Let x(r) be the first derivative of 2/5*r**3 - 2/15*r**6 - 6/25*r**5 + 2 + 0*r + u*r**2 + 1/10*r**4. Let x(p) = 0. What is p?
-1, -1/2, 0, 1
Let y(m) be the third derivative of -1/480*m**6 + 1/80*m**5 + 3*m**2 + 0*m + 1/24*m**3 + 0 - 1/32*m**4. Determine w so that y(w) = 0.
1
Let k(f) be the second derivative of -8*f**4/11 - 8*f**3/11 - 3*f**2/11 - 33*f. What is i in k(i) = 0?
-1/4
Find k, given that -1/4*k**2 - 1/4 + 1/2*k = 0.
1
Let n(t) be the second derivative of 0*t**2 - 1/36*t**4 + 1/18*t**3 - 2*t + 0. Factor n(u).
-u*(u - 1)/3
Let h(j) be the first derivative of 2*j**6/9 + 4*j**5/15 - j**4/3 - 4*j**3/9 - 45. Factor h(f).
4*f**2*(f - 1)*(f + 1)**2/3
Let z be ((-56)/(-56))/(1 + 12/(-15)). Factor 5/7*r**z + 4*r**3 + 0 + 22/7*r**4 + 8/7*r**2 + 0*r.
r**2*(r + 2)**2*(5*r + 2)/7
Let g be (-62)/(-33) - (-12)/(-22). Factor 6*x**3 + 10/3*x**4 + 14/3*x**2 + 0 + g*x + 2/3*x**5.
2*x*(x + 1)**3*(x + 2)/3
Let b(h) = h**3 - 4*h**2 - 19*h + 19. Let j(p) = 8*p**3 - 28*p**2 - 132*p + 132. Let c(q) = 20*b(q) - 3*j(q). Find i, given that c(i) = 0.
-2, 1, 2
Factor 0 - 21/8*t**2 - 3/4*t - 9/8*t**3.
-3*t*(t + 2)*(3*t + 1)/8
Let z(c) be the third derivative of -c**5/20 - 5*c**4/8 - 2*c**3 + 13*c**2. Let z(b) = 0. Calculate b.
-4, -1
Let k(q) be the first derivative of -q**4/4 - q**3/3 + 5*q**2/2 - 3*q - 8. Factor k(v).
-(v - 1)**2*(v + 3)
Let w = 58 + -1159/20. Let s(i) be the second derivative of 0*i**4 - w*i**5 - 1/4*i**2 + 0 + i + 1/60*i**6 + 1/6*i**3. Factor s(n).
(n - 1)**3*(n + 1)/2
Let d = 2109/35 - 1035/7. Let o = d + 88. Find s such that 0*s - o*s**3 - 2/5*s**2 + 0 = 0.
-1, 0
Suppose 2*u = 5*u - 12. Factor -u*l + l + 2*l**2 - 3*l + 4.
2*(l - 2)*(l - 1)
Suppose 3*j - 2*m - 5 = -3, 2*j = -4*m + 28. Factor -7 - 2*o**3 + o**2 + 5 + o**4 - o + j*o - o**3.
(o - 2)*(o - 1)**2*(o + 1)
Suppose -18 = -2*t + 2*y - 2, y = 2*t - 12. Let f(m) be the second derivative of 1/16*m**t - m - 1/80*m**5 - 1/12*m**3 + 0*m**2 + 0. Factor f(i).
-i*(i - 2)*(i - 1)/4
Factor 7*l**3 - 5*l**3 + 4*l**3 + 0*l**5 - 3*l**5 - 3*l**4.
-3*l**3*(l - 1)*(l + 2)
Let f(i) = -52*i**3 + 127*i**2 - 67*i + 7. Let b(d) = -17*d**3 + 42*d**2 - 22*d + 2. Let g(y) = 7*b(y) - 2*f(y). Determine x, given that g(x) = 0.
0, 2/3, 2
Factor -2*k - 2*k**2 - 4*k**2 - 3*k**2 + 8*k**2.
-k*(k + 2)
Let q(g) be the first derivative of -1 + 6*g - g**3 + 3/2*g**2. Find h, given that q(h) = 0.
-1, 2
Let u(k) be the third derivative of k**10/90720 + k**9/45360 + k**4/8 + 2*k**2. Let t(w) be the second derivative of u(w). What is j in t(j) = 0?
-1, 0
Suppose -30 = -5*j - 5*c, -4*c - 10 = -3*j - 3*c. Factor -3*n**5 + 2*n**j + 8*n**5 - 2*n**5 - 11*n**5.
-2*n**4*(4*n - 1)
Suppose 2/7*o - 1/7*o**2 - 1/7 = 0. Calculate o.
1
Find i, given that 2/7 - 2/7*i**2 + 4/7*i - 4/7*i**3 = 0.
