f z**8/3360 - z**7/1260 - z**6/360 + z**5/60 + z**4/6 - 2*z. Let a(b) be the third derivative of w(b). Factor a(p).
2*(p - 1)**2*(p + 1)
Let d(y) = 2*y**5 - y**4 + 5*y**3 + 3*y - 3. Let b(i) = 6*i**5 - 4*i**4 + 14*i**3 + 8*i - 8. Let u(m) = -3*b(m) + 8*d(m). Factor u(s).
-2*s**3*(s - 1)**2
Let y(p) be the third derivative of p**5/20 - p**4/8 + 8*p**2. Factor y(d).
3*d*(d - 1)
Let b(x) = 4*x**2 - 2*x - 8. Let k(r) be the third derivative of -r**5/60 - r**4/24 + r**3/6 - 5*r**2. Let y(h) = b(h) + 2*k(h). Let y(p) = 0. Calculate p.
-1, 3
Let z = 13 - 13. Let o(x) be the third derivative of 1/504*x**8 - 2*x**2 + z*x**4 + 0*x**7 + 0*x + 0 + 0*x**5 - 1/180*x**6 + 0*x**3. Solve o(u) = 0 for u.
-1, 0, 1
Let p(l) = l - 8. Let d be p(6). Let s(w) = w**2 - 2. Let k be s(d). Factor 4/5 - 6/5*r + 2/5*r**k.
2*(r - 2)*(r - 1)/5
Let -4*g**2 + 15*g**2 - 10*g**2 - 7*g - 3*g**3 - 9*g**2 - 2 = 0. What is g?
-1, -2/3
Let w(x) be the first derivative of -2*x**5/5 + x**4/2 + 2*x**3/3 - x**2 - 1. Suppose w(k) = 0. What is k?
-1, 0, 1
Let a(y) be the second derivative of -1/3*y**3 + 0*y**2 + 0 + 2*y - 1/6*y**4. Factor a(g).
-2*g*(g + 1)
Let y(i) be the third derivative of i**7/42 + i**6/120 - i**3/2 + 4*i**2. Let g(b) = -4*b**4 + 2. Let c(x) = 3*g(x) + 2*y(x). Find r such that c(r) = 0.
0, 1
Let x = -493/9 + 55. Factor 2/9*j**3 - x*j + 2/9*j**4 + 0 - 2/9*j**2.
2*j*(j - 1)*(j + 1)**2/9
Let q(h) = h**2 - 4*h + 4. Let f be q(4). Let v be (16/(-10))/(f/(-10)). Find m, given that -3*m**3 + 2 + 3*m + 4 + m**2 - v*m**2 - 3 = 0.
-1, 1
Let j(o) = -5*o**3 + 3*o**2 + 12*o - 10. Let p(x) = 10*x**3 - 5*x**2 - 25*x + 20. Let h(v) = 5*j(v) + 3*p(v). Factor h(i).
5*(i - 1)**2*(i + 2)
Let y(x) be the third derivative of x**8/4032 - x**6/720 + x**4/288 + 7*x**2. Find j, given that y(j) = 0.
-1, 0, 1
Let w(k) be the first derivative of -k**3/6 + 7*k**2/4 - 3*k - 3. Factor w(t).
-(t - 6)*(t - 1)/2
Let j(h) be the second derivative of -h**7/294 + h**6/210 + h + 10. Determine g, given that j(g) = 0.
0, 1
Let q(p) = -p**3 + 8*p**2. Let l(t) = -2*t**2. Let z = 3 - 1. Let h(d) = z*q(d) + 9*l(d). Factor h(r).
-2*r**2*(r + 1)
Factor 4/3*p - 2*p**2 + 4/3*p**3 - 1/3*p**4 - 1/3.
-(p - 1)**4/3
Let b(p) = p**3 - p**2 + 11. Let j be b(0). Let u be j/(-4) + (2 - -1). Factor 0 + 1/2*x**4 + 0*x - 1/4*x**5 - u*x**3 + 0*x**2.
-x**3*(x - 1)**2/4
Let i = 1248/7 + -178. Let 2/7*q + 0 + i*q**2 = 0. What is q?
-1, 0
Let o be (((-320)/(-75))/(-8))/(4/(-10)). Factor -o - 2/3*b + 2/3*b**3 + 4/3*b**2.
2*(b - 1)*(b + 1)*(b + 2)/3
Factor 8*v - 5*v**3 - 2*v**3 - 2*v**2 - 2*v**2 - 5*v**3 + 4*v**5 + 4*v**4.
