*k(f) - 5*l(f). Solve p(i) = 0.
-1, -1/3, 1
Let t(c) be the second derivative of 0*c**3 + 1/48*c**5 - 1/160*c**6 + 2*c**2 + 0 + 1/48*c**4 - 4*c. Let d(b) be the first derivative of t(b). Factor d(n).
-n*(n - 2)*(3*n + 1)/4
Let x(b) = -47*b + 50. Let f be x(1). Solve 2*c**2 + 4/3*c + 2/3*c**f + 0 = 0 for c.
-2, -1, 0
Let b be 2 - 2 - (-2)/4. Factor -b + 0*x + 1/2*x**2.
(x - 1)*(x + 1)/2
Let k(n) be the first derivative of n**2 - 2 + 2*n + 1/6*n**3. Factor k(j).
(j + 2)**2/2
Suppose 2*s - 20 = -2*b, -4*s - 19 = -b - 4. Let f(i) = i - 7. Let y be f(b). Factor 3*o**3 + 2*o**4 - 7*o**y + o**2 + 0*o**3 + o**2.
-o**2*(o - 1)*(5*o + 2)
Let a(j) be the second derivative of j**6/15 + j**5/5 + j**4/6 + 37*j. Find f, given that a(f) = 0.
-1, 0
Let m(i) be the second derivative of -2*i - 2/33*i**3 + 1/22*i**4 + 0 + 0*i**2 - 1/110*i**5. Factor m(g).
-2*g*(g - 2)*(g - 1)/11
Factor 6/5*o + 3*o**2 - 21/5*o**3 + 0.
-3*o*(o - 1)*(7*o + 2)/5
Let u(s) be the second derivative of -s**6/1440 - s**5/240 - s**4/96 - s**3/3 - 3*s. Let w(n) be the second derivative of u(n). Factor w(v).
-(v + 1)**2/4
Let o(f) be the second derivative of 1/18*f**3 + 0*f**4 + 0*f**2 - 6*f + 0 - 1/60*f**5. Let o(w) = 0. Calculate w.
-1, 0, 1
Suppose -2*g - 13 = -o, 5*g + 34 = 3*o - 0*g. Solve -7*d**2 - 17*d**o - 13*d**2 + d**4 - d**4 - 4*d**4 - 4*d = 0 for d.
-2, -1/4, 0
Let o(d) be the first derivative of -d**5/15 - d**4/2 - 4*d**3/3 - 5*d**2/3 - d - 7. What is y in o(y) = 0?
-3, -1
Let i(q) be the second derivative of -q**4/42 + 8*q**3/21 - 16*q**2/7 + 16*q. Factor i(a).
-2*(a - 4)**2/7
Let j be 26/10 - 2/(-5). Suppose 5*o + 35 = 5*t, j*t = 6*t + 3*o + 9. Let 6*y**3 + 11*y + 3 + 9 + 12*y + 27*y**t + 13*y = 0. What is y?
-2, -1/2
Let n(a) be the second derivative of 0 + 6*a + 0*a**2 + 1/30*a**4 - 1/5*a**3. Factor n(x).
2*x*(x - 3)/5
Let w(y) be the first derivative of 0*y - 2/27*y**3 - 3 + 0*y**2. Determine t, given that w(t) = 0.
0
Let w(c) be the third derivative of 0*c + 1/735*c**7 + 0*c**3 + 0 + 1/1176*c**8 + 0*c**6 + 0*c**4 + 0*c**5 + 3*c**2. Factor w(t).
2*t**4*(t + 1)/7
Let s(y) be the third derivative of -y**6/840 - y**5/420 + y**4/168 + y**3/42 + 17*y**2. Find o such that s(o) = 0.
-1, 1
Let g(d) be the first derivative of -5 + 2/9*d**3 + 4/3*d + d**2. Factor g(s).
2*(s + 1)*(s + 2)/3
Let q(t) be the second derivative of t**8/6720 - t**7/3360 - t**6/1440 + t**5/480 + 5*t**3/6 + 5*t. Let h(n) be the second derivative of q(n). Factor h(d).
d*(d - 1)**2*(d + 1)/4
Let x(q) = -q + 7. Let v be x(8). Let r be (v - 0)*20/(-12). Factor 40/3*w**4 - 5/3*w**2 + 1/3 + r*w - 16/3*w**5 - 25/3*w**3.
-(w - 1)**3*(4*w + 1)**2/3
Let t be (2/3)/((-4)/(-6)). Solve 2*p**2 + 8*p - 2*p**4 + 0*p**5 + t - 2*p**3 - p**5 - 5*p - p**4 = 0.
-1, 1
Let v(k) be the second derivative of -k**6/105 + 2*k**5/35 - 5*k**4/42 + 2*k**3/21 - 5*k. Factor v(r).