-1, -1/2, 1
Let o(u) = u**4 - 3*u**3 + 2. Let b(t) = 2*t**4 - 4*t**3 + 4*t**3 - 4*t**3 + 3. Let p(m) = -2*b(m) + 3*o(m). Find k such that p(k) = 0.
-1, 0
Suppose -k = -0*k - 2. Factor -2*r**4 - k*r**4 + 3*r**5 - r**5 + 4*r**3 - 2*r**4.
2*r**3*(r - 2)*(r - 1)
Let a(q) be the second derivative of 7*q**8/3840 - q**7/360 + q**6/720 - q**4/6 + 8*q. Let r(w) be the third derivative of a(w). Suppose r(v) = 0. What is v?
0, 2/7
Let f(p) be the second derivative of -1/25*p**6 - 2*p - 1/105*p**7 + 1/5*p**2 + 0 + 1/15*p**4 + 1/5*p**3 - 1/25*p**5. Determine h, given that f(h) = 0.
-1, 1
Factor 4/3*n**2 + 8/15*n - 2/15*n**5 - 8/15*n**4 - 16/15 - 2/15*n**3.
-2*(n - 1)**2*(n + 2)**3/15
Let y(j) = 2*j**2 + 64*j + 65. Let l be y(-31). Find i such that i - 3/4*i**l - 1/4*i**4 + 0*i**2 + 0 = 0.
-2, 0, 1
Let v be 2/6 + 8/12. Factor -2*d**2 + v + 5 - 3 - 1.
-2*(d - 1)*(d + 1)
Find m such that 1/3*m**3 + 0 + 0*m + 0*m**2 - 1/3*m**4 = 0.
0, 1
Determine w, given that 10/7*w**3 + 18/7*w**2 + 2/7*w**4 + 2*w + 4/7 = 0.
-2, -1
Let s(a) be the second derivative of a**7/70 + a**6/10 + a**5/4 + a**4/4 - 7*a**2/2 + 4*a. Let u(w) be the first derivative of s(w). Factor u(y).
3*y*(y + 1)**2*(y + 2)
Let b(a) = -a**3 - 6*a**2 - 5*a + 2. Let d be b(-5). Suppose -d*g - 2 = -3*x - x, 4*x = -4*g + 20. Factor -2*f**5 + 4*f**4 - 6*f**4 + 3*f**5 + f**g.
f**3*(f - 1)**2
Let l(p) be the first derivative of -p**6/9 - 2*p**5/15 + p**4/3 + 4*p**3/9 - p**2/3 - 2*p/3 - 27. Factor l(z).
-2*(z - 1)**2*(z + 1)**3/3
Let y(u) = 7*u**3 + 4*u**2 - u - 4. Let o(p) = 6*p**3 + 3*p**2 - p - 3. Let a(i) = -6*o(i) + 5*y(i). Find r such that a(r) = 0.
-1, 1, 2
Let s = -3 - 5. Let m be (0 - s) + -7 + 4. Solve 2/7 + 4/7*d**3 - 8/7*d**2 + 0*d - 4/7*d**m + 6/7*d**4 = 0 for d.
-1, -1/2, 1
Let z(x) be the third derivative of -x**5/15 - x**4/6 + 4*x**3 + 27*x**2. Factor z(a).
-4*(a - 2)*(a + 3)
Suppose 13*p**2 - 21*p**5 + 2*p + p**4 + 16*p**4 + 24*p**3 + 25*p**5 = 0. What is p?
-2, -1, -1/4, 0
Let l(b) = b - 2. Let r be (-30)/(-14) + (-2)/14. Let k be l(r). Let k - 1/6*z - 1/6*z**2 = 0. What is z?
-1, 0
Let d(y) = 2*y**4 - 34*y**3 - 86*y**2 - 48*y - 26. Let r(u) = -u**4 + 11*u**3 + 29*u**2 + 16*u + 9. Let g(j) = 5*d(j) + 14*r(j). Let g(i) = 0. Calculate i.
-1
Suppose -m - 4*x - 7 = 0, 4*m = 4*x + 25 + 7. Solve -4*d**4 - 4*d**2 + 0*d**3 + 3*d**5 + d + 6*d**3 - 2*d**m + 0*d**5 = 0 for d.
0, 1
Let o be (-24)/18*(-1)/24. Let z(j) be the second derivative of 0*j**2 + 0*j**3 - 2*j + 0 - o*j**4. Suppose z(m) = 0. What is m?
0
Let q(p) = -p**2 + p - 1. Let n be q(0). Let i be 0 - 0 - (n + 1). Factor i + 2/5*r - 2/5*r**2.
-2*r*(r - 1)/5
Let j = -1933/9 + 215. Let -2/9*b - 2/9 + 2/9*b**3 + j*b**2 = 0. Calculate b.