4*v*(v - 1)**2*(v + 1)*(v + 2)
Suppose -3*v = 26 - 110. Let a(r) = 4*r + 10*r - 3*r**2 + 6*r + v*r - 57. Let h(g) = g**2 - 12*g + 14. Let l(t) = 2*a(t) + 9*h(t). Find i, given that l(i) = 0.
2
Let q be 2/(-19) + (-52)/(-133). Factor 2/7*f**3 - q*f - 2/7 + 2/7*f**2.
2*(f - 1)*(f + 1)**2/7
Let n = 6 - 35/6. Let w(u) be the second derivative of -n*u**4 + 0*u**2 + 1/3*u**3 + u + 0. Let w(z) = 0. Calculate z.
0, 1
Factor 3*h**3 - 2*h**4 + 37*h - 4 + 4*h**3 + 3*h**3 - 23*h - 18*h**2.
-2*(h - 2)*(h - 1)**3
Suppose -8*t = -6*t. Let c(y) be the second derivative of 0*y**2 + 0*y**3 + 1/18*y**4 + t + 1/30*y**5 + 2*y. Find u such that c(u) = 0.
-1, 0
Let h(k) be the third derivative of -k**9/15120 + k**8/13440 + k**7/5040 - 5*k**4/24 - k**2. Let s(x) be the second derivative of h(x). Factor s(z).
-z**2*(z - 1)*(2*z + 1)/2
Suppose -3*l - 3 = -3*p, 0 = -3*p - 2*p - l + 11. Factor 2/7*f**p + 2/7*f + 0.
2*f*(f + 1)/7
Suppose 0 = -16*g + 19*g - 6. Suppose g - 5/2*q**4 + 8*q + 15/2*q**2 - q**3 = 0. What is q?
-1, -2/5, 2
Let n(t) be the third derivative of t**7/420 + t**6/180 - t**5/60 - t**4/12 - t**3/3 + 3*t**2. Let r(q) be the first derivative of n(q). Factor r(f).
2*(f - 1)*(f + 1)**2
Let d(z) be the third derivative of 49*z**5/450 - 7*z**4/90 + z**3/45 - 4*z**2. Solve d(f) = 0.
1/7
Let u = 3 + -1. Let p be 1 - u/(-2*1). Factor 0 + 0 + m**p + m.
m*(m + 1)
Let a(i) be the third derivative of 0*i - 5*i**2 + 1/80*i**5 - 1/160*i**6 + 0*i**3 + 0*i**4 + 0. Find s such that a(s) = 0.
0, 1
Suppose 5*w = -3*s + 37, -2*w = -4*w - 2*s + 18. Let n = w - 2. Factor 0 - 1/3*j**2 + 0*j - 1/3*j**n.
-j**2*(j + 1)/3
What is x in -8*x - 17*x**5 - 2562*x**3 + 7*x**5 + 4*x**4 + 2592*x**3 + 5*x**2 + 3*x**2 = 0?
-1, 0, 2/5, 2
Factor -10/17*m**2 + 6/17*m**3 - 2/17*m**5 + 2/17*m**4 + 0 + 4/17*m.
-2*m*(m - 1)**3*(m + 2)/17
Let x(f) be the first derivative of -f**7/210 + f**6/75 - f**5/100 - 6*f + 2. Let k(z) be the first derivative of x(z). Determine g so that k(g) = 0.
0, 1
Let t(w) = w**4 - w**3 - w**2 - w - 1. Let b(x) = -3*x**4 + 10*x**3 + 12*x**2 - 2*x - 5. Let d(j) = b(j) + 4*t(j). Determine l, given that d(l) = 0.
-3, -1, 1
Let y be 18/(-45) + (-7)/(-5). Let q(l) be the first derivative of 0*l + 1/2*l**2 - 1/6*l**3 + y. Find s, given that q(s) = 0.
0, 2
Let b(n) be the second derivative of 0*n**4 + 1/50*n**5 - 1/75*n**6 + 0*n**3 + 2*n + 0 + 0*n**2. Suppose b(t) = 0. Calculate t.
0, 1
Let b be 9 + 1/1*-1. Factor 2*v**2 + 3*v**3 + b*v - 14*v + v**2.
3*v*(v - 1)*(v + 2)
Factor 0 - 4/11*r + 5/11*r**2 - 1/11*r**3.
-r*(r - 4)*(r - 1)/11
Let b(w) be the first derivative of 2*w**5/55 + w**4/11 - 2*w**3/11 - 4*w**2/11 + 8*w/11 + 14. Factor b(t).
2*(t - 1)**2*(t + 2)**2/11
Let j(p) be the second derivative of p**5/30 - p**3/3 - p**2 + p. Let b(x) be the first derivative of j(x). Suppose b(v) = 0. Calculate v.
