 c**4 + c. What is v in f(v) = 0?
-1, -1/4, 1
Let v be 3/(-2*(-1)/4). Let z(d) = -d**3 - 2*d**2 + d - 1. Let t be z(-3). What is m in -4*m**3 - 2*m + v*m**t - m**2 + 8*m**4 - 7*m**2 + 0*m**2 = 0?
-1, -1/3, 0, 1
Factor -16 - 9*y - 11*y - 20*y - 5*y**3 - 5*y**3 - 33*y**2 - y**4.
-(y + 1)**2*(y + 4)**2
Let u(z) be the second derivative of z**7/4200 + z**6/450 + z**5/120 + z**4/60 - z**3/3 + z. Let y(j) be the second derivative of u(j). Factor y(m).
(m + 1)**2*(m + 2)/5
Suppose 0 = o + 2*o. Suppose 0 = 3*q - 18 - o. Find d such that d**3 - 2*d**3 + 3*d**3 + q*d**2 + 4*d = 0.
-2, -1, 0
Let l(v) = -4*v**5 + 10*v**4 + 25*v**3 - 10*v**2 - 29*v - 1. Let q(t) = -t**4 - t - 1. Let h(i) = -5*l(i) - 35*q(i). Suppose h(z) = 0. What is z?
-2, -1, -1/4, 2
Let j(t) = t + 6. Let y be j(7). Let u be 2/y + (-444)/(-156). Factor 0*x**2 - 2/11*x**4 + 0 + 0*x + 2/11*x**u.
-2*x**3*(x - 1)/11
Factor 169/4*s**3 + s + 13*s**2 + 0.
s*(13*s + 2)**2/4
Factor -11*z**3 + 26*z**2 + 2 - 15*z**2 - 31*z**2 - 7*z.
-(z + 1)**2*(11*z - 2)
Suppose 3*c + z = 3, 4*c + 4 = 5*z - 11. Suppose c = 4*s + s. Solve s*r**2 + 3*r**2 - 2*r**2 = 0 for r.
0
Suppose 2*r - 2*m - 12 = 0, -2*m = 4*r - 10 + 4. Let l be 1*(3 - 2)*2. Factor v**l + v**2 - 3*v**r - v + 4*v - 2.
-(v - 1)*(v + 1)*(3*v - 2)
Suppose -3*n + 2*n = -2. Factor 3 - 3 + n - 2*p**2 + 4 + 4*p.
-2*(p - 3)*(p + 1)
Suppose 0*w = w - 1. Let t be (-17)/(-4) - 3/12. Factor 6*h**2 + 2*h**t - h + 4*h**3 + w - h**4 + 5*h.
(h + 1)**4
Let i(u) be the first derivative of -2/25*u**5 + 0*u + 0*u**3 - 7 + 0*u**2 + 1/10*u**4. Factor i(b).
-2*b**3*(b - 1)/5
Let m(r) be the second derivative of -1/30*r**6 + 2/3*r**3 + 3*r - 1/2*r**4 + 0 + 1/5*r**5 - 1/2*r**2. Let m(c) = 0. What is c?
1
Suppose 7*d + 75 = 4*d. Let a be (-2)/5 - 85/d. Factor 2/7*t**5 + 6/7*t**a - 2/7*t**2 - 6/7*t**4 + 0 + 0*t.
2*t**2*(t - 1)**3/7
Factor 5*z**3 - 16*z**3 + 2*z**4 + 4*z**3 + 4*z + 4*z**2.
z*(z - 2)**2*(2*z + 1)
Let r(l) be the second derivative of -l**5/150 - l**4/30 - 3*l**2/2 + 3*l. Let c(z) be the first derivative of r(z). Factor c(h).
-2*h*(h + 2)/5
Factor 6*l**3 + 4*l - 2*l + 8*l**4 - 9*l**4 + l**2 - 8*l**3.
-l*(l - 1)*(l + 1)*(l + 2)
Factor 0 - 2*a**3 - 3/2*a**2 + 1/2*a.
-a*(a + 1)*(4*a - 1)/2
Let r(y) = -14*y**2 - 4*y - 5. Let v(f) = 7*f**2 + 2*f + 3. Let c(d) = 3*r(d) + 5*v(d). Solve c(o) = 0 for o.
-2/7, 0
Suppose 4*m - 8 = -2*z, m + 0*m - 2 = -z. Find v, given that -3*v + v + 0*v + z*v**2 + 2*v**2 = 0.
0, 1
Let c(v) = 4*v**2 - 106*v + 784. Let b(g) = g. Let t(n) = -6*b(n) + c(n). Factor t(r).
4*(r - 14)**2
Let s(u) be the second derivative of 2*u - 1/21*u**3 + 0 + 1/30*u**5 + 1/105*u**6 + 1/42*u**4 - 1/2*u**2. Let l(j) be the first derivative of s(j). Factor l(w).
