t v(n) be the first derivative of l(n). What is k in v(k) = 0?
0, 1
Let o(w) be the first derivative of w**4/5 - 2*w**3/15 - 4. Factor o(f).
2*f**2*(2*f - 1)/5
Let q(h) be the first derivative of -h**4/4 + h**3 - 4*h - 4. Find u such that q(u) = 0.
-1, 2
Let j(a) be the second derivative of a**4/32 + a**3/48 - a**2/8 - 16*a. Find d, given that j(d) = 0.
-1, 2/3
Let i(y) be the third derivative of -y**5/450 + y**4/60 + 4*y**3/45 - 20*y**2. Factor i(j).
-2*(j - 4)*(j + 1)/15
Let r = 0 - -6. Let s = r + 3. Determine h, given that 2*h**3 + s*h**2 - 4*h**3 - 3*h**2 + 2 - 2*h - 4*h = 0.
1
Let r(a) be the second derivative of 3*a**6/20 - 3*a**5/10 - 5*a**4/24 + a**3 - a**2 - 25*a. What is c in r(c) = 0?
-1, 2/3, 1
Let n(o) = -o**2 - 7*o + 7. Let f be n(-6). Suppose -4*m = -f - 3. Factor -1 + 1 - 4*r - m*r**3 + 1 - 6*r**2 - 2 - r**4.
-(r + 1)**4
Let i be (5/(-3))/((-365)/438). Factor 0 + t + 5/2*t**i.
t*(5*t + 2)/2
Factor 8*o**2 + o - 3*o**4 + 12*o**3 + 11*o**4 + 2*o**5 + 0*o + o.
2*o*(o + 1)**4
Let d = -293 - -296. Solve 0 + 8/7*c + 2/7*c**d + 8/7*c**2 = 0 for c.
-2, 0
Let x = -82/7 + 24607/2100. Let n(c) be the third derivative of -x*c**5 + 0 + 0*c**3 - 1/120*c**4 + c**2 + 0*c. Factor n(w).
-w*(w + 1)/5
Let k be (-4)/(-24)*3 - (-95)/(-200). Let v(a) be the third derivative of 0*a - 1/100*a**5 + k*a**4 + 0 + 4*a**2 + 0*a**3. Suppose v(r) = 0. What is r?
0, 1
Let k(f) = -f**2 - f + 4. Let o be k(0). Factor -2*m**2 - 4 - 3 + 5 + o*m.
-2*(m - 1)**2
Let i = 203/6 + -67/2. Find y, given that -1/3 - i*y + 1/3*y**3 + 1/3*y**2 = 0.
-1, 1
Determine n, given that -16/5*n**2 + 0 + 4/5*n = 0.
0, 1/4
Let h(x) be the third derivative of -x**6/540 + x**5/180 + 2*x**3/3 - 3*x**2. Let z(m) be the first derivative of h(m). Suppose z(t) = 0. Calculate t.
0, 1
Let z be (-1)/(-3) - (5 - 112/21). Find m, given that -1/3*m**2 + 2/3*m**3 + 0 + 1/3*m**4 - z*m = 0.
-2, -1, 0, 1
Let m(r) be the third derivative of r**5/570 - r**4/57 - 5*r**3/57 - 4*r**2. Factor m(h).
2*(h - 5)*(h + 1)/19
Let k(t) be the first derivative of 1/24*t**4 + 2 - 1/40*t**5 + 1/12*t**3 - 1/4*t**2 + t. Let n(c) be the first derivative of k(c). Factor n(y).
-(y - 1)**2*(y + 1)/2
Let f(j) = 6*j**2 + 8*j - 34. Let n(y) = 2*y**2 + 3*y - 11. Let k(h) = 6*f(h) - 20*n(h). Solve k(z) = 0.
-4, 1
Let b(i) be the second derivative of i**5/60 + i**4/12 + 3*i**2/2 + i. Let v(q) be the first derivative of b(q). Determine z so that v(z) = 0.
-2, 0
Let u = -2 - -1. Let y be u/(-5) + (-95)/(-25). Factor 5*a**4 + a**4 - 5*a**3 + y*a**2 - 5*a**3.
2*a**2*(a - 1)*(3*a - 2)
Let v(r) = r**2 + r. Let s = 13 + -15. Let w(h) = -h**4 - h**3 - 8*h**2 - 8*h. Let q(l) = s*w(l) - 18*v(l). Factor q(u).
2*u*(u - 1)*(u + 1)**2
Suppose 0 + 12/7*g**3 + 0*g + 4/7*g**4 + 8/7*g**2 = 0. Calculate g.
-2, -1, 0
Factor -748 + 4*f**2 + 2*f**3 + 748.
