 -4 - f - f**h - f**2 + 5.
-(f + 1)*(2*f - 1)
Let c(u) be the first derivative of -u**7/3360 - u**6/1440 - 4*u**3/3 - 8. Let f(y) be the third derivative of c(y). Find w, given that f(w) = 0.
-1, 0
Let r = -72 + 72. Let n(y) be the second derivative of 2*y + 0*y**3 + r*y**4 + 0 + 0*y**2 + 1/30*y**5. Factor n(l).
2*l**3/3
Factor 40*i - 201 - 4*i**2 + 0*i**2 + 8*i**2 + 237.
4*(i + 1)*(i + 9)
Let p(g) be the third derivative of -13/540*g**6 + 2/315*g**7 + 1/30*g**5 + 0*g + 0 + 5*g**2 + 0*g**3 - 1/54*g**4. Let p(z) = 0. Calculate z.
0, 1/2, 2/3, 1
Let r(v) be the second derivative of 0 + 8*v**2 - 32/3*v**3 + 1/3*v**4 + 7*v + 21/5*v**5. Find k such that r(k) = 0.
-1, 2/7, 2/3
Let r(f) be the third derivative of 1/20*f**5 + 1/8*f**4 + 0 + 0*f - f**3 + f**2. Factor r(m).
3*(m - 1)*(m + 2)
Let y(p) = p + 3. Let c be y(0). What is d in 4*d**2 - c*d - 6*d**3 + 2*d**3 + d + 2*d**3 = 0?
0, 1
Let m(u) be the third derivative of u**8/1680 + u**7/420 + u**6/360 + u**3/2 - 4*u**2. Let j(l) be the first derivative of m(l). Suppose j(k) = 0. What is k?
-1, 0
Let k(b) be the third derivative of b**8/1176 - 2*b**7/735 + b**6/420 + 3*b**2. Factor k(s).
2*s**3*(s - 1)**2/7
Let i = 67 + -66. Let r(q) be the first derivative of 1/18*q**4 + 0*q**3 + 0*q - i + 0*q**2. Factor r(o).
2*o**3/9
Suppose -2*s = 6, -1 = -j - 3*s + 2*s. Let a(w) be the third derivative of 4*w**2 + 1/150*w**5 + 0 + 1/60*w**j - 2/15*w**3 + 0*w. Factor a(o).
2*(o - 1)*(o + 2)/5
Let m(y) be the first derivative of -y**6/540 + y**4/36 + 8*y**3/3 + 8. Let d(f) be the third derivative of m(f). Find l, given that d(l) = 0.
-1, 1
Factor 10/3 + 2/15*f**2 + 4/3*f.
2*(f + 5)**2/15
Determine m so that 3/2*m**2 - 9/4 - 15/4*m = 0.
-1/2, 3
What is q in 16/3*q**4 + 0 - 28/3*q**2 - 16/3*q**3 - 8/3*q = 0?
-1/2, 0, 2
Let m be (2/(-2))/((-1)/2). Let s be (-2)/(-6)*(2 - 2). Determine p so that -3*p + 3*p - p + s*p**2 + p**m = 0.
0, 1
Let l(j) = -j**2 - 4*j + 1. Let z be l(-3). Suppose 21 = 4*x - i, x + 3*i = -x - 7. What is c in 0*c**x + 9*c**5 - z*c**5 + c**4 + c**4 = 0?
-2/5, 0
Let m(h) = 3*h**2 - 61*h + 22. Let a be m(20). Let 3/5*b**a - 6/5*b + 0 = 0. What is b?
0, 2
Suppose 4*y = -5*d + 8, -8 = -4*y - 0*y + 4*d. Solve 6*p**4 - y*p**4 + 4*p**3 + p**5 - 2*p**4 - 3*p**5 = 0.
-1, 0, 2
Let n(s) be the third derivative of s**7/210 - s**6/15 + 23*s**5/60 - 7*s**4/6 + 2*s**3 - 32*s**2. Solve n(r) = 0.
1, 2, 3
Let c(n) be the second derivative of -n**7/441 + 4*n**6/315 - 2*n**5/105 + 21*n. Factor c(l).
-2*l**3*(l - 2)**2/21
Let f(n) be the second derivative of n**4/72 - n**2/3 - 8*n. Factor f(g).
(g - 2)*(g + 2)/6
Let c(d) be the third derivative of d**5/135 - d**4/18 - 8*d**2. Suppose c(u) = 0. Calculate u.
0, 3
Solve -4 - 10/3*x - 2/3*x**2 = 0.
-3, -2
Let g(i) = -i**3 + 2*i**2 + 5*i + 9. Let f(w) = w**2 + w + 1. Let p(s) = 5*f(s) - g(s). Factor p(n).
