f(a) be the third derivative of -a**7/840 + a**6/480 + a**5/240 - a**4/96 + 5*a**2. Solve f(i) = 0.
-1, 0, 1
Let z(l) = -l - 4. Let r(w) = -w**3 + 6*w**2 + 5*w + 8. Let i be r(7). Let o be z(i). Factor -2*q**o - 3 + 3 + 4*q**2.
2*q**2
Let k = 1/119 - -355/238. Find r such that -3/2*r + 1 + k*r**3 + 5/2*r**4 - 7/2*r**2 = 0.
-1, 2/5, 1
Let w be ((-1)/(-12))/(7/8). Let p(n) be the first derivative of w*n**3 - 2/7*n + 0*n**2 - 2. Factor p(k).
2*(k - 1)*(k + 1)/7
Let k be -1*0*(4 - (-3 - -6)). Determine v so that -3/5*v**4 + 9/5*v**3 + k + 3/5*v - 9/5*v**2 = 0.
0, 1
Let j = 8 + -22/3. Suppose -7 = -4*f + 1. Factor v - j + 2/3*v**f.
(v + 2)*(2*v - 1)/3
Let a(k) be the third derivative of 0*k**5 + 0*k + 1/60*k**4 - 1/30*k**3 - 1/300*k**6 + 7*k**2 + 1/1050*k**7 + 0. Factor a(b).
(b - 1)**3*(b + 1)/5
Suppose -58*c + 65*c = 21. What is i in -16/3 + 8*i + 12*i**2 + 10/3*i**c = 0?
-2, 2/5
Let j(n) = -n**2 + 7*n - 7. Let k be (-1 + (-21)/(-6))*2. Let p be j(k). Let 1/2*u + 0 - u**2 + u**4 - 2*u**p + 3/2*u**5 = 0. Calculate u.
-1, 0, 1/3, 1
Let i(l) = 7*l**3 - 2*l**2. Let s(a) = 8*a**3 + 2*a**3 - 4*a**2 - 2*a**2 + 10*a**3. Let v(x) = -14*i(x) + 5*s(x). Factor v(f).
2*f**2*(f - 1)
Let k = 24 - 18. Let i be k/18 + (-2)/(-18). Solve 0 + 14/9*x**3 + i*x - 2*x**2 = 0 for x.
0, 2/7, 1
Suppose 4*z = 45 - 9. Let v be -1 - 0 - (-15)/z. Find f, given that 0 - 1/3*f**3 - v*f + f**2 = 0.
0, 1, 2
Let u(f) = 2*f + 10. Let z be u(-5). Let g(r) be the first derivative of -1/10*r**5 + 0*r + z*r**2 + 1/6*r**3 - 1 + 1/12*r**6 - 1/8*r**4. Factor g(m).
m**2*(m - 1)**2*(m + 1)/2
Factor -3*i - 3*i**4 + 3*i**2 + 2*i - i + 2*i**4.
-i*(i - 1)**2*(i + 2)
Suppose -4*r - 4 = 4*j + j, 0 = -4*j - 3*r - 3. What is w in 54*w + 33 + 2*w**3 + 21 + 18*w**2 + j*w**3 = 0?
-3
Let f be (-1)/(1 + 10/(-8)). Let u(k) = -k**2 - k. Let o be u(-1). Determine a, given that o*a + 1/3*a**3 + 1/3*a**f + 0 - 2/3*a**2 = 0.
-2, 0, 1
Let v(g) = 2*g**2. Let t be v(1). Let j(w) be the second derivative of -2*w + 1/4*w**4 + 0 - 1/20*w**5 - 1/2*w**3 + 1/2*w**t. Solve j(a) = 0.
1
Let q be (2/(-8))/((-8)/96). Suppose 2*t**5 + t**3 + 4*t**2 - 5*t**4 - 4*t + t**3 - 1 - 1 + q = 0. What is t?
-1, 1/2, 1
Let h(t) be the first derivative of 4*t**7/945 + t**6/180 - t**5/270 + 3*t**2/2 - 9. Let n(r) be the second derivative of h(r). Find j, given that n(j) = 0.
-1, 0, 1/4
Let p(a) be the second derivative of 5*a**4/12 + 2*a**3/21 - 2*a**2/7 + 5*a. Suppose p(q) = 0. What is q?
-2/5, 2/7
Let j(w) = w**2 + 4*w. Let x(s) = -s + 3. Let n be x(7). Let t be j(n). Determine c, given that -c**4 + c**2 - c**3 + 3*c**3 - 2*c + t*c**2 = 0.
-1, 0, 1, 2
Let a(u) = 28*u**3 - 176*u**2 - 153*u + 56. Let r(k) = 42*k**3 - 264*k**2 - 230*k + 84. Let z(l) = 8*a(l) - 5*r(l). Factor z(g).
