**3/3
Determine m so that 3*m - 8*m**3 + 3*m**4 - 6*m**2 + 3*m**2 + 5*m**3 = 0.
-1, 0, 1
Suppose 0*w = 2*w. Let v be (-24)/(-10) - (w + 2). Solve 0 - v*o**3 - 2/5*o**4 + 2/5*o**2 + 2/5*o = 0 for o.
-1, 0, 1
Let f(r) be the third derivative of -1/30*r**5 - 1/24*r**4 + 0 + 0*r + 0*r**3 - 1/120*r**6 - 3*r**2. Determine m, given that f(m) = 0.
-1, 0
Let o be -1 + 0 + (5 - (-2 - -4)). Factor -1/3 - z - 1/3*z**3 - z**o.
-(z + 1)**3/3
Let h be 9/18 + (-3)/(-2). Let n(r) be the third derivative of -1/24*r**4 + 1/210*r**7 + r**h + 1/20*r**5 + 0*r**3 + 0 + 0*r - 1/40*r**6. Factor n(a).
a*(a - 1)**3
Suppose -57 = 5*m - 7. Let o be m/(-4)*(-36)/(-315). Factor 0 + 0*n**3 + 0*n - 2/7*n**5 + o*n**4 + 0*n**2.
-2*n**4*(n - 1)/7
Let x be -5 - (6006/(-90))/13. Factor -x + 2/15*d**2 + 0*d.
2*(d - 1)*(d + 1)/15
Let v(o) = 2*o**3 - 4*o**2 - 2*o - 5. Suppose 5*i - 4 = i. Let j(f) = -f**4 - f**3 - f**2 + f - 1. Let n(y) = i*v(y) - 3*j(y). Let n(x) = 0. What is x?
-1, -2/3, 1
Let w(t) = 2*t**2 - t - 4. Let c(m) = -m**2 + m + 1. Let g(x) = -3*c(x) - w(x). Factor g(h).
(h - 1)**2
Let r = 6 - 4. Let f = 11 + -7. Factor f*w**r - w**2 + 1 - w - 4*w**2 + w**3.
(w - 1)**2*(w + 1)
Let s be 33/6 + -4 - 1. Suppose -4*f = -1 - 3. Determine i, given that -1/2*i + f - i**2 + s*i**3 = 0.
-1, 1, 2
Suppose 37*u - 2 = 36*u. Factor 2/5*o + 4/5 - 6/5*o**u.
-2*(o - 1)*(3*o + 2)/5
Let q(p) be the first derivative of p**7/70 + p**6/25 + 3*p**5/100 + 9*p + 4. Let t(g) be the first derivative of q(g). What is a in t(a) = 0?
-1, 0
Let h(d) be the third derivative of d**5/12 + 5*d**4/12 - 5*d**3/2 + 21*d**2. Let h(p) = 0. What is p?
-3, 1
Let g = -36/7 + 38/7. Let -4/7*b**2 + 0 - g*b = 0. Calculate b.
-1/2, 0
Let t(c) = -3*c**2 + 4*c - 5. Let w(r) = -2 - 2*r - 3*r + 4*r + 3*r - r**2. Let d(z) = -2*t(z) + 5*w(z). Factor d(n).
n*(n + 2)
Let n be (4 + 147/(-28))*-4. Suppose -20/9*b**2 + 2*b - 10/9*b**n + 8/3*b**4 - 8/9*b**3 - 4/9 = 0. Calculate b.
-1, 2/5, 1
Let x = 6/17 - -50/51. Suppose 2*o**4 + 10*o**2 - 6*o - 22/3*o**3 + x = 0. Calculate o.
2/3, 1
Let z(v) be the first derivative of 4 - 2*v - 1/4*v**4 - 3/2*v**3 - 3*v**2. Let a(q) be the first derivative of z(q). Factor a(d).
-3*(d + 1)*(d + 2)
Let k(h) = h + 1. Let t be k(3). Suppose y - u - 12 = -y, 5*y = -5*u. Factor -2/3 + 8/3*x**3 - y*x**2 - 2/3*x**t + 8/3*x.
-2*(x - 1)**4/3
Let k(n) be the third derivative of -1/3*n**3 - 1/30*n**5 - 2*n**2 + 0*n - 1/6*n**4 + 0. Suppose k(p) = 0. Calculate p.
-1
Let n = 13 + 0. Suppose 0 = -4*j - 0*s + 3*s + 1, 2*j - n = -s. Factor 3*l**2 - 3*l**j + 19 - 19.
-3*l**2*(l - 1)*(l + 1)
Let n be (3/2)/(0 + 12/16). Suppose k + 2/5 + 3/5*k**n = 0. What is k?
-1, -2/3
Let q(g) be the second derivative of -g**7/189 + 4*g**6/135 - g**5/90 - 5*g**4/27 + 4*g**3/27 + 8*g**2/9 + 4*g + 3. Factor q(a).
