. Let -2/5*l**x + 0 - 1/5*l**4 + 0*l**2 + 0*l = 0. What is l?
-2, 0
Let u be 6/(-6) + 10/8. Let s(c) be the first derivative of 0*c**2 - 1/5*c**5 + 1/24*c**6 + 0*c**3 - 1 + 0*c + u*c**4. Factor s(h).
h**3*(h - 2)**2/4
Let b be (10/(-15))/((-4)/18). Let o(z) be the first derivative of -7*z**2 + 3*z**2 + 2*z**2 + 2*z**b - 2. Factor o(y).
2*y*(3*y - 2)
Let m(h) be the second derivative of h**4/8 + 3*h**3/4 + 3*h**2/2 + 3*h. Suppose m(k) = 0. Calculate k.
-2, -1
Let z(s) be the third derivative of -s**7/1260 - s**6/720 + 30*s**2. Factor z(h).
-h**3*(h + 1)/6
Factor 14*c**3 + 19*c**4 - 16*c**4 - 2*c**3 + 15*c**2 + 6*c.
3*c*(c + 1)**2*(c + 2)
Let l(z) = -5*z**3 - 19*z**2 - 11*z - 5. Let k(a) = a**2 - a. Let m(r) = -4*k(r) - l(r). Factor m(s).
5*(s + 1)**3
Let p(u) = -u. Let r be p(8). Let h be ((-3)/(-2))/((-18)/r). Factor -8/3*q**3 + 0 - q**4 - h*q - 7/3*q**2.
-q*(q + 1)**2*(3*q + 2)/3
Suppose 13 = 4*b - 43. Suppose -8*k + 88*k**2 - 242*k**3 + b - 14 = 0. Calculate k.
0, 2/11
Let u = -9 + 3. Let y be (2 - 8)*2/u. Factor -5*z**3 + 4 - 4*z**y + 10*z - 5*z**3 + 0*z**3.
-2*(z - 1)*(z + 1)*(5*z + 2)
Factor 3/7*m**3 + 0 + 18/7*m**2 + 15/7*m.
3*m*(m + 1)*(m + 5)/7
Let l be (-32)/(-24) - (-2)/(-3). Factor -l*d + 2/3*d**3 - 1/6 + 1/6*d**2.
(d - 1)*(d + 1)*(4*d + 1)/6
Let q(f) be the second derivative of f**7/147 - f**6/105 - 15*f. Factor q(s).
2*s**4*(s - 1)/7
Let r(j) = j**2 + 1. Let a(c) = 5*c**2 + c + 2. Let z(w) = -3*a(w) + 12*r(w). Factor z(h).
-3*(h - 1)*(h + 2)
Let r(b) = b**2 + 8*b + 3. Let v be (9 + -1)*(5 - 6). Let p be r(v). Factor 0*z + 1/2*z**2 - 3/4*z**p + 0.
-z**2*(3*z - 2)/4
Factor 19*m - 16*m - 3*m**2 + m**3 + 3*m**2 + 4*m**2.
m*(m + 1)*(m + 3)
Let o(b) be the second derivative of b**4/8 - b**3/18 - 22*b. Suppose o(q) = 0. What is q?
0, 2/9
Let b(n) = 12*n**3 + 13*n**2 - 6. Let c(u) = 18*u**3 + 19*u**2 - 9. Let p(o) = -8*b(o) + 5*c(o). What is f in p(f) = 0?
-1, 1/2
Let j(g) be the third derivative of -g**9/15120 + g**7/2520 - 5*g**4/24 - 5*g**2. Let h(r) be the second derivative of j(r). Factor h(w).
-w**2*(w - 1)*(w + 1)
Let i(q) be the third derivative of 0*q - 8/1155*q**7 - 1/33*q**6 - 3/55*q**5 + 0 + q**2 - 1/33*q**3 - 7/132*q**4. Suppose i(l) = 0. What is l?
-1, -1/2
Let v(x) be the second derivative of -1/28*x**4 + 1/14*x**3 + 0 + 0*x**2 - 3*x. Let v(u) = 0. What is u?
0, 1
Let j(b) be the third derivative of -2*b**7/315 + 2*b**5/45 - 2*b**3/9 - 12*b**2. Factor j(p).
-4*(p - 1)**2*(p + 1)**2/3
Let s be (-1)/2*0 - 0. Determine d, given that -4/3*d**4 + 0 - 2*d**3 + s*d + 4/3*d**2 = 0.
-2, 0, 1/2
Let j(g) = -g**3 - 12*g**2 - 4*g + 12. Let m(l) = -2*l**3 - 12*l**2 - 4*l + 12. Let f(s) = -6*j(s) + 5*m(s). Factor f(q).