2*(g - 7)*(g + 1)*(7*g - 2)
Let c(m) = 4*m**4 + 15*m**3 + 72*m**2 + 67*m + 32. Let x(l) = -l**4 - 4*l**3 - 18*l**2 - 17*l - 8. Let g(w) = 6*c(w) + 26*x(w). Suppose g(s) = 0. What is s?
-2, -1
Find p, given that 2/7*p**2 - 2/21*p**4 + 0*p + 4/21*p**3 + 0 = 0.
-1, 0, 3
Let r(o) be the first derivative of o**5/140 - o**4/84 - o**3/42 + o**2/14 - 9*o + 6. Let m(h) be the first derivative of r(h). What is u in m(u) = 0?
-1, 1
Let s be 9/18*8/18. Let -s*v**2 + 2/9*v**3 + 0 - 2/9*v + 2/9*v**4 = 0. What is v?
-1, 0, 1
Let w(x) be the second derivative of 0 + 2/15*x**6 - 3/10*x**5 - 1/6*x**3 - 2*x + 0*x**2 + 1/3*x**4 - 1/42*x**7. Suppose w(v) = 0. What is v?
0, 1
Let x(p) = p**2 + p - 26. Let y be x(-6). Let i(h) be the third derivative of 0*h + 0*h**y - h**2 + 0 + 1/24*h**3 - 1/240*h**5. Factor i(s).
-(s - 1)*(s + 1)/4
Let j(z) be the third derivative of -1/150*z**6 - 1/15*z**3 + 0*z - 1/75*z**5 + 0 + 1/175*z**7 - 1/840*z**8 + 1/20*z**4 - z**2. Factor j(x).
-2*(x - 1)**4*(x + 1)/5
Let i = 4/151 + 139/453. Suppose l**3 + 1/3*l**4 - i*l**5 - 1/3*l**2 + 0 - 2/3*l = 0. Calculate l.
-1, 0, 1, 2
Let s(k) = -2*k - 2. Let u be s(-2). Factor 28*c + c**u + 2 - 24*c + 2.
(c + 2)**2
Let d(o) = -14*o**2 + 10*o - 12. Let a(s) = -s**2 - 1. Let j(i) = -12*a(i) + d(i). Find n such that j(n) = 0.
0, 5
Solve -10*p**4 - 34*p**2 + 18*p**3 + 18*p**3 - 304 + 312 = 0 for p.
-2/5, 1, 2
Suppose 4*c = 34 + 202. Determine q so that -2 + 9*q**2 + 17*q - 13*q - c*q**2 + 16*q = 0.
1/5
Let l(d) be the second derivative of -2*d**6/75 + 2*d**4/15 - 2*d**2/5 - 8*d. Factor l(w).
-4*(w - 1)**2*(w + 1)**2/5
Determine r so that 2/15*r**3 - 2/15 + 2/5*r - 2/5*r**2 = 0.
1
Let r be (-58)/(-493) - 64/(-34). Suppose -2/5*n**3 + 4/5*n + 0 + 2/5*n**r = 0. What is n?
-1, 0, 2
Let y(c) be the first derivative of -c**8/240 + c**7/70 + c**6/90 + 2*c**3/3 - 2. Let p(d) be the third derivative of y(d). Factor p(i).
-i**2*(i - 2)*(7*i + 2)
Suppose 0 = 25*x - 24*x - 2. Let h(g) be the third derivative of 0*g**5 + 0 + 0*g + 1/1344*g**8 + 0*g**6 + 0*g**3 - 1/420*g**7 + 0*g**4 - g**x. Factor h(m).
m**4*(m - 2)/4
Let z(d) be the second derivative of 0*d**3 + 0 + 0*d**2 - 1/12*d**4 + d - 1/20*d**5. Factor z(i).
-i**2*(i + 1)
Suppose 4*f = -f. Let m be f + 7/((-14)/(-4)). Factor 0*d**m + 1/3*d**3 + 0 - 1/3*d.
d*(d - 1)*(d + 1)/3
Let g(x) be the second derivative of -x**4/12 - x**3/3 + 9*x. Let r be g(-2). Determine t so that 1/5*t**3 + 0 + 0*t + 1/5*t**4 + r*t**2 = 0.
-1, 0
Suppose -10*k + 74 - 54 = 0. Factor 1/2*n**4 - 1/2*n + 1/2*n**3 - 1/2*n**k + 0.
n*(n - 1)*(n + 1)**2/2
Let u(o) = o**2 + 15*o + 11. Let v be u(-13). Let i = 15 + v. Let -2/3*d + 0*d**3 + 4/3*d**4 + 2/3*d**5 + i - 4/3*d**2 = 0. What is d?
-1, 0, 1
Factor 32/5*b + 12/5*b**4 + 56/5*b**3 + 16*b**2 + 0.