-2*(a - 2)**3*(a + 1)**2/9
Factor 3/2*w**2 - 3/2*w**3 + 6*w - 6.
-3*(w - 2)*(w - 1)*(w + 2)/2
Let f be (-5)/((-3)/(0 - -3)). Let q(w) = w**3 + 8*w**2 + 7*w. Let p(c) = -c**2 - c. Let o(l) = f*p(l) + q(l). Factor o(g).
g*(g + 1)*(g + 2)
Factor -7*i + 5*i**2 + 13*i + 4*i.
5*i*(i + 2)
Let r = -7 + 10. Factor -40*h + 10 - 726*h**r - 12 - 1250*h**4 - 274*h**3 - 300*h**2.
-2*(5*h + 1)**4
Let o(a) be the third derivative of a**6/120 + 11*a**5/240 + 5*a**4/96 - a**3/12 + 2*a**2. Factor o(y).
(y + 1)*(y + 2)*(4*y - 1)/4
Let b(t) be the first derivative of 5*t**2 - 4 - 1/2*t**4 - 4*t - 2*t**3 + 2/5*t**5. Factor b(x).
2*(x - 1)**3*(x + 2)
Let r(l) be the third derivative of l**8/1680 - l**6/300 + l**4/120 - 16*l**2. Let r(a) = 0. What is a?
-1, 0, 1
Suppose 3*u - u - 6 = 0. Let c(m) be the first derivative of 1/5*m**5 + 0*m + 1/2*m**2 + 1 + 3/4*m**4 + m**u. Factor c(o).
o*(o + 1)**3
Factor 0 - 2*x - 2/3*x**4 - 2/3*x**3 + 10/3*x**2.
-2*x*(x - 1)**2*(x + 3)/3
Let w be (-6)/10 - 132/(-20). Solve -7*z**4 + 2*z**3 + w*z**4 - 2*z**3 = 0.
0
Let j(a) be the third derivative of a**6/480 - a**5/80 + a**4/32 - a**3/24 - 38*a**2. Factor j(h).
(h - 1)**3/4
Let o(b) be the third derivative of -7*b**5/12 + 5*b**4/3 - 5*b**3/6 + 16*b**2. Determine c so that o(c) = 0.
1/7, 1
Let 4/5*m**5 + 52/5*m**3 - 48/5*m**2 - 24/5*m**4 + 16/5*m + 0 = 0. Calculate m.
0, 1, 2
Let i(s) be the third derivative of 1/120*s**5 + 0*s**3 - 1/240*s**6 + 0 - s**2 + 1/24*s**4 + 0*s. Factor i(o).
-o*(o - 2)*(o + 1)/2
Find q such that 3 - 48*q - 20*q**2 - 19 + 31*q**3 + 36*q**4 + 9*q**3 + 8*q**5 = 0.
-2, -1, -1/2, 1
Let q be 1 + 4/((-20)/3). Let u = -1/115 - -93/115. Factor -2/5*f**2 + 0 - q*f**4 + u*f**3 + 0*f.
-2*f**2*(f - 1)**2/5
Let a(u) be the second derivative of -1/21*u**3 - 16/147*u**7 + 32/105*u**6 + 3*u + 0 + 4/21*u**4 - 12/35*u**5 + 0*u**2. Factor a(s).
-2*s*(2*s - 1)**4/7
Suppose 5*m**2 - 4*m**3 - m**2 - 2*m**2 + 4*m + 0*m**2 - 2*m**4 = 0. What is m?
-2, -1, 0, 1
Let p(a) be the first derivative of -5*a**6/6 + 2*a**5 + 5*a**4/2 - 20*a**3/3 - 5*a**2/2 + 10*a - 8. What is l in p(l) = 0?
-1, 1, 2
Let a = -1253/6 - -210. Let v(r) be the second derivative of a*r**3 + 9/80*r**5 + r**2 - 2*r + 0 + 5/8*r**4. Suppose v(k) = 0. Calculate k.
-2, -2/3
Let y(a) be the second derivative of 1/105*a**7 - 1/5*a**2 - 1/75*a**6 + 0 + 1/15*a**3 - 1/25*a**5 + 1/15*a**4 - 2*a. Find i, given that y(i) = 0.
-1, 1
Let d be (-3)/((-50)/16 + 3). Let j be (-2)/(-8) - 6/d. Factor t**2 - 1/2*t**3 - 1/2*t + j.
-t*(t - 1)**2/2
Suppose -2*o - 4*c + 2 = o, 4*o = -5*c + 3. Determine m, given that 1/2*m**4 - 1/2*m**3 + 0*m**o + 0 + 0*m = 0.