-4*(q - 3)*(q - 1)*(q + 1)
Let c(h) be the first derivative of 0*h**2 - h**3 - 2 + 3/4*h**4 + 0*h. Factor c(w).
3*w**2*(w - 1)
Let l(i) be the second derivative of -i + 0*i**4 + 0 + 1/2*i**6 + 0*i**2 + 0*i**3 - 3/10*i**5. Find k, given that l(k) = 0.
0, 2/5
Let g(b) = b**2 + 5*b - 10. Let f be g(-7). Let r = 0 + 2. Factor -22*x**4 + 8*x**5 + 2*x**2 + 17*x**3 - f*x**r + 1 + 3*x**2 - 5*x.
(x - 1)**3*(2*x + 1)*(4*x - 1)
Let a = -40 - -39. Let x be 1/((4/(-6))/a). What is k in -3/2*k**2 - 3*k - x = 0?
-1
Let c(f) = 5*f**5 + 12*f**4 - 17*f**3 - 17*f**2 + 5*f + 12. Let q(j) = -3*j**5 - 8*j**4 + 11*j**3 + 11*j**2 - 3*j - 8. Let s(x) = 5*c(x) + 7*q(x). Factor s(g).
4*(g - 1)**2*(g + 1)**3
Let m(g) be the second derivative of 1/30*g**4 + 1/50*g**5 - 2*g - 1/5*g**2 - 1/15*g**3 + 0. Factor m(p).
2*(p - 1)*(p + 1)**2/5
Let u(n) be the second derivative of n**4/28 - 3*n**3/7 + 27*n**2/14 - 2*n. Factor u(h).
3*(h - 3)**2/7
Let o = -53 + 56. Let g(k) be the first derivative of 0*k - 2/9*k**o - 3 + 0*k**2. Factor g(i).
-2*i**2/3
Let g(v) be the third derivative of -5*v**8/672 + v**7/42 + v**6/16 - v**5/6 - 5*v**4/12 - 11*v**2. Suppose g(x) = 0. What is x?
-1, 0, 2
Let j(k) = 2*k**3 - k + 1. Let g(p) = -p + 1. Let q(b) = -g(b) + j(b). Solve q(r) = 0.
0
Factor -4/7*d**2 - 5/7*d - 1/7*d**3 - 2/7.
-(d + 1)**2*(d + 2)/7
Let h(n) be the second derivative of n**6/15 + 3*n**5/10 - n**4/6 - n**3 - n - 1. Factor h(k).
2*k*(k - 1)*(k + 1)*(k + 3)
Factor 6*i**2 + 12*i**2 - 17*i**2 - 2*i - 3*i.
i*(i - 5)
Let u(i) be the second derivative of i**6/60 - i**5/30 - i**4/12 + i**3/3 + i**2/2 - 2*i. Let c(d) be the first derivative of u(d). Solve c(p) = 0.
-1, 1
Let p(g) be the first derivative of -1/9*g**2 + 0*g - 8 + 8/27*g**3 - 1/27*g**6 - 1/3*g**4 + 8/45*g**5. Factor p(o).
-2*o*(o - 1)**4/9
Let v(j) be the third derivative of -j**7/945 + j**6/135 - j**5/54 + j**4/54 + 6*j**2. Factor v(g).
-2*g*(g - 2)*(g - 1)**2/9
Let u(b) be the third derivative of -b**7/315 - 7*b**6/900 - b**5/225 - 6*b**2. Factor u(g).
-2*g**2*(g + 1)*(5*g + 2)/15
Let c(l) be the first derivative of 2*l**6/3 - 8*l**5/5 - 2. Factor c(j).
4*j**4*(j - 2)
Suppose -3*x = 3*k - 18 - 3, k = -4*x + 22. Let v(y) be the third derivative of 0*y + y**k - 1/90*y**5 + 0*y**4 + 0 + 0*y**3. Factor v(a).
-2*a**2/3
Let b(y) be the third derivative of -y**5/100 - 3*y**4/40 - 24*y**2. Solve b(l) = 0 for l.
-3, 0
Suppose -7*b + 3*b = -12. Let c = -48 + 99/2. Factor 0*z + 0 - z**2 + c*z**b.
z**2*(3*z - 2)/2
Let a be -5*((-2)/(-2) + 111/(-105)). Let b = 220/623 + -6/89. Find k such that -a*k + b*k**2 - 4/7 = 0.
-1, 2
Suppose -2*n + 0*n + 2*q + 8 = 0, 3*q + 24 = 5*n. Suppose -3*p + 5*p = n. Solve -a**p + a + 2*a - a - a**2 = 0 for a.
-2, 0, 1
Let i = -12 - -17. Suppose -2*r + 5 = -k, -2*r = r + k - i. What is h in -r*h**4 - 2*h**3 - h**3 + 0*h**2 - h**2 = 0?
