*u - 2. Let x(o) = o**4 - o**2 - 1. Let j(n) = -2*b(n) + 4*x(n). Let j(a) = 0. What is a?
-2, -1, -2/13, 0
Suppose -l = 7 - 9. Let p be -1 + (-3)/(-2) + 0. Suppose 0*s - 1/2*s**3 - 1/2*s**4 + p*s**l + 0 + 1/2*s**5 = 0. Calculate s.
-1, 0, 1
Let c = 10 - 2. Suppose 12*v = 14*v - c. Factor 2*o**2 + 1/3 + 1/3*o**v + 4/3*o**3 + 4/3*o.
(o + 1)**4/3
Let y = -3 + 5. Determine p, given that -4 + 6*p - 6*p**2 + 3*p**y + 4*p**2 - 3*p**2 = 0.
1, 2
Let g(s) be the second derivative of s**4/42 - s**3/21 - 2*s**2/7 - 20*s. Factor g(m).
2*(m - 2)*(m + 1)/7
Let p = 208 - 208. Factor p*y + 1/6 - 1/6*y**2.
-(y - 1)*(y + 1)/6
Let c(i) be the third derivative of -1/8*i**3 - 1/8*i**5 - 1/56*i**7 + 0 + 1/448*i**8 + 2*i**2 + 0*i + 1/16*i**6 + 5/32*i**4. Factor c(y).
3*(y - 1)**5/4
Let x(b) be the third derivative of -b**5/120 - b**4/24 + 2*b**2. Determine l, given that x(l) = 0.
-2, 0
Let g(j) be the third derivative of -j**6/60 + j**5/10 - j**4/4 + j**3/3 - 7*j**2. Suppose g(o) = 0. Calculate o.
1
Let i(y) be the second derivative of y**7/84 + y**6/15 + y**5/8 + y**4/12 - 8*y. Factor i(a).
a**2*(a + 1)**2*(a + 2)/2
Let c be (-2)/4*(0 - 1/3). Let g(z) be the second derivative of c*z**2 + 2*z + 1/18*z**3 - 1/36*z**4 + 0 - 1/60*z**5. What is t in g(t) = 0?
-1, 1
Let z be 162/63 - (-8)/(-14). Suppose -1/4 + 1/2*a**3 - 1/2*a**z - 3/4*a + 3/4*a**4 + 1/4*a**5 = 0. What is a?
-1, 1
Let n(h) be the second derivative of 0*h**2 + 1/50*h**5 - 1/105*h**7 + 0*h**6 + 0*h**3 + 0 + 0*h**4 - 3*h. Factor n(s).
-2*s**3*(s - 1)*(s + 1)/5
Let m(z) be the first derivative of -z**6/27 - 8*z**5/45 - 5*z**4/18 - 4*z**3/27 + 1. Factor m(l).
-2*l**2*(l + 1)**2*(l + 2)/9
Let f(z) be the first derivative of -1/24*z**3 + 1/32*z**4 + 0*z + 2 + 1/40*z**5 + 0*z**2 - 1/48*z**6. Determine l so that f(l) = 0.
-1, 0, 1
Let u(z) be the second derivative of -3*z**7/350 - z**6/200 + 2*z**2 + 4*z. Let w(y) be the first derivative of u(y). Factor w(g).
-3*g**3*(3*g + 1)/5
Let x(j) = -3*j**5 - 12*j**4 - 6*j**3 - 3*j - 3. Let m(f) = 9*f**5 + 35*f**4 + 19*f**3 + f**2 + 8*f + 8. Let v(q) = 3*m(q) + 8*x(q). Factor v(n).
3*n**2*(n + 1)**3
Let u be (-78)/(-14) + (-4)/7. Let z(y) = -8*y**2 - 3*y - 2. Let j(f) = 2*f**2 + 5*f + 2 + 6*f**2 - f. Let g(s) = u*j(s) + 4*z(s). What is k in g(k) = 0?
-1/2
Suppose -105 + 9 = -24*x. Let v = -43/2 - -231/10. What is r in 22/5*r + 32/5*r**3 - 42/5*r**2 - v*r**x - 4/5 = 0?
1/2, 1, 2
Let t(i) = -4*i**2 + 8*i + 4. Let p(g) = 8*g**2 - 17*g - 9. Let y(k) = -4*p(k) - 9*t(k). Let y(z) = 0. Calculate z.
0, 1
Suppose 3*x - 47 = -p + 2*x, -3*x + 3 = 0. Find z such that 36*z**3 - 4*z - 3*z**4 - 59*z**4 - 18*z**5 + p*z**5 + 2*z**2 = 0.
-2/7, 0, 1/2, 1
Factor -3 - 3 + 4*d**4 - 8*d + 0 + 8*d**3 + 2.
