2 = 0. Calculate k.
-2, -1, -2/5, 1
Let c(n) be the second derivative of 0 + 5/66*n**4 - 3*n - 3/110*n**5 - 2/33*n**3 + 0*n**2. Factor c(a).
-2*a*(a - 1)*(3*a - 2)/11
Let o(n) = -n + 5 + 2 - 5 + n**2. Let d = 15 - 11. Let f(u) = 5*u**2 - 5*u + 11. Let x(k) = d*f(k) - 22*o(k). Find y, given that x(y) = 0.
0, 1
Let u(r) = r + 2. Let a = -11 + 12. Let k be u(a). Let -2/7*d**4 - 2/7*d**5 + 0*d + 2/7*d**k + 0 + 2/7*d**2 = 0. What is d?
-1, 0, 1
Factor 0 + 0*l - 2/7*l**2 + 2/7*l**4 + 0*l**3.
2*l**2*(l - 1)*(l + 1)/7
Let g be (3/4)/(270/36). Let b(o) be the first derivative of 1 - g*o**4 + 1/5*o**2 + 4/15*o**3 - 4/5*o. Suppose b(r) = 0. Calculate r.
-1, 1, 2
Let v(f) be the first derivative of -2/3*f**3 - 3 + 2*f**2 - 2*f. Factor v(x).
-2*(x - 1)**2
Solve 22*a**5 + 7*a**2 - 2*a**5 + 5*a**2 + 8*a - 28*a**3 - 12*a**4 = 0.
-1, -2/5, 0, 1
Let d(x) be the first derivative of -x**4/10 + 4*x**3/15 + x**2/5 - 4*x/5 - 8. Suppose d(m) = 0. What is m?
-1, 1, 2
Let q(m) = -147*m**3 + 80*m**2 - 16*m. Let k = -5 + 9. Let o(d) = 147*d**3 - 79*d**2 + 17*d. Let n(g) = k*o(g) + 5*q(g). Suppose n(u) = 0. What is u?
0, 2/7
Let j = 43/3 - 11. Let z(w) be the first derivative of 5/3*w**5 - 7/3*w**3 - j*w**2 + 3 + 5/3*w**4 - 4/3*w. Factor z(v).
(v - 1)*(v + 1)*(5*v + 2)**2/3
Let t(s) = 2*s**2 - 5. Let j(k) = -k**2 + 2. Let g(x) = 15*j(x) + 6*t(x). Factor g(y).
-3*y**2
Solve -4*l**2 - 20/7*l + 8/7 = 0 for l.
-1, 2/7
Let f(m) be the third derivative of 1/12*m**6 + 19/315*m**7 + 1/90*m**5 + 1/72*m**8 - 1/18*m**4 + 0*m**3 + 0*m + 0 + 2*m**2. Suppose f(x) = 0. Calculate x.
-1, 0, 2/7
Let n be -4 + (21/3 - 3). Let g(l) be the third derivative of 0*l**3 + 0 + 0*l - 1/150*l**6 + 1/150*l**5 - 2*l**2 + n*l**4 + 1/525*l**7. Factor g(p).
2*p**2*(p - 1)**2/5
Let o(l) be the second derivative of l**5/30 - l**4/6 - 5*l**2/2 + 5*l. Let h(m) be the first derivative of o(m). Solve h(q) = 0 for q.
0, 2
Let n = 31 - 31. Let s(b) be the second derivative of n - 1/6*b**4 + 0*b**2 + 0*b**3 - 1/4*b**5 - b. Factor s(t).
-t**2*(5*t + 2)
Let x(v) be the first derivative of 169*v**3/3 - 26*v**2 + 4*v - 8. Factor x(z).
(13*z - 2)**2
Let x = 9 + -7. Factor 9*n + 3*n**2 + 2*n**2 - 4*n**2 + 2*n**x.
3*n*(n + 3)
Let x(m) be the third derivative of m**6/480 - m**5/80 + m**4/32 - m**3/24 - 6*m**2. Solve x(v) = 0 for v.
1
Let b(o) be the second derivative of o**5/270 - o**3/27 - 2*o**2 - 2*o. Let q(s) be the first derivative of b(s). Determine k, given that q(k) = 0.
-1, 1
Let h be (9/27)/(4/3). Suppose -5*z - 3 = -18. Solve -1/4*g + 1/4*g**z - 1/4 + h*g**2 = 0.
-1, 1
Let k(p) be the first derivative of p**7/14 - p**6/10 - 3*p**5/10 + p**4/2 + p**3/2 - 3*p**2/2 - 3*p - 2. Let w(d) be the first derivative of k(d). Factor w(z).
3*(z - 1)**3*(z + 1)**2
Let u(b) be the second derivative of -2*b - 2/15*b**6 + 0*b**3 + 0*b**4 + 0 + 0*b**2 - 1/5*b**5. Determine l, given that u(l) = 0.
