derivative of s**7/210 + s**6/50 + s**5/50 - 14*s. Factor w(p).
p**3*(p + 1)*(p + 2)/5
Suppose -5*b = -18 - 7. Let m(o) be the third derivative of -2/3*o**3 - 1/4*o**4 - 1/48*o**6 + 0*o + 3/20*o**b + 0 + 4*o**2. Find a such that m(a) = 0.
-2/5, 2
Let l(y) be the second derivative of y**6/1440 + y**5/120 + y**4/32 + 5*y**3/6 + 3*y. Let w(n) be the second derivative of l(n). Factor w(i).
(i + 1)*(i + 3)/4
Let p(j) be the third derivative of j**8/13440 + j**7/5040 + j**4/24 + 8*j**2. Let t(y) be the second derivative of p(y). Factor t(i).
i**2*(i + 1)/2
Let s(d) = -d**3 + d**2. Let h(r) = -4*r**4 + 32*r**3 - 112*r**2 + 156*r - 72. Let z(f) = h(f) - 4*s(f). Determine n, given that z(n) = 0.
1, 2, 3
Let b(t) be the third derivative of 0*t**4 - 1/60*t**5 + 1/120*t**6 + t**2 + 0 + 0*t**3 + 0*t. Factor b(k).
k**2*(k - 1)
Let l = -2611/4 - -653. Factor l*d - 1/2 - 7/4*d**3 + 1/2*d**4 + 3/2*d**2.
(d - 2)*(d - 1)**2*(2*d + 1)/4
Let a(p) be the third derivative of p**5/15 + 5*p**4/6 + 4*p**3 + 2*p**2 + 35. What is f in a(f) = 0?
-3, -2
Let c = 19 + -15. Suppose v**3 + c*v - 3*v + 4*v - v - 4*v**2 = 0. What is v?
0, 2
Let q(i) be the first derivative of -i**6/42 + 2*i**5/35 - 2*i**3/21 + i**2/14 + 18. Factor q(d).
-d*(d - 1)**3*(d + 1)/7
What is v in 8*v**4 - 4*v - 1/2 - 15/2*v**2 + 4*v**3 = 0?
-1, -1/4, 1
Let d(l) be the first derivative of -20*l**3/3 - 23*l**2/2 - 17*l + 1. Let w(v) = -7*v**2 - 8*v - 6. Let t(p) = -6*d(p) + 17*w(p). Factor t(b).
b*(b + 2)
Let l = 5 - 3. Suppose 4*k - 3*h - 3 = 0, 4 = -5*k - 2*h + 2. Determine s so that s + k*s - s**l - s + 1 = 0.
-1, 1
Let d(a) = a**3 - 10*a**2 - 5*a - 12. Let t be d(11). Suppose 54*o**2 - o - t*o**2 + 2*o**3 - o**5 = 0. What is o?
-1, 0, 1
Let w(h) = h**3 + 5*h**2 + 5*h + 6. Let i be w(-4). Factor -4*r**3 + r**3 - 2*r**4 + 4*r**i - r**3 - 2*r**4 + 4*r.
-4*r*(r - 1)*(r + 1)**2
Factor r**3 + 4 - 72*r**2 - 75*r**2 + 9*r + 153*r**2.
(r + 1)**2*(r + 4)
Let a be 0*4*1/16. Factor 0 - 4/11*k**4 + 0*k + a*k**2 - 2/11*k**3 - 2/11*k**5.
-2*k**3*(k + 1)**2/11
Suppose -4*k = -0*k - 48. Let o be (k + -8)/(2*5). Factor 2/5*t**3 - 3/5*t + 1/5*t**5 - o*t**2 + 3/5*t**4 - 1/5.
(t - 1)*(t + 1)**4/5
Let n(v) = -v + 8. Let r be n(5). Suppose 3*f - f**2 - f**2 - 4*f - f**r = 0. What is f?
-1, 0
Let r = 6 + -3. Let p be 3 - (11/r + -1). Factor p*y**4 - 2/3 - 5/3*y - y**2 + 1/3*y**3.
(y - 2)*(y + 1)**3/3
Let y(i) be the third derivative of -i**7/420 + i**6/45 - i**5/15 + i**3/2 + 3*i**2. Let a(j) be the first derivative of y(j). Factor a(z).
-2*z*(z - 2)**2
Let k = 691/7686 + -5/61. Let p(j) be the second derivative of 1/18*j**3 + j + 1/18*j**4 - 1/30*j**5 + k*j**7 - 1/6*j**2 + 0 - 1/90*j**6. Factor p(a).
(a - 1)**3*(a + 1)**2/3
Let t(c) be the first derivative of c**6/2 - 9*c**5/5 - 3*c**4/4 + 7*c**3 - 12*c - 7. Let t(y) = 0. Calculate y.