-1, 1
Suppose -2*o = -4*n + 16, -4*o - 14 = -o - n. Let u(f) = -3*f**3 + 2*f**2 - 3*f. Let c(z) = z**3 - z**2 + z. Let a(t) = o*c(t) - u(t). What is g in a(g) = 0?
0, 1
Let b(h) be the first derivative of -h**6/60 - 3*h**5/80 - h**4/48 + 4*h - 2. Let k(i) be the first derivative of b(i). Determine d, given that k(d) = 0.
-1, -1/2, 0
Let u(c) be the third derivative of c**6/120 + c**5/60 - 3*c**2. Determine y, given that u(y) = 0.
-1, 0
Let l be (-8)/(-6) - (0 + -4). Let l*v**2 - 7/3*v**3 + 2/3 - 11/3*v = 0. Calculate v.
2/7, 1
Let u be 0 - (-3 + 4 + -942). Let w = 10359/11 - u. What is q in 8/11*q**3 + 0*q**2 + 0 + 0*q - 70/11*q**5 - w*q**4 = 0?
-2/5, 0, 2/7
Let u(n) be the first derivative of -1/6*n**3 + 1 - 1/4*n**2 + n. Suppose u(c) = 0. Calculate c.
-2, 1
Let l = -136 + 136. Let o(c) be the third derivative of -c**4 + l + 0*c - 11/10*c**5 - 9/70*c**7 + 4*c**2 - 3/5*c**6 - 1/2*c**3. Find h, given that o(h) = 0.
-1, -1/3
Let h be 6 - 7 - (-57)/45. Let a(w) be the first derivative of -1/5*w**2 - 2/5*w + h*w**3 - 1/15*w**6 - 3 - 2/25*w**5 + 1/5*w**4. Factor a(b).
-2*(b - 1)**2*(b + 1)**3/5
Factor 20*j - 12*j**2 + 8*j**4 + 4*j**4 - 8*j**4 - 4*j**3 - 8.
4*(j - 1)**3*(j + 2)
Suppose 5*c - 9 = 2*c. Suppose -3*d = -28 + 4. Factor c*k**2 + 10*k**3 + 2*k**5 + 3*k**2 + d*k**4 - 2*k**2 + 0*k**2.
2*k**2*(k + 1)**2*(k + 2)
Let x be 4/2 + 20/(-24)*2. Let m(r) be the first derivative of 1 - x*r**2 - 2/27*r**3 - 4/9*r. What is s in m(s) = 0?
-2, -1
Let n(c) be the third derivative of c**7/630 - c**6/180 + c**5/180 - 7*c**2 + 3. Suppose n(r) = 0. Calculate r.
0, 1
Let y(t) be the first derivative of -t**5/40 - t**4/8 - t**3/6 - 2*t - 3. Let r(c) be the first derivative of y(c). Suppose r(p) = 0. Calculate p.
-2, -1, 0
Let y(t) be the third derivative of 2*t**2 + 1/210*t**7 + 1/15*t**5 + 0 + 1/36*t**6 + 1/12*t**4 + 0*t + 1/18*t**3. Let y(a) = 0. Calculate a.
-1, -1/3
Let o(w) be the first derivative of 2/15*w**5 + 3 + 0*w + 0*w**2 + 2/9*w**3 - 1/3*w**4. Solve o(v) = 0.
0, 1
Let d(b) be the first derivative of -1/11*b**2 - 1 + 13/22*b**4 - 6/11*b**3 - 2/11*b**5 + 4/11*b. Factor d(i).
-2*(i - 1)**3*(5*i + 2)/11
Let y(l) be the second derivative of -l**5/4 + 55*l**4/12 - 175*l**3/6 + 125*l**2/2 - 40*l. Factor y(w).
-5*(w - 5)**2*(w - 1)
Let r = 41 + -38. Solve 1/3*b**4 + 0*b + 0*b**2 + 1/3*b**r + 0 = 0 for b.
-1, 0
Let w(i) = i**3 - 10*i**2 - 25*i + 12. Let u be w(12). Determine a, given that -1/2*a**4 - 1/4*a**5 + 0*a + 0 + u*a**2 - 1/4*a**3 = 0.
-1, 0
Let f(n) be the first derivative of 2*n**3/9 + 43. Factor f(u).
2*u**2/3
What is p in -3*p**3 + 9/5*p**2 - 9/5*p**4 + 0 + 12/5*p + 3/5*p**5 = 0?
-1, 0, 1, 4
Let h(n) be the third derivative of 1/84*n**7 - n**2 + 5/96*n**4 - 1/12*n**3 - 1/48*n**6 - 1/448*n**8 + 0 + 0*n**5 + 0*n. Solve h(u) = 0 for u.
-2/3, 1
Let j(s) be