1 - -4). Determine x so that -k*x + 2*x - x**2 + 3*x**2 = 0.
0, 1
Let h(f) be the second derivative of f**5/240 - f**4/96 - f**3/12 + 3*f**2/2 + f. Let c(d) be the first derivative of h(d). Find b, given that c(b) = 0.
-1, 2
Let u(j) = 46 - 3*j - 35 + 11*j - 3*j**2 + 2*j**2. Let x be u(9). Factor -4*g**x + 2*g - 1/4.
-(4*g - 1)**2/4
Let u(b) = 3*b**3 - b**2 - 4*b - 2. Let h(d) = -7*d**3 + 3*d**2 + 9*d + 5. Let r(z) = 2*h(z) + 5*u(z). Find n such that r(n) = 0.
-2, 0, 1
Let t(k) be the first derivative of k**5/2 - 5*k**4/4 - 5*k**3/2 + 10*k**2 - 10*k + 19. Factor t(l).
5*(l - 2)*(l - 1)**2*(l + 2)/2
Let n(x) be the first derivative of -2/15*x**3 + 2/5*x + 0*x**2 - 1. Determine v so that n(v) = 0.
-1, 1
Let y(r) be the second derivative of r**7/840 + r**6/360 - r**3/2 - r. Let m(p) be the second derivative of y(p). Suppose m(w) = 0. Calculate w.
-1, 0
Factor 0 + 2/7*j**4 + 0*j + 2/7*j**3 + 0*j**2.
2*j**3*(j + 1)/7
Let n(c) = -7*c**5 - 5*c**3 + 2*c**2 + 6*c + 1. Let v(a) = -19*a**5 - a**4 - 14*a**3 + 6*a**2 + 17*a + 3. Let w(u) = -8*n(u) + 3*v(u). Let w(h) = 0. What is h?
-1, 1
Let b(o) be the first derivative of 1/3*o**3 + 1/2*o**6 + 7/5*o**5 + 0*o + 5/4*o**4 + 0*o**2 + 4. Find k, given that b(k) = 0.
-1, -1/3, 0
Let i(a) = -a**2 - 6*a + 1. Let g be i(-6). Let k = g + -1. Factor o**3 + 2*o + k*o**3 - 5*o**2 - 8*o**3.
-o*(o + 1)*(7*o - 2)
Let w(k) be the first derivative of -4*k**3/3 - 6*k**2 - 8*k + 35. Factor w(d).
-4*(d + 1)*(d + 2)
Let d(c) be the second derivative of c**4/6 + 25*c**3/12 + 3*c**2/2 - 10*c. Factor d(t).
(t + 6)*(4*t + 1)/2
Let n = -5 - -23. Let c = n - 15. Factor 4/9*s**2 + 0 + 0*s - 2/9*s**c.
-2*s**2*(s - 2)/9
Let z(n) be the third derivative of 0 + 2/9*n**3 - 1/36*n**4 + 0*n - 1/90*n**5 + 3*n**2. Let z(y) = 0. Calculate y.
-2, 1
Suppose 4 = 4*o + 16, -o = 2*q - 7. Let t(r) = -20*r**2 - 8*r. Let c(d) = -19*d**2 - 7*d. Let p(x) = q*c(x) - 4*t(x). Suppose p(u) = 0. What is u?
-1/5, 0
Let o(m) be the third derivative of m**6/210 - 2*m**5/105 + m**4/42 + 36*m**2. Factor o(k).
4*k*(k - 1)**2/7
Let z be 3 + (3/3 - 0). Let p(m) be the second derivative of -16/3*m**3 + z*m**2 - 2*m + m**4 + 5/12*m**6 + 2*m**5 + 0. Solve p(j) = 0 for j.
-2, 2/5
Suppose 0 = -7*s + 5*s + 10. Let i be ((-3)/14)/((-9)/12). Factor i*p**s + 0 + 0*p**2 + 2/7*p**4 + 0*p + 0*p**3.
2*p**4*(p + 1)/7
What is i in 9*i**3 - 9/2*i**4 + 0 + 3/4*i**5 - 6*i**2 + 0*i = 0?
0, 2
Let a(j) be the second derivative of j**10/60480 + j**9/30240 - j**8/13440 - j**7/5040 + j**4/12 - 6*j. Let k(b) be the third derivative of a(b). Factor k(l).
l**2*(l - 1)*(l + 1)**2/2
Let w(s) be the first derivative of 2*s**3/9 - 2*s**2 + 6*s + 6. What is q in w(q) = 0?
3
Let b(u) be the first derivative of -9*u**4/2 + 14*u**3/3 + 20*u**2 + 8*u + 6. What is y in b(y) = 0?
-1, -2/9, 2
Factor 3*u**4 + 3 - 2*u + 18*u**2 + 0*u + 12*u**3 + 6*u + 8*u.