-1, 1, 2
Suppose -o + v = -13, 5*o = 4*o + 2*v + 10. Let x = -16 + o. Factor 2/5*s + x*s**2 - 2/5*s**3 + 0.
-2*s*(s - 1)*(s + 1)/5
Let t(z) be the first derivative of 2*z**5/65 - 2*z**4/13 + 8*z**3/39 - 16. What is r in t(r) = 0?
0, 2
Factor -2*h**2 + 3*h + 0*h**2 - 5*h.
-2*h*(h + 1)
Factor -2*p + 3*p**2 + 0*p**4 + 0*p**4 + p**4 + 3*p + 3*p**3.
p*(p + 1)**3
Let s(t) be the third derivative of t**8/2240 - t**6/240 + t**4/8 + t**2. Let f(q) be the second derivative of s(q). Determine y, given that f(y) = 0.
-1, 0, 1
Suppose -23*b + 32*b = 27. Let 2/5*r**4 + 0 - 2/5*r**2 + 0*r**b + 0*r = 0. What is r?
-1, 0, 1
Solve -k**3 - 4*k**2 - 3*k + 8*k + 0*k**2 + 2*k**3 - 2 = 0 for k.
1, 2
Let x be 2/(-7) - 46/(-14). Solve 6*d - 3*d**x + 3*d**4 + 0*d - 6*d = 0.
0, 1
Suppose 2*a + 3*x = 5*a - 3, 0 = 2*a + x + 1. Let -1/2*m**5 + 0 + 0*m + 0*m**2 + a*m**3 - 1/2*m**4 = 0. Calculate m.
-1, 0
Factor 7*m**3 - 15*m**4 + 0*m**2 - 11*m**3 + 4*m**2.
-m**2*(3*m + 2)*(5*m - 2)
Let a = -422 + 2111/5. Determine q, given that 0*q - 3/5*q**4 + 3/5*q**3 + 0 - 1/5*q**2 + a*q**5 = 0.
0, 1
Suppose t + 0*t = -5*n + 20, t - 4*n = -7. Let b(d) be the third derivative of 0*d + 0 + 0*d**t + 1/240*d**6 - 1/48*d**4 + 0*d**3 + 2*d**2. Factor b(l).
l*(l - 1)*(l + 1)/2
Let j(b) be the third derivative of 3*b**2 + 0*b - 1/18*b**3 + 1/720*b**6 - 1/144*b**4 + 1/180*b**5 + 0. Let j(f) = 0. What is f?
-2, -1, 1
Let b(o) = 9*o**3 + o**2 + o + 4. Let d(n) = -4*n**3 - 2. Let s(i) = -4*b(i) - 10*d(i). Suppose s(x) = 0. Calculate x.
-1, 1
Let u(k) be the first derivative of -2*k**3/3 + 4*k**2/5 + 2*k/5 + 2. Factor u(q).
-2*(q - 1)*(5*q + 1)/5
Let i(y) be the third derivative of y**6/40 - 2*y**5/5 + 13*y**4/8 - 3*y**3 - 3*y**2 - 2*y. Solve i(o) = 0.
1, 6
Let c be ((-24)/20)/((-3)/(-10)). Let d be (c/(-1))/(15 - 1). Factor -d*o + 0 + 2/7*o**3 + 0*o**2.
2*o*(o - 1)*(o + 1)/7
Let i(h) = 4*h**3 + 9*h**2 + 5*h + 3. Let o(t) = 9*t**3 + 18*t**2 + 9*t + 5. Let d be (-4)/(-2) + (-9)/(-3). Let g(v) = d*i(v) - 3*o(v). Factor g(z).
-z*(z + 1)*(7*z + 2)
Let q(i) be the third derivative of i**6/60 - i**5/10 + i**4/6 - i**2. Factor q(a).
2*a*(a - 2)*(a - 1)
Factor 5*r**4 - 11*r**2 + 8*r**2 - 2*r**4.
3*r**2*(r - 1)*(r + 1)
Let f(o) = -o**3 + 6*o**2 + o + 2. Let h be f(6). Determine q, given that 10*q**2 + 8*q**2 - 4*q**3 + h*q**2 - 10*q**2 - 12*q = 0.
0, 1, 3
Let d(z) be the first derivative of 1/12*z**3 - 3/5*z**5 - 1/4*z + 17/16*z**4 - 3 - 5/8*z**2. Determine k so that d(k) = 0.
-1/3, -1/4, 1
Factor 9*v**3 - 2*v + 9*v**2 + 2*v**4 + 5*v + 0*v**4 + v**4.
3*v*(v + 1)**3
Let u(h) be the second derivative of h**5/70 + 5*h**4/42 + 4*h**3/21 + 2*h - 9. Factor u(d).