-1, 1
Let b(j) = 12*j**2 + 4*j - 2. Let t be b(-1). Find s such that 6*s**2 + t*s**4 - 12*s**5 + 141/4*s**3 - 39/4*s + 3/2 = 0.
-1, 1/4, 2
Let c(f) be the second derivative of -f**4/24 + f**3/4 - f**2/2 - 6*f. Determine w so that c(w) = 0.
1, 2
Let k = -6179/60 + 103. Let u(c) be the second derivative of -1/3*c**4 + 1/8*c**5 - c + 0*c**2 + 0 - k*c**6 + 1/3*c**3. Factor u(j).
-j*(j - 2)**2*(j - 1)/2
Suppose 0 = -3*r + 3*b - 12, 2*r + 2*b + 3 = 11. What is i in -2/3*i**2 + r*i + 0 - 2/3*i**3 = 0?
-1, 0
Let s(p) be the third derivative of -p**6/30 - 23*p**5/15 - 143*p**4/6 - 242*p**3/3 + 28*p**2. Solve s(y) = 0 for y.
-11, -1
Let n(d) be the third derivative of -d**6/96 - d**5/120 + 7*d**2. Factor n(k).
-k**2*(5*k + 2)/4
Let a be (4/24)/((-3)/(-12)). Let a*c**2 + 0 - 2*c = 0. Calculate c.
0, 3
Let p(b) be the second derivative of -b**7/147 + b**6/35 - b**5/70 - b**4/14 + 2*b**3/21 + 36*b. Suppose p(j) = 0. What is j?
-1, 0, 1, 2
Factor -2*s**4 - s**3 + 0*s**4 + 3*s**4.
s**3*(s - 1)
Let o(q) be the third derivative of -2*q**5/105 + 3*q**4/7 - 27*q**3/7 + 2*q**2 + 2*q. What is j in o(j) = 0?
9/2
Let n(m) be the second derivative of m**6/70 - 3*m**5/140 - 3*m**4/28 + m**3/14 + 3*m**2/7 + 2*m. Factor n(g).
3*(g - 2)*(g - 1)*(g + 1)**2/7
Let h be ((-3)/2)/((-6)/16). Let r = -7/2 + h. Let 1/4*g**2 + r*g**3 + 0 + 0*g + 1/4*g**4 = 0. Calculate g.
-1, 0
Let q be (1 + -59)/(3/(-3)). Let s = q + -404/7. Factor s*z**2 - 2/7 + 0*z.
2*(z - 1)*(z + 1)/7
Determine m so that 3*m**2 + 6*m - 1 - m**2 - 8*m - 3 = 0.
-1, 2
Let q(c) be the second derivative of c**7/21 + 4*c**6/25 + 9*c**5/50 + c**4/15 + 8*c. Find i such that q(i) = 0.
-1, -2/5, 0
Let m be (-1)/4 + -1 + (-14)/(-8). Suppose 1/2*y**5 - y**3 + m*y + 1 - 2*y**2 + y**4 = 0. Calculate y.
-2, -1, 1
Let c be 2/(-6)*(2 + -2). Factor -7/3*i**3 - 49/2*i**4 + 22/3*i**2 - 4/3*i + c.
-i*(3*i + 2)*(7*i - 2)**2/6
Let p(o) be the second derivative of 3*o**5/80 - o**4/8 - 17*o. Factor p(z).
3*z**2*(z - 2)/4
Factor 0*a**3 + 0*a + 2/5*a**4 + 0 - 2/5*a**2.
2*a**2*(a - 1)*(a + 1)/5
Suppose 0 = -3*c + 4*o - 5, -4*c + 2*c + 2*o = 0. Suppose 4*h - 21 = -c*k, -4 = 2*k - 4*h - 18. Determine y so that 4*y**2 + 3*y**3 + 2*y**2 + k*y - 2*y = 0.
-1, 0
Let l(f) be the first derivative of -f**5/35 + f**4/28 + f**3/7 - f**2/14 - 2*f/7 + 15. Determine q, given that l(q) = 0.
-1, 1, 2
Factor 0*c + 1/6*c**2 - 1/6.
(c - 1)*(c + 1)/6
Suppose 2*b - 8 = -0*b. Let u be (-4)/(b/(-3)) + 1. Let 0*k + 2/7*k**2 - 2/7*k**3 + 0 - 4/7*k**u = 0. Calculate k.
-1, 0, 1/2
Let o(q) be the first derivative of q**6/6 + 8*q**5/5 + 4*q**4 - 53. Factor o(f).
f**3*(f + 4)**2
Let q(r) be the third derivative of -r**6/40 + 3*r**5/20 - 3*r**4/8 + r**3/2 - 21*r**2. Factor q(m).
-3*(m - 1)**3
Let o(a) be the second derivative of a**7/252