-1, 0
Let m(s) be the first derivative of 2 + s**2 - 31/20*s**5 + 1/2*s**3 - s - 1/2*s**6 - 5/4*s**4. Let p(n) be the first derivative of m(n). What is j in p(j) = 0?
-1, -2/5, 1/3
Suppose 0 = -2*o - 3*o + 5*k, 0 = -4*o + 3*k. Let q = 0 - o. Factor 0 + 1/2*v**2 - 3/2*v**3 + q*v + v**4.
v**2*(v - 1)*(2*v - 1)/2
Suppose -h**2 - 7 - 7 - 1 + 6*h + 6 = 0. Calculate h.
3
Suppose -2*k = 5*d - 14, 4*d + k + 2 - 12 = 0. Solve -2 + 2*q**d - 2 - 14*q - 6*q**2 - 2*q**2 = 0.
-2, -1/3
Let b(c) = -c - 1. Let z(f) = 2*f**2 + 7*f + 5. Let d(v) = -2*b(v) + 2*z(v). Let d(p) = 0. What is p?
-3, -1
Factor -4 - b**2 + 5 - b**2 + b**4.
(b - 1)**2*(b + 1)**2
Let l(i) be the first derivative of -i**6/72 + i**4/24 - i**2/24 + 15. Factor l(v).
-v*(v - 1)**2*(v + 1)**2/12
Factor 0 - 1/4*g**5 + 0*g**2 + 0*g - g**4 - 3/4*g**3.
-g**3*(g + 1)*(g + 3)/4
Let w(s) be the first derivative of 0*s**2 + 1/9*s**3 - 4*s - 1/18*s**4 + 4. Let y(n) be the first derivative of w(n). Factor y(d).
-2*d*(d - 1)/3
Suppose -2*l + 5*l - 4 = -t, -5*l - 5*t = 0. Let v be 3/9*3*l. Determine f, given that 0*f**v + 2/7*f**3 + 0 - 2/7*f = 0.
-1, 0, 1
Let y(j) = -6*j**2 - 5*j - 10. Let m(u) = u**2 + u + 2. Let x(i) = -22*m(i) - 4*y(i). Solve x(c) = 0.
-1, 2
Let a = 33/26 + 16/13. Factor -5*t**3 + 1/2 + a*t**4 + 5*t**2 - 1/2*t**5 - 5/2*t.
-(t - 1)**5/2
Let i(p) be the first derivative of p**6/8 + 3*p**5/4 + 9*p**4/8 - p**3/2 - 21*p**2/8 - 9*p/4 - 4. Factor i(n).
3*(n - 1)*(n + 1)**3*(n + 3)/4
Let s(j) = -7*j**2 + 26*j**3 + 17 + 10*j + 0*j**2 + 19*j. Let h(t) = -9*t**3 + 2*t**2 - 10*t - 6. Let k(c) = 17*h(c) + 6*s(c). Factor k(i).
i*(i - 2)*(3*i - 2)
Factor -1/4*d**2 + 0 + 0*d**4 + 3/8*d**3 - 1/8*d**5 + 0*d.
-d**2*(d - 1)**2*(d + 2)/8
Factor -2*b - 5*b**2 + 3*b + 2*b**2 + 5*b.
-3*b*(b - 2)
Let j(q) = -2*q + 5. Let v be j(1). Let z be (-12)/(-30)*10/26. Find b, given that 0*b**2 + 4/13*b**v + 0*b**4 - z*b**5 + 0 - 2/13*b = 0.
-1, 0, 1
Let n = -3467/3 - -1156. Factor 0 + n*t - 1/2*t**2 + 1/6*t**3.
t*(t - 2)*(t - 1)/6
Let s(r) be the first derivative of -r**4/4 - 2*r**3 - 9*r**2/2 + 6*r - 7. Let j(k) be the first derivative of s(k). Solve j(n) = 0 for n.
-3, -1
Let m(g) = -3*g**3 + 5*g**2 - g + 3. Let d(c) = 10*c**3 - 16*c**2 + 2*c - 10. Let z(s) = 4*d(s) + 14*m(s). Factor z(y).
-2*(y - 1)**3
Suppose 0 = -2*c - 3*s - 3 - 4, 0 = -4*c - 3*s + 1. Let f be 12*c*4/264. Solve 8/11*n**3 + 12/11*n**2 + 2/11*n**4 + 2/11 + f*n = 0.
-1
Factor 0*y + 0*y**4 + 0*y**2 + 1/3*y**3 + 0 - 1/3*y**5.
-y**3*(y - 1)*(y + 1)/3
Let d be (-12)/15*46/(-48). Let u = d + -4/15. Let 5/2*b**2 + u*b**3 + 4*b + 2 = 0. Calculate b.
-2, -1
Let n = -64 + 194/3. Let h = -289/6 - -99/2. Factor 0*f**3 + h*f**2 + 0 - 2/3*f + n*f**5 - 4/3*f**4.