3*(u + 1)**4
Let -9*t**3 - 4*t + 11*t**3 - 2*t + 4*t**2 = 0. What is t?
-3, 0, 1
Factor 8/3*o + 4/3 - 1/3*o**2 - 2/3*o**3.
-(o - 2)*(o + 2)*(2*o + 1)/3
Let b(x) be the first derivative of 3*x**4/4 - 3*x**3 + 34. Factor b(l).
3*l**2*(l - 3)
Let t(r) be the third derivative of r**8/112 + r**7/35 + r**6/40 - 5*r**2. Factor t(u).
3*u**3*(u + 1)**2
Factor 0*r + 1/4*r**4 - 8 + 11/2*r**2 + 9/4*r**3.
(r - 1)*(r + 2)*(r + 4)**2/4
Solve -2/3 + 2/3*g**2 + 2/3*g**3 - 2/3*g = 0 for g.
-1, 1
Find p, given that 56/19*p**2 + 16/19*p + 0 + 52/19*p**3 - 18/19*p**5 - 6/19*p**4 = 0.
-1, -2/3, 0, 2
Let x = 18 + -18. Let w(i) be the first derivative of x*i - 5/14*i**4 - 3 - 2/7*i**3 + 2/7*i**2. Factor w(m).
-2*m*(m + 1)*(5*m - 2)/7
Let v(k) = k**3 - k - 3. Let s be v(2). Let b(g) be the first derivative of 0*g**2 + 0*g**s + 1/4*g**4 - 1/5*g**5 + 3 + 0*g. Factor b(h).
-h**3*(h - 1)
Let j(n) = -3*n**4 + n**3 - 4*n - 4. Let r(g) = 9*g**4 - 2*g**3 + 11*g + 11. Let y(m) = -11*j(m) - 4*r(m). Factor y(k).
-3*k**3*(k + 1)
Factor -20*s**4 - 54*s**2 + 2*s**4 - 3*s**5 + 54*s**2 - 27*s**3.
-3*s**3*(s + 3)**2
Factor 1/2 + 5/4*a + a**2 + 1/4*a**3.
(a + 1)**2*(a + 2)/4
Find v such that 0*v - 2/3*v**3 + 0 + 1/3*v**4 + 1/3*v**2 = 0.
0, 1
Factor -2/3*a - 3/2*a**4 + 0 + 4/3*a**2 + 1/2*a**3.
-a*(a + 1)*(3*a - 2)**2/6
Suppose 4*n + 4*u - 42 = -14, -2*u = -5*n + 7. Suppose -3*d**4 - n*d**4 + 4*d**3 + 7*d**4 + 3*d**4 = 0. What is d?
-1, 0
Let l(p) be the second derivative of -2*p + 1/16*p**4 + 1/8*p**3 + 1/80*p**5 + 0 + 1/2*p**2. Let q(y) be the first derivative of l(y). Factor q(x).
3*(x + 1)**2/4
Let z = 8701/60 - 145. Let f(n) be the third derivative of 1/45*n**5 - 4*n**2 + 0*n + 0 - z*n**6 + 0*n**3 + 1/315*n**7 + 0*n**4. Solve f(v) = 0 for v.
0, 1, 2
Suppose 0 = q + u - 3, 2*u - 15 = -3*u. Suppose o = -2*h, h - 1 = -o - q*o. Solve 0*i - 2*i + 0*i**2 - 4 + 2*i**o = 0.
-1, 2
Suppose 2*g - 7*g + 15 = 0. Factor -4*o**2 + 3*o**2 + 3*o**3 + o**2 + o**2 + g*o**4 + o**5.
o**2*(o + 1)**3
Let p(w) be the third derivative of -4*w**2 + 0 + 0*w - 1/150*w**5 + 0*w**3 + 0*w**4 + 0*w**6 + 1/525*w**7. Factor p(y).
2*y**2*(y - 1)*(y + 1)/5
Let b be 1/((-13)/(-2) + -5). Suppose 0*f + 2/9*f**3 + b*f**2 - 8/9 = 0. What is f?
-2, 1
Let q(b) = -144*b**3 - 129*b**2 - 12*b. Let w(a) be the third derivative of 11*a**6/120 + a**5/6 + a**4/24 + 3*a**2. Let u(t) = -2*q(t) - 27*w(t). Factor u(n).
-3*n*(n + 1)*(3*n + 1)
Let j(h) be the first derivative of -7*h**4/4 + 5*h**3/3 + h**2 + 34. Factor j(m).
-m*(m - 1)*(7*m + 2)
Let j(a) be the first derivative of -a**4/18 - 2*a**3/27 - 1. Suppose j(y) = 0. Calculate y.
-1, 0
Factor 0 - 4/11*b + 6/11*b**3 + 10/11*b**2.
