3*b**2.
-(b - 1)*(b + 1)**2*(b + 2)/3
Let k be (-7 - 56/(-6))*4/7. Solve -k*w**4 + 0*w**3 + 2/3*w + 0 + 4/3*w**2 - 2/3*w**5 = 0 for w.
-1, 0, 1
Let k(o) be the second derivative of o**6/135 - o**5/90 - 17*o. Factor k(t).
2*t**3*(t - 1)/9
Let f(c) be the third derivative of 0*c**3 + 1/420*c**7 + 1/120*c**5 + 0 + 0*c**4 - 3*c**2 + 1/120*c**6 + 0*c. Solve f(g) = 0 for g.
-1, 0
Let z be (-30)/(-8) + (-9)/12. Let y(i) be the first derivative of 0*i + 0*i**z - 1/21*i**6 + 0*i**5 + 0*i**2 + 1/14*i**4 + 2. Factor y(s).
-2*s**3*(s - 1)*(s + 1)/7
Determine v so that 4/9*v + 10/9*v**2 - 4/9*v**3 + 0 - 10/9*v**4 = 0.
-1, -2/5, 0, 1
Factor -78/7*r**2 - 24/7 + 80/7*r + 18/7*r**3.
2*(r - 3)*(3*r - 2)**2/7
Factor -1/2*h**3 + 0 + 0*h + 0*h**2 + 9/4*h**4.
h**3*(9*h - 2)/4
Let k be (-11232)/(-2704) - 8/6*3. Factor 12/13*q + 18/13 + k*q**2.
2*(q + 3)**2/13
Let v be (-14)/21*(-6)/16. Factor -1/4*q + 0 - 1/2*q**2 - v*q**3.
-q*(q + 1)**2/4
Let n be (3 + -3)/1 + (3 - 1). Let r(h) be the first derivative of 2*h - 1/2*h**4 + n*h**3 - 3*h**2 + 3. Find u such that r(u) = 0.
1
Suppose -5*f = -3*f. Let v(s) be the third derivative of 0*s + 1/840*s**7 - 3*s**2 + 0*s**3 + 0*s**6 + 0 + 0*s**4 + f*s**5. Find q, given that v(q) = 0.
0
Suppose 9/2*u**4 + 0 + 3*u**3 - 9/2*u**2 - 3*u = 0. What is u?
-1, -2/3, 0, 1
Let s(g) = 2*g**3 + 3*g**2 + 5*g. Let a(p) = p**2 + 3*p**2 + p**2 - p**2 + 3*p**3 + 7*p. Let c(h) = 5*a(h) - 7*s(h). Determine j, given that c(j) = 0.
0, 1
Solve -2*u**2 + 2/3 + 4/3*u = 0 for u.
-1/3, 1
Let g = 252 + -250. Factor 2/7*y + 0 + 2/7*y**g.
2*y*(y + 1)/7
Let j(c) = c**2 + c - 2. Let i(m) = -4*m**2 - 5*m + 7. Let z(d) = -d. Let y(n) = -i(n) + 2*z(n). Let t(s) = 7*j(s) - 2*y(s). Solve t(w) = 0 for w.
0, 1
Let f be (-26)/(-8) - 33/(-44). Let j(b) be the second derivative of -b + 1/9*b**3 + 0 - 1/18*b**f + 2/3*b**2. Factor j(m).
-2*(m - 2)*(m + 1)/3
Let n(w) be the first derivative of 5*w**4/4 - 10*w**3 + 30*w**2 - 40*w + 74. Factor n(f).
5*(f - 2)**3
Let x(n) be the third derivative of n**7/840 + n**6/480 + 5*n**2. Factor x(i).
i**3*(i + 1)/4
Let r(c) be the first derivative of c**3/9 + c**2/6 + 3. Find o, given that r(o) = 0.
-1, 0
Suppose c - 2*b = 16, b = 4*c - 3*b - 56. Let d be ((-20)/(-35))/(c/14). Suppose 0 + d*n**2 - 2/3*n**5 + 0*n + 2/3*n**3 - 2/3*n**4 = 0. What is n?