-2*r*(r - 2)*(r - 1)**2/7
Factor 0 - 6/7*k**4 + 13/7*k**3 + 4/7*k - 12/7*k**2 + 1/7*k**5.
k*(k - 2)**2*(k - 1)**2/7
Factor -5*u**3 + 15*u**3 - u**2 - 44*u**2 + 20*u.
5*u*(u - 4)*(2*u - 1)
Suppose 4*g = -0*g - 3*g. Let q(j) be the third derivative of -1/16*j**4 - 1/8*j**3 + g*j - 1/80*j**5 + 0 - 3*j**2. Factor q(t).
-3*(t + 1)**2/4
Let v(z) = -z**3 - 13*z**2 - 20*z - 8. Let s(p) = -12*p**2 - 20*p - 8. Let h(q) = 3*s(q) - 4*v(q). Find f, given that h(f) = 0.
-2, -1
Let w(v) = 20*v**4 - 67*v**3 - 107*v**2 + 188*v - 40. Let z(t) = 40*t**4 - 135*t**3 - 215*t**2 + 375*t - 80. Let d(n) = -5*w(n) + 2*z(n). Solve d(b) = 0 for b.
-2, 1/4, 1, 4
Factor -15/4*d**3 - 3/2 + 6*d**2 - 3/4*d.
-3*(d - 1)**2*(5*d + 2)/4
Let b(c) be the third derivative of -c**6/840 - c**5/84 - c**4/24 - c**3/14 - 36*c**2. Factor b(i).
-(i + 1)**2*(i + 3)/7
Let y be 40/7 - (-12)/42. Let q(l) be the second derivative of 1/12*l**4 - 1/30*l**y - 1/6*l**3 + 0*l**2 + 0 + 4*l + 1/20*l**5. Factor q(p).
-p*(p - 1)**2*(p + 1)
Suppose 0*d + 4 = 2*d. Suppose -d*u + 2 + 2 = 0. Determine b, given that 2*b - 2*b**3 + 0*b - 5*b**2 + 0*b**3 + 3*b**u + 2*b**4 = 0.
-1, 0, 1
Suppose -10*w + 8 + 22 = 0. Let b(r) be the first derivative of 1/8*r**2 + 0*r - 2 - 1/24*r**6 + 1/10*r**5 - 1/6*r**w + 0*r**4. Factor b(c).
-c*(c - 1)**3*(c + 1)/4
Let l = -107/2 + 223/4. Suppose -1/2*t**3 - 3*t**4 + l*t**5 + t**2 + 1/4*t + 0 = 0. What is t?
-1/3, 0, 1
Let q(z) be the first derivative of -1/30*z**6 + 0*z**2 + 3 + 0*z**5 + 0*z + 1/20*z**4 + 0*z**3. Let q(f) = 0. Calculate f.
-1, 0, 1
Let x be (36/(-15) + 2)*-5. Let d(v) be the third derivative of 1/3*v**3 + 2*v**x + 2/15*v**5 + 0*v - 1/3*v**4 + 0. What is t in d(t) = 0?
1/2
Let b(x) be the second derivative of -2*x**6/45 + x**5/60 + x**4/3 + 5*x**3/18 - x**2/3 + 7*x. Determine k so that b(k) = 0.
-1, 1/4, 2
Let g(c) be the first derivative of -c**5 + 5*c**4/4 - 23. Determine t so that g(t) = 0.
0, 1
Let v be (-4)/((-24)/(-15)) - -3. Suppose 0 = -2*o - 4*d + 12, -o - 3*d + 9 = -0*d. Solve -1/2*f**3 + o - f**2 - v*f = 0.
-1, 0
Let n(l) be the second derivative of -9*l**4/4 + l**3 - 2*l. Factor n(z).
-3*z*(9*z - 2)
Let y = 952/15 + -314/5. Find t, given that -y*t**2 - 4/3 + 2*t = 0.
1, 2
Suppose 7*l + 3*l = 6*l. Factor l*x - 1/2*x**3 + 0 + 0*x**2 + 0*x**4 + 1/2*x**5.
x**3*(x - 1)*(x + 1)/2
Let t be 1/(-3) + (-30)/(-9). Suppose -u + m = -4, -5*u - 4*m + 8 = -t*m. What is j in -j**3 + 3*j**5 - j**3 + 2*j**3 + 2*j**2 - u*j**4 - 3*j**3 = 0?
-1, 0, 2/3, 1
Let c(m) be the first derivative of m**6/9 + 4*m**5/15 - m**4/2 - 8*m**3/9 + 4*m**2/3 + 23. Determine r, given that c(r) = 0.