4*(d - 1)*(d + 1)**3
Let q be 2 + (-2)/(-4)*4. Suppose q*i - 3 = 5. Factor 0 + 2/3*v**i - 1/3*v - 1/3*v**3.
-v*(v - 1)**2/3
Let -2*t**5 + 0*t - 8/3*t**3 - 1/3*t**2 + 0 - 13/3*t**4 = 0. What is t?
-1, -1/6, 0
Let b(d) be the first derivative of 1/36*d**4 + 3 + 0*d - 1/90*d**5 + 0*d**2 - d**3 + 1/540*d**6. Let w(u) be the third derivative of b(u). Solve w(l) = 0.
1
Let t(i) = -5*i**2 - 3*i + 6. Let z(p) = 4*p**2 + 2*p - 5. Let d(c) = -3*t(c) - 4*z(c). Let y be d(0). Factor w**3 + 5*w - w**2 + 4*w**2 - w - y*w.
w*(w + 1)*(w + 2)
Factor -9/2*t**2 + 3/2*t + 3 - 3/2*t**3 + 3/2*t**4.
3*(t - 2)*(t - 1)*(t + 1)**2/2
Let m(z) be the third derivative of z**6/180 - z**5/90 - z**4/36 + z**3/3 - z**2. Let a(b) be the first derivative of m(b). Factor a(g).
2*(g - 1)*(3*g + 1)/3
Let m(y) be the third derivative of -y**5/90 - y**4/18 + y**2. Factor m(a).
-2*a*(a + 2)/3
Factor 4/3*o**3 - 2*o**4 + 2/3 + 4/3*o**2 + 2/3*o**5 - 2*o.
2*(o - 1)**4*(o + 1)/3
Let y = -5 - -34. Let t = y + -27. Factor 6/5 + 3/5*b - 3/5*b**t.
-3*(b - 2)*(b + 1)/5
Let v = -24 + 24. Let u(j) be the third derivative of 0*j - 1/150*j**5 - 1/600*j**6 + 0*j**3 + j**2 + v - 1/120*j**4. Suppose u(y) = 0. Calculate y.
-1, 0
Factor -2/21*j**4 - 16/21*j**3 + 0*j - 32/21*j**2 + 0.
-2*j**2*(j + 4)**2/21
Let i be (-15)/100*1/(-9). Let k(s) be the third derivative of 0*s**4 - i*s**6 + 0 + s**2 + 0*s**3 + 0*s + 0*s**5 - 1/30*s**7. Find y such that k(y) = 0.
-2/7, 0
Let k(u) be the second derivative of u + 0 + 2/3*u**3 + 1/15*u**6 + 0*u**4 - u**2 - 1/5*u**5. Factor k(s).
2*(s - 1)**3*(s + 1)
Let g(q) be the first derivative of q**3/6 - q/2 - 1. Let g(y) = 0. What is y?
-1, 1
Let f(r) = 4*r - 2. Let g be f(3). Suppose u + 6 = -5*l + 28, 0 = 5*u - g. Determine j, given that -j**3 + 3*j**2 - j + j - l = 0.
-1, 2
Let b(t) = 4*t - 12. Let o be b(6). Let m be 22/o + (-6)/12. Factor 2/3*n**5 + 0*n**3 + m*n**2 - 4/3*n**4 + 0 - 2/3*n.
2*n*(n - 1)**3*(n + 1)/3
Let u(n) be the first derivative of -n**8/560 - n**7/175 - n**6/200 - 7*n**2/2 - 9. Let i(j) be the second derivative of u(j). Factor i(s).
-3*s**3*(s + 1)**2/5
Suppose 1015*r = 1018*r - 6. Factor -2197/2*q**3 + 507*q**r + 4 - 78*q.
-(13*q - 2)**3/2
Let p(g) be the second derivative of g**5/90 + g**4/6 + g**3 - g**2 - g. Let l(s) be the first derivative of p(s). Determine n, given that l(n) = 0.
-3
Let r(l) be the third derivative of l**5/300 + l**4/60 + l**3/30 + 13*l**2. Factor r(a).
(a + 1)**2/5
Let d(s) = 20*s**5 - 6*s**4 + 16*s**3 + 24*s**2 + 18*s - 18. Let c(f) = f**5 + f**3 + f**2 + f - 1. Let k(z) = -36*c(z) + 2*d(z). Let k(u) = 0. What is u?
-1, 0, 1, 3
Let q(y) be the first derivative of 1/30*y**6 + 0*y**5 - 1/4*y**4 + 0*y**2 - 1 + 1/3*y**3 + 2*y. Let g(v) be the first derivative of q(v). Factor g(a).
a*(a - 1)**2*(a + 2)
Find v, given that -8 + 5*v + 5*v**2 - 2 + 0 = 0.