-1, 0, 1
Let k be 11/3 - 1/(-3). Suppose 18 - 6 = k*x. Suppose -4*v**2 + 2*v**3 + x*v**2 - 3*v**2 = 0. Calculate v.
0, 2
Let q be (-2)/4*0/(-5). Suppose x - 3 = 1. Find y, given that q*y - 2/3*y**x + 0*y**3 - 2/3 + 4/3*y**2 = 0.
-1, 1
Suppose -4*y = -0*o + 4*o - 20, -3*y + 11 = 2*o. Let p(m) be the first derivative of 0*m + 6*m**2 + 3/4*m**4 + o*m**3 - 3. What is u in p(u) = 0?
-2, 0
Suppose 0 = -q + s + 30, -2*s + 90 = -q + 4*q. Let l be q/(-12) + 2 + 1. Factor -l + 1/2*w**4 + 0*w**2 + w - w**3.
(w - 1)**3*(w + 1)/2
Suppose -3*q + 4*s = -5*q, -4*q + 2*s = 0. Let o(j) be the third derivative of q*j**4 - 1/30*j**5 + 0*j**3 + 0*j + 0 + 1/60*j**6 + j**2. Factor o(x).
2*x**2*(x - 1)
Let t(a) be the second derivative of a**6/30 - 3*a**5/10 + a**4 - 4*a**3/3 - 4*a. Determine b so that t(b) = 0.
0, 2
Let b be 4 + 3 + -1 + -2. Let j(m) be the second derivative of 2*m + 0 + 0*m**2 + 1/3*m**3 - 1/6*m**b. Factor j(f).
-2*f*(f - 1)
Let p = 2 - 1. Solve -3 + a**2 + 2 + a - p = 0.
-2, 1
Let b(v) be the second derivative of -v**7/1008 - 7*v**6/1440 - v**5/120 - v**4/12 - 3*v. Let r(n) be the third derivative of b(n). Factor r(w).
-(w + 1)*(5*w + 2)/2
Suppose -1 = -4*d - 5*s - 6, 0 = 3*s + 3. Factor d + 12/11*m**3 + 2/11*m**5 - 8/11*m**4 - 8/11*m**2 + 2/11*m.
2*m*(m - 1)**4/11
Let r(l) be the first derivative of -3*l**4/4 + 2*l**3 + 3*l**2/2 - 6*l + 35. Factor r(f).
-3*(f - 2)*(f - 1)*(f + 1)
Let m(a) be the first derivative of -2*a**3/3 + 3*a**2 - 4*a + 16. Suppose m(q) = 0. Calculate q.
1, 2
Let w(v) be the first derivative of 0*v + 1/2*v**4 + 0*v**2 + 6 + 4/3*v**3. Factor w(k).
2*k**2*(k + 2)
Let h(g) = -6*g**4 - 26*g**3 + 2*g**2 + 16*g - 6. Let z(y) = -y**4 - y**3 - y**2 + 1. Let f(l) = h(l) - 10*z(l). What is s in f(s) = 0?
-1, 1, 2
Let l(y) = y**2 + 7*y. Suppose -x = -w - 2*x - 9, -w = -x + 5. Let d be l(w). Factor -1/2*a**3 + 1/2*a**5 + 1/2*a**4 + d + 0*a - 1/2*a**2.
a**2*(a - 1)*(a + 1)**2/2
Let b(s) = -s**2 - 8*s - 2. Let w be b(-3). Suppose 0 = w*c - 9*c - 12. Find t such that -6/7*t + 2/7 - 2/7*t**c + 6/7*t**2 = 0.
1
Let k be (-6)/165*6/((-36)/30). Factor -6/11*n**4 + 2/11*n**5 + 6/11*n**3 + 0 - k*n**2 + 0*n.
2*n**2*(n - 1)**3/11
Let u be (2 + 0 + -2)/2. Factor 0*q**2 + q**2 + q**3 + q + u*q**2 - 3*q.
q*(q - 1)*(q + 2)
Let g be 5 + (-2)/4*-2. Let y b