2*f**2*(f + 2)
Let g = -10/17 - -77/102. Let v(j) be the first derivative of 0*j + 0*j**4 + 2/5*j**5 + g*j**6 - 1/2*j**2 - 3 - 2/3*j**3. Solve v(r) = 0 for r.
-1, 0, 1
What is v in 6 + 3/2*v**3 + 5/2*v**4 - 4*v + 1/2*v**5 - 13/2*v**2 = 0?
-3, -2, 1
Let s = -30 - -30. Let k(h) be the third derivative of -1/180*h**5 + s*h - 2*h**2 + 0*h**3 + 1/72*h**4 + 0. Factor k(n).
-n*(n - 1)/3
Let y = 3/22 - -5/44. Solve -z + y*z**2 + 1 = 0.
2
Let p(u) be the first derivative of u**7/84 + u**6/60 - u**5/40 - u**4/24 - u + 2. Let j(n) be the first derivative of p(n). Let j(l) = 0. Calculate l.
-1, 0, 1
Let v(o) = o**2 + o. Let a(u) = u**3 - 8*u**2 - 10*u - 1. Let g = -38 - -20. Let j(w) = g*v(w) - 2*a(w). Suppose j(f) = 0. Calculate f.
-1, 1
Factor 1/4 + 1/2*b + 1/4*b**2.
(b + 1)**2/4
Let v(u) be the first derivative of u**6/30 + u**5/25 - u**4/20 - u**3/15 - 14. Factor v(o).
o**2*(o - 1)*(o + 1)**2/5
Let q(a) be the third derivative of -a**5/150 + 4*a**4/15 - 64*a**3/15 - 23*a**2 - 1. Determine s, given that q(s) = 0.
8
Let n(j) be the second derivative of 2*j**7/21 + 4*j**6/15 + j**5/5 + j - 28. Factor n(q).
4*q**3*(q + 1)**2
Let v = -4/37 + 86/111. Determine o, given that -v*o**4 + 0*o - 2/3*o**2 + 0 - 4/3*o**3 = 0.
-1, 0
Suppose a - 4*a - 3 = 0. Let u = a - -1. Factor y**2 - 1 + u*y + 0*y.
(y - 1)*(y + 1)
Let 0 - 4/7*s**3 - 2/7*s**4 + 10/7*s**2 + 12/7*s = 0. What is s?
-3, -1, 0, 2
Determine u so that 0*u - 2/9*u**4 - 2/3*u**2 - 8/9*u**3 + 0 = 0.
-3, -1, 0
Let n be (-2)/18 + 513/243. Factor 0 + 0*r**3 + 2/3*r**4 - 4/3*r - n*r**2.
2*r*(r - 2)*(r + 1)**2/3
Let o(g) be the second derivative of g**7/2520 - g**6/540 + g**5/360 + 2*g**3/3 + 2*g. Let z(s) be the second derivative of o(s). Factor z(j).
j*(j - 1)**2/3
Factor -1/5*i**3 + 0 - 1/5*i**4 + 1/5*i + 1/5*i**2.
-i*(i - 1)*(i + 1)**2/5
Let b(d) be the second derivative of d**6/2 + 5*d**5/2 + 35*d**4/12 - 10*d**3/3 - 10*d**2 - 2*d. Let b(s) = 0. What is s?
-2, -1, 2/3
Factor -16/9 - 4/9*v**2 - 16/9*v.
-4*(v + 2)**2/9
Let m = 12 + -7. Let u(a) be the third derivative of 1/672*a**8 + 0 + 1/60*a**m + 0*a - 1/48*a**4 + a**2 + 0*a**6 + 0*a**3 - 1/210*a**7. Factor u(k).
k*(k - 1)**3*(k + 1)/2
Let q = 30 - 30. Factor q + 2/9*s**2 + 0*s.
2*s**2/9
Let c(t) = -11*t**3 - 2*t**2 + 7*t - 6. Let p(s) = s**2 - 5*s. Let i be p(4). Let w(h) = 10*h**3 + h**2 - 7*h + 5. Let k(g) = i*w(g) - 3*c(g). Factor k(u).
-(u - 1)*(u + 1)*(7*u - 2)
Suppose -s - w = -6, -6 = -6*w + 6. Factor v**3 - 4*v + 1/2*v**s - 2 - 3/2*v**2.
(v - 2)*(v + 1)**2*(v + 2)/2
Factor 2*p + 4*p**3 - 2*p**2 - 3*p - 6*p + 3*p + 2*p**4.
2*p*(p - 1)*(p + 1)*(p + 2)
Factor 10*g - 4*g - 46*g - 1 - 5*g**2 - 79.