2*(w + 1)**2*(4*w - 1)/7
Let c be (-8)/6*(-12)/22. Let y = c + -5/22. Suppose -1 + 3/2*x - y*x**3 + 0*x**2 = 0. Calculate x.
-2, 1
Let b(x) = -9*x**4 + 17*x**3 - 4*x**2 - 17*x + 13. Let s(a) = -4*a**4 + 8*a**3 - 2*a**2 - 8*a + 6. Let n(o) = 6*b(o) - 13*s(o). Let n(g) = 0. Calculate g.
-1, 0, 1
Solve 2/5 - 14/5*b**3 + 46/5*b**2 - 18/5*b - 48/5*b**4 + 32/5*b**5 = 0 for b.
-1, 1/4, 1
Let h(f) be the third derivative of f**7/210 - f**6/120 - f**5/60 + f**4/24 - 11*f**2. Let h(y) = 0. Calculate y.
-1, 0, 1
Suppose -13*s**3 - 3*s**4 + 12*s**3 + 2*s**4 = 0. What is s?
-1, 0
Let c(a) = -a**3 + 9*a**2 + 13*a - 27. Let b be c(10). Factor -7/3*f**2 - 3 + 5*f + 1/3*f**b.
(f - 3)**2*(f - 1)/3
Factor -1/2*r**3 + 1/2*r**2 + 0 + r.
-r*(r - 2)*(r + 1)/2
Let a = 2 - -10. Suppose -12*j + 4*j**3 - 2*j**2 - 2*j**4 + a*j = 0. What is j?
0, 1
Let g be 57/9 - 6/(-9). Find p, given that 3*p**5 + 6*p**5 - g*p**5 - 2*p**4 = 0.
0, 1
Suppose -j - 4*y = -y + 8, 0 = 2*j + y + 1. Factor 4*g**5 - 3*g**3 - 1 + j + 5*g**4 + 4*g**3.
g**3*(g + 1)*(4*g + 1)
Let j = -75 - -79. Factor 16/7*n**j + 0 + 8/7*n**3 - 48/7*n**2 - 36/7*n - 4/7*n**5.
-4*n*(n - 3)**2*(n + 1)**2/7
Let b(u) be the first derivative of u**4/6 + 2*u**3/3 + 10*u + 5. Let r(o) be the first derivative of b(o). Solve r(x) = 0 for x.
-2, 0
Let o(c) be the third derivative of -7*c**6/450 + c**5/150 + c**4/20 + 2*c**3/45 - c**2. Find s, given that o(s) = 0.
-1/2, -2/7, 1
Let t = 13 - 9. Let q be ((-8)/(-6))/(2/3). Suppose -2*x**3 + 3*x**q + 0*x**3 - 3*x**2 - 2*x**t = 0. Calculate x.
-1, 0
Factor 0*l + 0 + 0*l**2 + 1/2*l**4 - 1/2*l**3.
l**3*(l - 1)/2
Suppose -3*f = -z - 10, 3 = -2*z + 4*f - 9. Solve 8/3*p + 2/3 - 8/3*p**4 - 8/3*p**3 + 2*p**z = 0.
-1, -1/2, 1
Let o(j) = j + 4. Let a = 12 - 12. Let l be o(a). Solve -1/4*n**l + 0*n**3 + 0 + 1/4*n**2 + 0*n = 0 for n.
-1, 0, 1
Let n(l) be the first derivative of -4 + 1/18*l**4 - 2/9*l**2 - 2/27*l**3 + 0*l. Factor n(x).
2*x*(x - 2)*(x + 1)/9
Let k(m) be the third derivative of m**7/35 - 7*m**6/80 + m**5/20 + m**4/16 + 10*m**2. Factor k(f).
3*f*(f - 1)**2*(4*f + 1)/2
Let 1/4*j**3 - 5/4*j - 1/2 - 3/4*j**2 + 1/4*j**4 = 0. What is j?
-1, 2
Let w(k) be the third derivative of -k**8/30240 - k**7/7560 + k**6/540 - k**5/60 + k**2. Let b(n) be the third derivative of w(n). Factor b(t).
-2*(t - 1)*(t + 2)/3
Let x = -125 + 127. Let 2/3*z - 2/3*z**3 + 0*z**x + 1/3*z**4 - 1/3 = 0. Calculate z.
-1, 1
Let i = 883/42 + -21. Let l(x) be the second derivative of 0*x**3 + 0*x**5 + 0*x**2 - 1/30*x**6 + 0*x**4 + 0 + i*x**7 + 3*x. Suppose l(d) = 0. What is d?
0, 1
Let z be 6/(-50)*44/(-33). Let p(m) be the first derivative of -1/10*m**2 + 7/20*m**4 - 2 + z*m**5 + 0*m + 2/15*m**3. Factor p(s).
s*(s + 1)**2*(4*s - 1)/5
Suppose -u = -4*p + 33, -2 - 4 = -3*p - 3*u. Factor -p*x + x**2 + x + x**2 + 2*x.