2*f*(f - 1)**3*(f + 1)/3
Let d(n) be the first derivative of 3*n**5/25 - 3*n**4/10 + n**3/5 - 27. Determine v, given that d(v) = 0.
0, 1
Factor 0*m**4 + m**4 + 8*m**3 - 5*m**4 - 4*m**2.
-4*m**2*(m - 1)**2
Let i(p) be the second derivative of p**4/24 + 7*p**3/12 - 2*p**2 + 11*p. Factor i(b).
(b - 1)*(b + 8)/2
Let y(o) be the first derivative of -o**3/5 - 9*o**2/10 - 6*o/5 - 3. Determine q, given that y(q) = 0.
-2, -1
Solve 5*o + 7*o**4 + 77*o**3 - 5*o**2 - 155*o**3 + 73*o**3 - 2*o**4 = 0.
-1, 0, 1
Let c = -18 - -20. Let a(n) be the third derivative of -1/50*n**5 + 1/100*n**6 + 3*n**c - 1/525*n**7 + 0*n**3 + 1/60*n**4 + 0*n + 0. Solve a(k) = 0 for k.
0, 1
Factor -3/4*m**2 - 12 - 6*m.
-3*(m + 4)**2/4
Suppose 4*n - 2*w = 6*n - 28, -5*n + 54 = w. Suppose n = -5*m, 0*b + 3*m + 8 = b. Factor -2/5*p**b - 2/5*p + 0.
-2*p*(p + 1)/5
Let h = 7/24 - -5/24. Let j(p) be the first derivative of -h*p - 1 - 1/8*p**2 + 1/12*p**3. Let j(r) = 0. Calculate r.
-1, 2
Factor -4/5*g**3 + 6/5*g + 2/5 + 4/5*g**2 - 6/5*g**4 - 2/5*g**5.
-2*(g - 1)*(g + 1)**4/5
Factor -1 + 4*p**3 + 4*p**3 - 10*p**3 - 6*p**2 + 2*p + 7.
-2*(p - 1)*(p + 1)*(p + 3)
Suppose -4 + 8 = 2*y. Let v = 0 + 3. Factor y*l**3 - 4*l**3 - 24*l - 12*l**2 - 19 + v.
-2*(l + 2)**3
Suppose -838 + 852 = 7*y. Let -2/3*z**y + 2/9*z + 2/3*z**3 + 0 - 2/9*z**4 = 0. Calculate z.
0, 1
Let z(f) = f**3 + f**2 + 2*f - 2. Let b(a) = 4*a**3 + 3*a**2 + 8*a - 9. Let x(d) = 2*b(d) - 9*z(d). Factor x(q).
-q*(q + 1)*(q + 2)
Let c = 90 + -90. Let a(b) be the third derivative of -1/240*b**6 + 0 - 1/48*b**4 + 1/60*b**5 + c*b - 2*b**2 + 0*b**3. Determine r so that a(r) = 0.
0, 1
Suppose -2*f + 22 = 4*c, 3*c - 12 = -0. Factor -3*h**2 - 2*h**4 + h**2 - 6*h**3 + 2*h**f.
-2*h**2*(h + 1)**2
Let o(r) = r**2 - 4*r + 5. Let i be o(3). What is y in -1/2*y**3 - 1/2*y + 0 + y**i = 0?
0, 1
Factor 9/2*b**3 + 3/2*b**4 + 0*b + 0 - 6*b**2.
3*b**2*(b - 1)*(b + 4)/2
Let t(d) be the first derivative of 0*d**4 - 2/3*d**3 + 2/5*d**5 + 3 + 0*d**2 + 0*d. Find z such that t(z) = 0.
-1, 0, 1
Let c(w) = -w**3 - 6*w**2 - 5*w + 5. Let z be c(-5). Let -5*m**4 + 3*m**2 + 3*m**5 - 6*m**z - 9*m**3 + 14*m**4 = 0. Calculate m.
0, 1
Let w = 17 + -16. Factor -7*l**5 + 5*l**5 - 4*l**2 + 3*l**4 - w + 2*l**3 + 2.
-(l - 1)**3*(l + 1)*(2*l + 1)
Let t(q) = 4*q**3 + 5*q**2 - 2*q. Suppose -2*i = -5*v - 6, i + 4*v = 2*i - 6. Let l(s) = 3*s**3 + 4*s**2 - s. Let d(a) = i*t(a) + 3*l(a). Factor d(o).
o*(o + 1)**2
Let c(z) be the second derivative of 1/6*z**4 - 1/15*z**3 + 0*z**2 - 2/25*z**5 - 3*z + 0. Let c(x) = 0. Calculate x.
0, 1/4, 1
Let n(o) be the second derivative of 0 + 1/2*o**2 - 2*o + 5/6*o**3 + 1/3*o**4. Factor n(f).
(f 