-5*(g + 4)**2
Let n(b) be the third derivative of -b**9/7056 + b**8/3920 + b**3 - 5*b**2. Let j(p) be the first derivative of n(p). Determine i, given that j(i) = 0.
0, 1
Let n(f) be the third derivative of -f**5/60 - 7*f**4/24 + 4*f**3/3 + 28*f**2. Factor n(p).
-(p - 1)*(p + 8)
Let c = -29 + 11. Let k be c/(-2) - (-2 + 5). Factor -7 - 2 - k*o + 0*o - o**2.
-(o + 3)**2
Let x(p) be the third derivative of 3*p**7/280 - p**6/60 + 4*p**3/3 - 8*p**2. Let d(m) be the first derivative of x(m). Factor d(t).
3*t**2*(3*t - 2)
Let c = 880/7 + -124. Factor 18/7 + 2/7*s**2 - c*s.
2*(s - 3)**2/7
Let d(z) = -z**3 - 8*z**2 + z + 10. Let o be d(-8). Factor 5*w**o - 5*w**2 + 0*w**2 + w**3 + w**2.
w**2*(w + 1)
Factor -2*h - 1/2*h**2 - 2.
-(h + 2)**2/2
Determine b so that -4*b - 24*b**3 - 20*b + 44*b**2 - 8 + 0 + 12 = 0.
1/3, 1/2, 1
Let y(x) = x**2 - x - 3. Let b be y(3). Suppose 0 = -3*i + 3 + b. Factor 0*a**i - 3*a**4 + 0*a**4 + 3*a**2.
-3*a**2*(a - 1)*(a + 1)
Let -20/3*c + 28/3*c**2 - 8/3 = 0. What is c?
-2/7, 1
Let q be 2/((-144)/38) - 30/(-40). Factor -2/9*n**4 + 8/9*n - q + 8/9*n**3 - 4/3*n**2.
-2*(n - 1)**4/9
Let c = 14 + -6. Suppose -c = -5*t + 32. Find v, given that t*v**3 + 2 + v + 0*v**2 - 12*v**4 - 9*v**5 + 14*v**2 - 4 = 0.
-1, -2/3, 1/3, 1
Suppose 0 = -0*x + 4*x - 12. Factor 10*t**2 + t**3 + 2*t**3 + 5*t + t**x - t.
2*t*(t + 2)*(2*t + 1)
Suppose 0 + 5/4*s**3 - 23/4*s**2 - 5/2*s = 0. Calculate s.
-2/5, 0, 5
Let r(y) be the second derivative of 0 - 1/6*y**3 - 1/6*y**4 + 1/2*y**2 + 1/30*y**6 - 1/42*y**7 - 3*y + 1/10*y**5. Suppose r(t) = 0. Calculate t.
-1, 1
Let z(t) = -t**3 - 4*t**2 - t + 5. Let b be z(-4). Factor 5*l**2 - 27*l - b*l**4 + 0*l**4 + 1 + 15*l + 12*l**3 + 3.
-(l - 1)*(l + 1)*(3*l - 2)**2
Suppose 35 = -4*i - 2*f - 15, 0 = 5*i - 5*f + 40. Let w = i - -56/5. Factor -w*u**4 + 0*u**2 + 0 + 0*u**3 + 0*u.
-u**4/5
Let n(o) be the first derivative of -o**4/4 + 7*o**3/3 - 4*o**2 - 16*o - 2. Factor n(f).
-(f - 4)**2*(f + 1)
Let p(i) be the third derivative of -i**5/90 + i**4/12 - 2*i**3/9 - 42*i**2. Factor p(r).
-2*(r - 2)*(r - 1)/3
Let y(j) be the third derivative of -j**10/75600 - j**9/10080 + j**7/630 - j**5/12 - 2*j**2. Let c(z) be the third derivative of y(z). Factor c(k).
-2*k*(k - 1)*(k + 2)**2
Suppose -m + 0 - 2 = 0. Let v be m*(-2 + (-1)/2). Find n such that n**4 - 2*n**5 - 5*n**4 - 4*n**3 + n**v = 0.
-2, 0
Let r(h) be the second derivative of -h**9/40320 + h**7/2240 + h**6/960 - h**4/2 + 2*h. Let u(a) be the third derivative of r(a). Suppose u(d) = 0. Calculate d.
-1, 0, 2
Let c(k) be the third derivative of 1/525*k**7 + 0 + 1/150*k**6 + 0*k**3 + 3*k**2 + 0*k**4 + 0*k + 1/150*k**5. Factor c(h).
2*h**2*(h + 1)**2/5
Let i be (-10)/35 + 6/(-21). Let n = 29/14 + i. Suppose 1/2*w + 0 + 3/2*w**3 + 1/2*w**4 + n*w**2