(n - 1)*(n + 2)**2
Suppose 0 + 12/7*k**3 - 16/7*k + 2/7*k**5 + 10/7*k**4 - 8/7*k**2 = 0. Calculate k.
-2, 0, 1
Let j(r) be the third derivative of 7*r**6/60 - 11*r**5/30 + 8*r**4/21 - 4*r**3/21 - 13*r**2. Find k, given that j(k) = 0.
2/7, 1
Factor -2/3*r**2 - 1/3*r**3 - 1/3*r + 0.
-r*(r + 1)**2/3
Let r(p) = 9*p**3 + 3*p**2 - 3*p - 9. Let k(t) = -8*t**3 - 3*t**2 + 3*t + 8. Let f(q) = 6*k(q) + 5*r(q). Factor f(x).
-3*(x - 1)*(x + 1)**2
Let 0 + 0*v + 2/7*v**5 + 0*v**2 + 8/7*v**3 + 10/7*v**4 = 0. Calculate v.
-4, -1, 0
Let q(t) be the second derivative of t**6/10 + t**5/10 - t**4/3 - t**3/3 + t**2/2 - 11*t. Find j, given that q(j) = 0.
-1, 1/3, 1
Let f(k) be the first derivative of -2 - 6/5*k**5 - 1/2*k**6 + 0*k + 3/2*k**2 + 0*k**4 + 2*k**3. Factor f(u).
-3*u*(u - 1)*(u + 1)**3
Determine v, given that -4*v - 16*v**2 - 21*v + 31*v**2 = 0.
0, 5/3
Let f(c) = 3*c**2 + 3*c + 3. Let q be f(-1). Let x(n) be the third derivative of 0 + 1/27*n**q - 1/54*n**4 + 1/270*n**5 + 2*n**2 + 0*n. Solve x(d) = 0 for d.
1
Suppose 0*p - 10 = 2*p, 0 = -3*x + 4*p + 26. Let v(y) be the first derivative of -2/27*y**3 + 1 + 0*y + 1/9*y**x. Factor v(c).
-2*c*(c - 1)/9
Let v(f) be the third derivative of f**5/20 - f**4/60 - 3*f**2. Factor v(k).
k*(15*k - 2)/5
Let s(l) = l**2 + 3*l - 4. Let o be s(-6). Let n = o - 14. Factor 4/7*v**2 + 0 - 10/7*v**3 + n*v.
-2*v**2*(5*v - 2)/7
Let q = 26 - 259/10. Let s(a) be the first derivative of 0*a**5 + 1/15*a**6 - q*a**4 + 0*a + 0*a**2 + 0*a**3 - 2. Factor s(m).
2*m**3*(m - 1)*(m + 1)/5
Find f, given that -4 - 5*f**3 - 5*f**2 + 0*f**3 + 10 + 5*f - 1 = 0.
-1, 1
What is s in 76/13*s - 16/13 - 74/13*s**2 + 14/13*s**3 = 0?
2/7, 1, 4
Let z(t) be the third derivative of t**6/480 + t**5/120 + 19*t**2. Factor z(y).
y**2*(y + 2)/4
Let l = 20 - 16. Let g(k) be the second derivative of -1/90*k**6 + 0*k**3 + 0 - 2*k - 1/126*k**7 + 1/36*k**l + 1/60*k**5 + 0*k**2. Factor g(j).
-j**2*(j - 1)*(j + 1)**2/3
Let r(d) be the second derivative of 1/10*d**5 - 3*d - 1/21*d**4 - 1/3*d**3 + 0 + 2/7*d**2. Factor r(g).
2*(g - 1)*(g + 1)*(7*g - 2)/7
Let u = 2824/5 - 563. Solve 3/5*h**4 + 0 + 0*h**3 - 6/5*h - u*h**2 = 0 for h.
-1, 0, 2
Let g(r) = -3*r**4 + 3*r**3 + 3*r**2 + r - 4. Suppose -3*y = -15 + 3. Let n(k) = -k**4 - 1. Let x(j) = y*n(j) - g(j). Factor x(u).
-u*(u + 1)**3
Let n be (21/(-35))/(4/(-5)). Factor -3/2*r**2 + 0 + 0*r + 3/4*r**4 - n*r**3.
3*r**2*(r - 2)*(r + 1)/4
Suppose 11*n + 10*n**2 - 7*n - 4*n - 5*n**3 - 5*n = 0. What is n?
0, 1
Let o(y) = -3*y**2 - 5*y - 7. Let z(i) = i**2 + 2*i + 3. Let f be 1/((-1)/(-6)*3). Let d(b) = f*o(b) + 5*z(b). Factor d(k).