-1, -1/2, 0
Let t = 6 + 5. Suppose -4*o + 1 = -43. Factor o + y**2 - t.
y**2
Let v = 2 - -1. Let g be (21/15 - 3)/(-2). Find h, given that 0*h + g*h**2 + 0 + 2*h**v = 0.
-2/5, 0
Let b(d) be the second derivative of d**7/17640 - d**4/12 + 4*d. Let w(q) be the third derivative of b(q). Factor w(u).
u**2/7
Let b be (1/3)/(3/18). Let s(n) be the first derivative of 2 + 0*n + 1/9*n**4 + 0*n**b - 2/27*n**3 - 2/45*n**5. Factor s(i).
-2*i**2*(i - 1)**2/9
Let c(w) be the third derivative of w**5/120 - w**4/24 + 17*w**2. Solve c(f) = 0 for f.
0, 2
Factor 2/21 - 2/21*l**2 + 2/21*l**3 - 2/21*l.
2*(l - 1)**2*(l + 1)/21
Let 0*j + 0 - 6/7*j**2 - 16/7*j**3 = 0. What is j?
-3/8, 0
Factor -5/4*j**3 - 135*j - 270 - 45/2*j**2.
-5*(j + 6)**3/4
Let z(j) = 4*j**2 - 3*j - j**2 - 2*j**2 + 4. Let c be z(3). Factor p**4 - 2*p**5 + 0*p**c + 3*p**5.
p**4*(p + 1)
Let s(r) be the first derivative of -r**4 - 4*r**3/3 + 34. Factor s(k).
-4*k**2*(k + 1)
Let a(u) = -2*u**3 - 10*u**2 - 13*u - 18. Let b be a(-4). Solve 2/5*m**b + 0*m - 2/5 = 0.
-1, 1
Let k be 9/45 + 122/(-10). Let r be (5/45)/((-2)/k). Factor 1/3*y**3 - 1/3*y + 2/3 - r*y**2.
(y - 2)*(y - 1)*(y + 1)/3
Let x(t) be the first derivative of -t + 3/4*t**4 + 1/3*t**3 - 3/2*t**2 - 2. Factor x(s).
(s - 1)*(s + 1)*(3*s + 1)
Let u be (-10)/(-4)*(-8)/(-10). Factor -2*f**4 + 21*f - 21*f + u*f**2.
-2*f**2*(f - 1)*(f + 1)
Let q(g) be the third derivative of g**8/840 - g**7/105 + g**6/50 + g**5/75 - 7*g**4/60 + g**3/5 - 74*g**2. Find z such that q(z) = 0.
-1, 1, 3
Let m(b) be the third derivative of b**6/210 - b**5/15 - b**4/42 + 2*b**3/3 - 37*b**2. Find c such that m(c) = 0.
-1, 1, 7
Factor 1/8*x**3 + 0 - 1/8*x + 0*x**2.
x*(x - 1)*(x + 1)/8
Let r(w) be the second derivative of w**5/40 - w**3/4 + 2*w**2 + 2*w. Let n(b) be the first derivative of r(b). Factor n(f).
3*(f - 1)*(f + 1)/2
Suppose 0 = -3*k + 2*u - 5, 4*u = -2*k + 2*u - 10. Let l be (-13)/2 - k - -4. Factor -1/4 - 1/4*m**2 - l*m.
-(m + 1)**2/4
Let u be (-2)/6*12/(-5). Let s = 387/335 - -3/67. Solve u - s*i + 2/5*i**2 = 0 for i.
1, 2
Let w(h) be the first derivative of 9 + 0*h - 2/3*h**6 - 3*h**4 + 12/5*h**5 + 4/3*h**3 + 0*h**2. Factor w(g).
-4*g**2*(g - 1)**3
Suppose -s = -3*s + 4. Let m**3 - 4*m - 6*m**s - 4*m**4 - 10*m**4 + 23*m**3 = 0. Calculate m.
-2/7, 0, 1
Factor 75*r**2 + 67 + 12*r**3 + 126*r + 54 - 145 + 51.
3*(r + 3)**2*(4*r + 1)
Let a(g) = -g**4 + g**2 + g. Let m(h) = 8*h**4 - 12*h**3 + 20*h**2 - 30*h + 8. Let f(z) = -6*a(z) - m(z). Factor f(d).
-2*(d - 2)**2*(d - 1)**2
Let i(y) be the first derivative of y**3 - 9*y**2/2 + 4. Factor i(o).
3*o*(o - 3)
Let g(s) = s**2 - 5*s - 4. Let p be g(6). What is w in w**2 + w**2 - 2*w**2 + 2*w - p*w**3 = 0?
-1, 0, 1
Let x = -3 -