2*x*(x - 2)
Factor 2*t**3 - 448 + 448 + 12*t**2 + 10*t.
2*t*(t + 1)*(t + 5)
Let r be 9/15*(5 + 1). Let f = -142/45 + r. Determine q so that 2/9*q - f + 2/9*q**2 = 0.
-2, 1
Let q be (-3)/(-5) + (-146)/260. Let m(h) be the first derivative of -2/13*h + 3/13*h**2 - 2/13*h**3 + q*h**4 + 3. Factor m(r).
2*(r - 1)**3/13
Determine o, given that 4 + 10*o + 8 + 97*o**2 - 99*o**2 = 0.
-1, 6
Let v be (-4)/(-18)*(-4 - (-344)/80). Let w(m) be the first derivative of -1/5*m + v*m**3 + 0*m**2 - 4. Factor w(i).
(i - 1)*(i + 1)/5
Let q(b) be the first derivative of b**7/2940 + b**6/210 + b**5/35 + 2*b**4/21 - b**3/3 - 3. Let f(w) be the third derivative of q(w). Factor f(j).
2*(j + 2)**3/7
Suppose 2*h - 4*a + 2*a - 14 = 0, 0 = -4*h + 5*a + 33. Determine u so that -2/7*u + 0*u**h + 0 + 2/7*u**3 = 0.
-1, 0, 1
Suppose -4*m = -5*o - 12, 0 = 4*o - m + 1 + 2. Factor 3/5*s**3 + 6/5*s**2 + 0*s + o.
3*s**2*(s + 2)/5
Suppose 2*f = -2*f - o + 7, -20 = 4*o. Let p(h) be the first derivative of -3 + 2*h - 1/3*h**f + 1/2*h**2. Solve p(s) = 0 for s.
-1, 2
Let i(o) = -o**2 - 3 + 1 + 1 + 5*o - 1. Let z be i(3). Factor h + h**3 + 1/4*h**z + 1/4 + 3/2*h**2.
(h + 1)**4/4
Let r(n) be the first derivative of -2/3*n**3 + 2*n**2 + 2/5*n**5 - 4 - 5/2*n**4 + n**6 + 0*n. Suppose r(c) = 0. What is c?
-1, 0, 2/3, 1
Let s be 1*-1 - 11/(-6). Suppose 6*w - 30*w + 48 = 0. Factor s*r**w - 2*r + 2/3.
(r - 2)*(5*r - 2)/6
Suppose 0 = -5*h + 15 - 0. Factor 2/3 - 2/3*a - 2/3*a**2 + 2/3*a**h.
2*(a - 1)**2*(a + 1)/3
Let v(z) = z + 1. Let i be v(3). Let o(t) = -5*t**2 - 3*t + 9. Let q(f) = -3*f**2 - 2*f + 5. Let n(j) = i*o(j) - 7*q(j). Factor n(g).
(g + 1)**2
Determine x, given that -30*x**3 + 27/4*x**5 - 9/2 + 93/4*x + 12*x**4 - 15/2*x**2 = 0.
-3, -1, 2/9, 1
Let t(s) = s**3 - s**2 - 4*s. Let r(k) = -k**2 - 8*k + 3. Let w be r(-8). Let j be t(w). Solve 12*x**2 - 14*x**2 - j*x - 1 - 2 - 1 = 0 for x.
-2, -1
Let c(o) = 14*o**2 + o + 5. Suppose 2*y + 6 = g, 0 = 5*g - y - 0*y - 12. Let p(q) = 7*q**2 + 2. Let j(d) = g*c(d) - 5*p(d). Factor j(k).
-k*(7*k - 2)
Let c(z) be the first derivative of -z**4/10 + 4*z**3/15 + z**2/5 - 4*z/5 - 5. Factor c(v).
-2*(v - 2)*(v - 1)*(v + 1)/5
Suppose -a**5 + 4*a**2 - 7*a**5 + 10*a**5 - 6*a**3 = 0. Calculate a.
-2, 0, 1
Let -p**2 + 9*p**2 + 0*p**3 - 4*p**2 + 2*p**3 + 2*p = 0. What is p?
-1, 0
Suppose -6 = f - 4*f. Factor -z**3 + 0*z**3 + z**f - 3*z**2 - 2*z**4 - 3*z**3.
-2*z**2*(z + 1)**2
Let c(t) be the first derivative of -6/5*t**2 - 18/5*t + 1 - 2/15*t**3. Suppose c(n) = 0. What is n?
-3
Let o(a) be the third derivative of -a**6/1200 + a**5/200 - a**3/15 + 66*a**2. Factor o(f).
-(f - 2)**2*(f + 1)/10
Factor -27*d - 4*d**2 - 17*d + 36*d.
-4*d*(d + 2)
Suppose -8 = 5*o + 2*l, 0 = 3*l + 2*l +