2*b*(b + 2)*(3*b - 1)/11
Suppose -8 = -4*x + 16. Factor 6*s**4 - x*s + 3*s**4 + 3*s**4 - 15*s**2 - 3*s**4 + 12*s**3.
3*s*(s - 1)*(s + 2)*(3*s + 1)
Factor 1/5*s**3 - 7/5*s**2 - 6/5 - 13/5*s + 1/5*s**4.
(s - 3)*(s + 1)**2*(s + 2)/5
Let z(l) be the second derivative of l**7/14 + l**6/5 - l**4/2 - l**3/2 - 5*l. Suppose z(i) = 0. What is i?
-1, 0, 1
Let o(s) be the second derivative of 1/2*s**2 + 1/18*s**3 + 0 + 3*s + 1/90*s**6 - 1/180*s**5 - 1/18*s**4. Let r(t) be the first derivative of o(t). Factor r(a).
(a - 1)*(a + 1)*(4*a - 1)/3
Let w(r) be the third derivative of -1/18*r**3 + 6*r**2 + 0*r + 0*r**4 + 0 + 1/180*r**5. Let w(g) = 0. Calculate g.
-1, 1
Let v = 5/32 + 1/96. Find a, given that v + 1/3*a - 1/2*a**2 = 0.
-1/3, 1
Suppose 4*b + k = 15, 17 + 4 = 2*b + 5*k. Find w such that 0*w**3 - w**2 - 6*w**4 + 4*w**2 + b*w**3 = 0.
-1/2, 0, 1
Let n = 719 - 717. Factor 3/5*k**n - 3/5*k + 0.
3*k*(k - 1)/5
Solve 0*j + 0 - 2/7*j**4 - 4/7*j**2 + 6/7*j**3 = 0.
0, 1, 2
Solve -2/3*k**2 + 5/3*k**3 + 0 + 0*k = 0 for k.
0, 2/5
Let k(n) be the third derivative of 0 + 1/240*n**6 + 1/120*n**5 + 0*n**4 + 0*n**3 - 1/672*n**8 + 4*n**2 - 1/420*n**7 + 0*n. What is p in k(p) = 0?
-1, 0, 1
Suppose 2*z + 0*u - 2 = -4*u, 4*u - 11 = z. Let g = z - -7. Factor 34*w**3 + 3*w**5 + 15*w**g - 6*w**2 + 18*w**2 - 10*w**3.
3*w**2*(w + 1)*(w + 2)**2
Let g(m) be the second derivative of -9*m**5/140 - m**4/4 - m**3/7 + 19*m. Factor g(x).
-3*x*(x + 2)*(3*x + 1)/7
Let c(s) be the second derivative of 2*s**6/15 + s**5/10 - s**4/2 - s**3/3 + s**2 + 5*s. Solve c(m) = 0 for m.
-1, 1/2, 1
Let f(s) be the first derivative of 2*s**5/5 + s**4 + 2*s**3/3 - 1. Factor f(h).
2*h**2*(h + 1)**2
Factor t**4 - 6*t**2 - 2*t**3 - 8 + 5 - 8*t + 2*t**3.
(t - 3)*(t + 1)**3
Let p = -28 + 12. Let b(w) = -6*w**2 + 6*w + 16. Let h(u) = u**2 - u - 3. Let g(y) = p*h(y) - 3*b(y). Solve g(i) = 0 for i.
0, 1
Suppose -3*l - 15 = -4*x - 1, 4*x = -5*l + 30. Let w be (-10)/(-6) + l/(-3). Factor -i**2 - 3/2*i + w.
-(i + 2)*(2*i - 1)/2
Suppose 4*c - 6 = 2*c. Suppose -5*m**3 + c*m**3 + 4*m**2 + 0*m**2 = 0. Calculate m.
0, 2
Factor 1/10*c**2 + 1/5 + 3/10*c.
(c + 1)*(c + 2)/10
Let z(y) be the first derivative of y**4/14 + 2*y**3/21 - y**2/7 - 2*y/7 + 4. Factor z(l).
2*(l - 1)*(l + 1)**2/7
Let v be 2*1*(-20)/(-8). Factor v*m**2 - 8*m - 2*m**2 + 2*m - 2*m**2 + 9.
(m - 3)**2
Let h be (-3)/((-6)/4) + (3 - 5). Determine m, given that 2/5*m**2 + h + 0*m + 2/5*m**5 + 6/5*m**4 + 6/5*m**3 = 0.
-1, 0
Let c(b) be the first derivative of -b**4/4 + 7*b**2/2 - 2*b + 1. Let z = -6 + 10. Let p(x) = -x**3 + 8*x - 2. Let v(t) = z*p(t) - 5*c(t). Solve v(o) = 0 for o.
-2, 1
Let 5/3*h**2 + 1/3*h**3 + 0 - 1/3*h**4 + h = 0. What is h?
-1, 0, 3
Let y = -110 + 114. Fac