-2, 0, 1
Suppose 15*u - 18*u + 2*s = -8, 0 = 3*s - 6. Factor 0*c + 2/13*c**5 + 0*c**2 + 2/13*c**3 + 0 - 4/13*c**u.
2*c**3*(c - 1)**2/13
Let 3 + 7/4*r**2 + 4*r + 1/4*r**3 = 0. Calculate r.
-3, -2
Let n = -1 + 1. Let v = n - -2. Suppose -2*q - 3*q**2 - 2*q + q**v - 2 = 0. What is q?
-1
Let -2*g**2 - 1/3 - 1/3*g**4 + 4/3*g**3 + 4/3*g = 0. What is g?
1
Let t(l) be the first derivative of -l**3/15 + l**2/10 + 13. Factor t(x).
-x*(x - 1)/5
Let r(z) be the third derivative of 1/30*z**5 + 3*z**2 + 1/8*z**4 + 0 - 1/336*z**8 + 0*z - 1/60*z**6 - 1/70*z**7 + 1/6*z**3. Factor r(k).
-(k - 1)*(k + 1)**4
Let y(a) be the first derivative of -1/16*a**4 + 0*a - 2 + 1/8*a**2 + 0*a**3. Determine i, given that y(i) = 0.
-1, 0, 1
Factor 0*l**3 + 0*l**2 + 0*l + 0 + 1/8*l**4.
l**4/8
Let c(y) be the third derivative of y**8/336 + 2*y**7/105 + y**6/20 + y**5/15 + y**4/24 - 4*y**2. Let c(m) = 0. What is m?
-1, 0
Let c(h) be the third derivative of 1/90*h**5 + 0*h + 7/900*h**6 - 1/90*h**4 + 0*h**3 + 2*h**2 + 0. Solve c(b) = 0.
-1, 0, 2/7
Let j = 2/821 - -1624/7389. Let 50/9*f**3 - 2*f + j + 10/3*f**2 = 0. Calculate f.
-1, 1/5
Let r(z) be the first derivative of 0*z - 2 - 1/6*z**3 - 1/4*z**2. Factor r(t).
-t*(t + 1)/2
Let r(p) be the second derivative of 3*p**5/20 - p**4/4 - 4*p**3 + 18*p**2 - 7*p. Determine a so that r(a) = 0.
-3, 2
Let y be 1 - (0 + 0 + -1)/3. Factor -2/3*f**5 + 0 + 4/3*f**2 - y*f**4 + 2/3*f + 0*f**3.
-2*f*(f - 1)*(f + 1)**3/3
Let f = -177/16900 - -7/507. Let m(j) be the third derivative of f*j**6 + 1/60*j**4 + 0*j**3 + 0 + 0*j - 2*j**2 + 1/75*j**5. Solve m(l) = 0.
-1, 0
Let j(a) = -a**3 - 8*a**2 - 7*a - 7. Let h be j(-7). Let m = h - -7. Factor -4*n - n**2 - n**2 + m*n.
-2*n*(n + 2)
Suppose 3*c - 4 = 5, 0 = -n - 4*c + 15. Let o = -2 - -2. Determine s so that -6/5*s**n + 0*s + 6/5*s**4 + 2/5*s**2 + o - 2/5*s**5 = 0.
0, 1
Let r(y) be the first derivative of -7*y**3/3 + y**2/2 + 6*y + 4. Let h(z) = -z**2 + z. Let f(a) = -4*h(a) + r(a). Find c such that f(c) = 0.
-2, 1
Let c = 15 - 10. Determine s so that 2 - c + 3*s - 3 + 3*s**2 = 0.
-2, 1
Let q(k) be the second derivative of -k**6/360 + k**5/120 + k**3/3 + 2*k. Let r(h) be the second derivative of q(h). Suppose r(p) = 0. Calculate p.
0, 1
Let h(i) be the third derivative of i**8/20160 - i**7/1680 + i**6/360 - i**5/12 + i**2. Let c(v) be the third derivative of h(v). Solve c(d) = 0 for d.
1, 2
Suppose 8 = -18*x + 44. Let f(c) be the first derivative of -3/5*c**x + 0*c + 3 + 1/5*c**3. Factor f(j).
3*j*(j - 2)/5
Suppose 2 = -a + 6. Let x(h) be the second derivative of 1/3*h**3 + 0*h**2 - 1/6*h**a - h + 0. Factor x(w).
-2*w*(w - 1)
Let n = -1233 - -1237. Solve 0 + 2/7*w**n + 2/7*w**3 - 2/7*w**5 - 2/7*w**2 + 0*w = 0 for w.
-1, 0, 1
Suppose 0 = -6*r + 2*r + 12. Let b(z) be the sec