-2, 1
Let l(h) be the second derivative of -1/54*h**4 + 3*h - 1/9*h**3 - 2/9*h**2 + 0. Let l(p) = 0. Calculate p.
-2, -1
Suppose 7 + 5 = 4*i. Determine p so that p - 2*p**4 - 3*p**2 - i*p**4 - 3*p**4 + 7*p**4 + 3*p**3 = 0.
0, 1
Let a be (-20)/175 - (-2)/5. Factor 2/7*y**3 - a*y + 0 + 0*y**2.
2*y*(y - 1)*(y + 1)/7
Let t(a) be the third derivative of a**5/100 + a**4/20 - 3*a**3/10 + 22*a**2. Factor t(w).
3*(w - 1)*(w + 3)/5
Let s = -1439/3 + 480. Factor -4/3*t**3 + 1/3 - 4/3*t + s*t**4 + 2*t**2.
(t - 1)**4/3
Factor 0*p + 0*p**2 + 0 + 2/3*p**3.
2*p**3/3
Let o(s) be the second derivative of 0 - 1/4*s**4 + 3/2*s**2 - 1/4*s**3 - s + 3/40*s**5. Factor o(y).
3*(y - 2)*(y - 1)*(y + 1)/2
Let f(c) be the third derivative of c**7/70 - c**6/10 + c**5/5 - 3*c**2. Factor f(m).
3*m**2*(m - 2)**2
Let b(i) be the first derivative of -i**6/2 + 3*i**4/2 - 3*i**2/2 - 43. Determine j so that b(j) = 0.
-1, 0, 1
Let t(j) be the first derivative of -j**6/3 - 4*j**5/5 + j**4 + 8*j**3/3 - j**2 - 4*j + 20. Solve t(z) = 0.
-2, -1, 1
Suppose -5*q - o = 3*o + 15, 19 = 4*q - 3*o. Let t be q/(-2)*12/(-8). Factor 1/4*b**2 - t*b + 1/2.
(b - 2)*(b - 1)/4
Let u(t) be the second derivative of t**4/9 - 2*t**3/3 + 4*t**2/3 - 28*t. Factor u(l).
4*(l - 2)*(l - 1)/3
Let x = 13 - 38/3. Let d(s) be the second derivative of -2/45*s**6 + 7/30*s**5 - 1/2*s**4 - s - x*s**2 + 0 + 5/9*s**3. Suppose d(u) = 0. Calculate u.
1/2, 1
Let t(v) be the third derivative of -5*v**7/42 - 19*v**6/24 - 19*v**5/10 - 13*v**4/6 - 4*v**3/3 - 3*v**2. Solve t(y) = 0.
-2, -1, -2/5
Let v(k) = 4*k**2 + 2*k. Let m(l) = 7*l**2 + 4*l - 1. Let o(p) = 3*m(p) - 5*v(p). Find q such that o(q) = 0.
-3, 1
Let n = 115 + -572/5. Let v(t) be the third derivative of 1/10*t**4 - 1/150*t**5 - n*t**3 + 0*t + 2*t**2 + 0. Factor v(x).
-2*(x - 3)**2/5
Let c(a) be the second derivative of -a**5/10 + 7*a**4/6 + 17*a**3/3 + 9*a**2 - 3*a. Factor c(g).
-2*(g - 9)*(g + 1)**2
Let z(o) be the first derivative of -o**6/3 + 2*o**5/5 + 3*o**4/2 - 10*o**3/3 + 2*o**2 + 4. Determine g, given that z(g) = 0.
-2, 0, 1
Let k(a) = 14*a**3 - 26*a**2 + 17*a. Let m(y) = 5*y**3 - 9*y**2 + 6*y. Let q(s) = 6*k(s) - 17*m(s). Factor q(l).
-l**2*(l + 3)
Let i(w) be the third derivative of w**6/180 - w**4/12 + w**3/6 - 2*w**2. Let c(a) be the first derivative of i(a). Factor c(v).
2*(v - 1)*(v + 1)
Let i = 12 - 10. Solve -2*w + w**2 + 6*w**2 - 5*w**i = 0 for w.
0, 1
Let j be (-1*(-3)/(-9))/((-3)/36). Let t(x) be the first derivative of -1/3*x**3 + 0*x + 2 + 1/5*x**2 + 3/20*x**j. Solve t(w) = 0.
0, 2/3, 1
Determine c so that 0*c - 56/5*c**4 + 118/5*c**2 + 54/5*c**3 - 8/5 = 0.
-1, -2/7, 1/4, 2
Let y(w) = 3*w**4 - 12*w**3 - 39*w**2 - 42*w - 18. Let r(p)