0, 1
Let t(n) = 4*n**4 + 2*n**3 - 6*n**2 + 6*n. Let y(a) = a**3 - a**2 + a. Let c(b) = -t(b) + 6*y(b). Factor c(i).
-4*i**3*(i - 1)
Let v(c) be the first derivative of -c**7/420 + c**6/40 - 13*c**5/120 + c**4/4 - c**3/3 + c**2 + 2. Let b(g) be the second derivative of v(g). Factor b(o).
-(o - 2)**2*(o - 1)**2/2
Let x(f) = f**4 + f**2 - f + 1. Let l(q) = 15*q**4 - 3*q**3 + 12*q**2 - 12*q + 12. Let m(w) = l(w) - 12*x(w). Factor m(a).
3*a**3*(a - 1)
Let p be 1 + -13 - (3 + -5). Let s = 10 + p. Factor s*x**2 + 0 + 1/5*x**4 + 0*x + 1/5*x**5 + 0*x**3.
x**4*(x + 1)/5
Let l(a) be the first derivative of -a**4/6 - 2*a**3/9 + 5*a + 6. Let m(v) be the first derivative of l(v). Factor m(h).
-2*h*(3*h + 2)/3
Let y(r) be the first derivative of -2*r**5/5 - 7*r**4 - 32*r**3 + 14*r**2 + 98*r + 23. What is c in y(c) = 0?
-7, -1, 1
Let f(t) be the second derivative of -t**6/30 - 9*t**5/20 - 2*t**4 - 8*t**3/3 - 38*t. Factor f(p).
-p*(p + 1)*(p + 4)**2
Let o(g) be the second derivative of 0 + 1/10*g**5 + 1/6*g**4 - g**2 - 1/3*g**3 - 3*g. Factor o(d).
2*(d - 1)*(d + 1)**2
Let l = 17 - 50/3. Find n, given that 3 - 2*n + l*n**2 = 0.
3
Suppose 0 = 2*k - 3*k + 3. Suppose 2*g + 4*b = 16, 0 = g + 4*g + k*b - 12. Factor 3/2*s**2 + 3*s + g.
3*s*(s + 2)/2
Let t be (-322)/(-300) + 14/(-21). Let p = t + -1/150. Factor -2/5*v + p*v**3 + 0 + 0*v**2.
2*v*(v - 1)*(v + 1)/5
Let p(n) be the first derivative of 1/48*n**4 + 1/8*n**2 - n + 1/12*n**3 - 1. Let w(q) be the first derivative of p(q). Determine i so that w(i) = 0.
-1
Find v such that 4 - 12*v + 11*v - 4*v**2 - 3*v + 4*v**3 = 0.
-1, 1
Let b = 9 + -1. Factor 5*f + 4*f + 3*f - 4*f**2 - b*f.
-4*f*(f - 1)
Factor -142*o**2 + 3*o**3 - 4*o - o**3 + 144*o**2.
2*o*(o - 1)*(o + 2)
Suppose -3*w + w + 6 = 0. Let u be (8/(-25))/((-2)/5). Factor 1/5 - u*h**w + 9/5*h**2 - 6/5*h.
-(h - 1)**2*(4*h - 1)/5
Factor 1/2*w**4 + 0*w + w**3 + 1/2*w**2 + 0.
w**2*(w + 1)**2/2
Suppose 2*f = -q + 7, q = -3*f + 2*q + 13. Suppose m - f = -m. Let 1 + 2*n**m - n**2 + 3*n + 1 = 0. What is n?
-2, -1
Let z(m) be the second derivative of -3*m + 0 + 10/63*m**7 + 0*m**3 + 1/15*m**5 + 1/5*m**6 + 0*m**4 + 0*m**2. Factor z(r).
2*r**3*(2*r + 1)*(5*r + 2)/3
Let s be (15/210)/((-90)/(-4)). Let p(k) be the third derivative of 0*k + 0*k**6 + 0 - 1/90*k**5 + s*k**7 + 0*k**4 + 0*k**3 + k**2. Find g such that p(g) = 0.
-1, 0, 1
Let y = 131/532 + 3/76. Let v(k) be the first derivative of -y*k**2 - 2/21*k**3 - 2 + 0*k. Let v(n) = 0. Calculate n.
-2, 0
Let t(k) be the second derivative of k**7/56 - k**6/8 + 21*k**5/80 - 3*k**4/16 + 28*k. Factor t(x).
3*x**2*(x - 3)*(x - 1)**2/4
Let h = -6 - -4. Let c(g) = g + 2. Let p be c(h). Factor 0*v**3 + p*v + 2*v - 2*v**3.
-2*v*(v - 1)*(v + 1)
Suppose 5*o - x = 446 + 216, 0 = o + 5*x - 122. Factor -2*r**4 - o*r**3 + 2*r**5 + 126*r**3 + 2*r + 2*r + 2*r