4*b*(b + 2)**2*(3*b + 2)/5
Let y(s) be the first derivative of 0*s**2 + 2/9*s**3 + 1/15*s**5 + 0*s - 2 + 1/4*s**4. Solve y(l) = 0 for l.
-2, -1, 0
Suppose 3*p = -3*u + 5*p + 16, -2*p = 10. Let q(d) = d. Let j be q(u). Find f, given that -15/2*f**4 + 19/2*f**2 - 2 + j*f - 2*f**3 = 0.
-1, -2/3, 2/5, 1
Let v(j) be the first derivative of 2*j**5/5 + j**4/2 - 2*j**3 - j**2 + 4*j - 3. Factor v(i).
2*(i - 1)**2*(i + 1)*(i + 2)
Let h = 2 + 3. Suppose -h*b = -0*b. Factor b*f**3 + f**3 + f**3.
2*f**3
Let b(t) be the second derivative of t**7/840 + t**6/40 + 9*t**5/40 - t**4/12 - t. Let h(z) be the third derivative of b(z). What is v in h(v) = 0?
-3
Let y(h) = -4*h**4 + 20*h**3 + 12*h**2 - 4*h. Let c(f) = 3*f**4 - 13*f**3 - 8*f**2 + 3*f. Let n(b) = 8*c(b) + 5*y(b). Factor n(a).
4*a*(a - 1)**2*(a + 1)
Let r(x) be the second derivative of x**6/6 + x**5/2 - 5*x**3/3 - 5*x**2/2 - 23*x. Factor r(h).
5*(h - 1)*(h + 1)**3
Let c be (0 - 6)*1/(-3). Determine s so that s**4 - 4*s - 5*s**4 - 5*s**c - 12*s**3 - 7*s**2 = 0.
-1, 0
Let p = 941/40 + -47/2. Let d(k) be the third derivative of -1/48*k**4 + 0*k + 0*k**3 + 0 + 3*k**2 + 1/60*k**6 + p*k**5. Solve d(w) = 0 for w.
-1, 0, 1/4
Let a(u) be the third derivative of u**8/5040 + u**7/210 + u**6/20 + u**5/12 - 8*u**2. Let m(g) be the third derivative of a(g). Factor m(p).
4*(p + 3)**2
Let v be (2/4)/((-3)/(-18)). Factor -5*f**2 - 3*f**2 + 5*f**2 - 3*f + 2 + 1 + 3*f**v.
3*(f - 1)**2*(f + 1)
Let y(r) be the third derivative of -2*r**7/35 - 3*r**6/40 + r**5/4 + 3*r**4/8 - r**3/2 - 5*r**2. Suppose y(z) = 0. Calculate z.
-1, 1/4, 1
Let q(k) = -4*k**3 - 5*k**2 + 7*k - 1. Let x(h) = h**4 - 4*h**3 - 4*h**2 + 6*h - 1. Let m(p) = -2*p + 7. Let f be m(5). Let v(i) = f*x(i) + 2*q(i). Factor v(w).
-(w - 1)**2*(w + 1)*(3*w - 1)
Factor -21*o**3 + 4*o**2 - 66*o**4 - 3*o**3 + 70*o**4 + 96*o + 64.
4*(o - 4)**2*(o + 1)**2
Let r(g) = g**3 - 3*g**2 + 2*g + 2. Let p be r(4). Let l = -26 + p. Factor l*y - 1/3*y**2 + 0 - 1/3*y**3.
-y**2*(y + 1)/3
Let t = -3/2 - -2. Find d such that -3*d**3 - 9/4*d**2 + 0 - t*d - d**4 = 0.
-2, -1/2, 0
Factor -119*l**2 + 60*l**2 + l + 60*l**2.
l*(l + 1)
Factor -3*t + 0 - 3/2*t**2.
-3*t*(t + 2)/2
Determine f, given that -f**2 + 2/3*f**4 + 1/3 + 1/3*f**3 - 1/3*f = 0.
-1, 1/2, 1
Let h(k) be the first derivative of -5*k**4/16 - 5*k**3/3 - 33. Suppose h(w) = 0. Calculate w.
-4, 0
Let v = -64 - -64. Factor 1/3*s**5 + 1/3*s**4 + 0*s**3 + 0*s**2 + v*s + 0.
s**4*(s + 1)/3
Let g(i) be the first derivative of -3*i**5/5 + 3*i**4 - 3*i**3 - 6*i**2 + 12*i + 28. Factor g(p).
-3*(p - 2)**2*(p - 1)*(p + 1)
Let m(r) be the first derivative of -2*r**2 + 16/3*r**3 + 5*r**4 + 0*r - 4. Factor m(i).
4*i*(i + 1)*(5*i - 1)
Let z(b) = -2*b**2 + 4*b - 6.