-(k - 1)*(k + 1)
Let a(u) be the third derivative of -1/20*u**5 + 0*u**3 + 0*u + 1/40*u**4 + 4*u**2 + 0. Factor a(m).
-3*m*(5*m - 1)/5
Determine a so that 6 - 27*a**3 - 3 - 48*a**2 - 15*a + 1 + 2 = 0.
-1, 2/9
Let l be -4*(-3 - 20/(-8)). Let g(m) be the third derivative of 0*m + 1/30*m**5 + 0*m**3 + 0*m**4 + 0 + 2*m**l + 1/60*m**6. Let g(h) = 0. What is h?
-1, 0
Let s(d) = -2*d**3 + 2*d**2 + 25*d - 2. Let n be s(4). Determine j so that -n*j - 2/3*j**3 + 2*j**2 + 2/3 = 0.
1
Let t(g) be the third derivative of g**9/98280 - g**8/43680 + g**4/8 + 2*g**2. Let j(i) be the second derivative of t(i). Suppose j(x) = 0. What is x?
0, 1
Let z(n) be the third derivative of 2*n**7/735 + n**6/70 + 2*n**5/105 - 9*n**2. Determine o, given that z(o) = 0.
-2, -1, 0
Suppose -5*o - 3*k + 10 = 0, 6 = -0*o + 3*o + 5*k. Factor 2*z**o - z**2 - 3 + 2*z**2 + 0.
3*(z - 1)*(z + 1)
Let g(o) be the second derivative of -o**7/280 + o**6/60 - o**5/40 - o**3/2 + 4*o. Let k(z) be the second derivative of g(z). Determine v, given that k(v) = 0.
0, 1
Let -9*n**5 - 27/2*n**3 - 3*n**2 + 0*n - 39/2*n**4 + 0 = 0. What is n?
-1, -2/3, -1/2, 0
Let w = -639 + 1281/2. Suppose w*l + 0 + 9*l**3 + 6*l**2 + 3/2*l**5 + 6*l**4 = 0. Calculate l.
-1, 0
Let h(g) = g**3 + 5*g**2 - 8*g - 9. Let p be h(-6). Factor 2*f**5 + 2*f**4 - f**3 - 2*f**2 - f**p + 0*f**2.
2*f**2*(f - 1)*(f + 1)**2
Let u(r) be the first derivative of -4/35*r**5 + 2/7*r**2 + 4/21*r**3 + 2 - 1/7*r**4 + 0*r. Factor u(l).
-4*l*(l - 1)*(l + 1)**2/7
Let c be 85/165 + (-24)/132. Let 2/3*z**2 + 0*z + 0 - c*z**3 = 0. What is z?
0, 2
Let m(r) be the third derivative of -5*r**8/308 - 3*r**7/55 + r**6/44 + 6*r**5/55 - r**4/11 + 8*r**2. Determine g, given that m(g) = 0.
-2, -1, 0, 2/5, 1/2
Let c be (1/(-4))/(23/(-4) + 5). Factor -c*q**3 + 1/3*q**2 + 0 + 1/3*q - 1/3*q**4.
-q*(q - 1)*(q + 1)**2/3
Let k = -27 + 45. Suppose 0 = n - 4*b + k, 0 = -0*n + 3*n + 3*b - 21. Factor -3*v**3 - v**3 + n*v + 3*v**5 - v**5.
2*v*(v - 1)**2*(v + 1)**2
Let u(p) be the first derivative of p**4/6 + 2*p**3/9 - 14. Factor u(i).
2*i**2*(i + 1)/3
Let l(d) be the third derivative of -d**6/480 - 3*d**5/80 - 7*d**4/48 + 32*d**2. Find r such that l(r) = 0.
-7, -2, 0
Let q(n) = -6*n**2 + 6*n. Let p(i) = -5*i**2 + 5*i. Let l(m) = -4*p(m) + 3*q(m). Find o such that l(o) = 0.
0, 1
Let l(d) = d**2 - 11*d - 3. Let u(r) = -2*r**2 + 11*r + 3. Let g(n) = -2*l(n) - 3*u(n). Factor g(m).
(m - 3)*(4*m + 1)
Let o = 37/5 - 7. Let l = 7816/5 + -1563. Let -l*p - 3/5*p**2 + 1/5*p**3 + 1/5*p**4 + o = 0. What is p?
-2, -1, 1
Let u(a) be the third derivative of 0 + 3*a**2 - 2/9*a**3 + 0*a + 7/36*a**4 - 1/18*a**5. Determine f so that u(f) = 0.
2/5, 1
Let t(u) be the first derivative of -1 + 3/7*u**4 + 0*u - 8/21*u**3 + 1/21*u**6 - 8/35*u**5 + 1/7*u**2. Factor t(b).
2*b*(