2*d*(d + 1)*(d + 4)/7
Let n be 2 - (1 - 2 - 0). Suppose -4*b + 11 - n = 0. Solve 0 - b + 6 + 2*j**4 + 18*j**2 - 16*j + 2*j - 10*j**3 = 0.
1, 2
Let p be (2/3)/(2/12). Suppose 0 = 3*n + p*y + 7, y = 6*n - n - 19. Solve -2*s**2 + 2*s**n - 2*s**5 + 4*s**3 + 12*s**4 - 14*s**5 = 0 for s.
-1/2, 0, 1/4, 1
Let g be 4/(-2) + 7/3. Suppose -4 = -3*s + a, -3*s = -6*s - 2*a + 19. Factor g*y**2 + 1/3*y**s - 1/3*y - 1/3*y**4 + 0.
-y*(y - 1)**2*(y + 1)/3
Let h(u) be the first derivative of -3*u**4/22 - 30*u**3/11 - 225*u**2/11 - 750*u/11 - 15. Solve h(w) = 0 for w.
-5
Factor 6/7*m**2 - 6/7*m**3 + 0 - 2/7*m + 2/7*m**4.
2*m*(m - 1)**3/7
Let v(o) be the second derivative of o**8/5880 - o**7/2940 + o**3 + 2*o. Let c(t) be the second derivative of v(t). Solve c(y) = 0 for y.
0, 1
Let z(b) = b**5 - b**4 - b**3 - b**2 + b + 1. Let a(j) = -3*j**5 - 3*j**4 + 15*j**3 + j**2 - 5*j - 5. Let q(u) = a(u) + 5*z(u). Factor q(p).
2*p**2*(p - 2)*(p - 1)**2
Let v(p) be the third derivative of -1/27*p**3 + 0 + 0*p + 1/36*p**4 + 3*p**2 + 2/135*p**5. Factor v(t).
2*(t + 1)*(4*t - 1)/9
Let h be (2 + (-26)/12)/((-3)/9). Solve -h*o**4 + 1/4*o**5 + 0*o**2 + 0 + 1/4*o**3 + 0*o = 0 for o.
0, 1
Let i(m) be the third derivative of -1/30*m**5 + 1/6*m**4 + 0*m + 3*m**2 - 1/3*m**3 + 0. Factor i(k).
-2*(k - 1)**2
Let m be -4*(-6)/(-24) + 7/5. Let a(l) be the first derivative of -1/5*l**2 - 2/15*l**3 + m*l - 1 + 1/10*l**4. Factor a(j).
2*(j - 1)**2*(j + 1)/5
Let v(a) = -2*a - 8. Let y be v(-6). Let u = 6 - y. Factor -1 + 0 + 1 + 2*q**3 - 4*q**2 + u*q.
2*q*(q - 1)**2
Let y(c) be the third derivative of 0*c**3 - 1/30*c**6 + 0 - 2/15*c**5 - 5*c**2 - 1/6*c**4 + 0*c. Let y(p) = 0. Calculate p.
-1, 0
Let d(k) be the second derivative of -k**7/63 + 7*k**6/45 - 7*k**5/30 - 23*k**4/18 + 8*k**3/9 + 16*k**2/3 + 20*k. Solve d(v) = 0.
-1, 1, 4
Let s(g) be the first derivative of g**7/525 + g**6/300 - g**2 - 4. Let x(d) be the second derivative of s(d). Factor x(k).
2*k**3*(k + 1)/5
Let o = 44/7 - 155/28. Factor -o*l**2 - 1/4*l**3 - 3/4*l - 1/4.
-(l + 1)**3/4
Let k be 1/(-4) + (-70)/8. Let j be -3*(-6)/k - -5. Suppose 0*g - 2*g**3 + j*g - g = 0. Calculate g.
-1, 0, 1
Suppose -2*r = -3*z - 4, 2*z + 0*z = -r + 9. Let 5/3*h + 2/3*h**2 + 2/3 - 1/3*h**r - 4/3*h**4 - 4/3*h**3 = 0. What is h?
-2, -1, 1
Let o(s) be the first derivative of -s**4/2 - 4*s**3/3 + s**2 + 4*s + 5. Factor o(x).
-2*(x - 1)*(x + 1)*(x + 2)
Let n(d) be the third derivative of -d**6/120 + d**5/40 - d**3/6 + 3*d**2. Let c(y) be the first derivative of n(y). Find q such that c(q) = 0.
0, 1
Let j = -34 - -77/2. Suppose 1/2*l**4 - 3/2*l**5 + l + j*l**3 + 0 - 9/2*l**2 = 0. Calculate l.
-2, 0, 1/3, 1
Let 8*r**3 - 6*r**2 + 4*r - 4*r**2 - 2*r**4 + 0*r = 0. Calculate r.
0, 1, 2
Suppose 4 = 2*g - 0. Factor -2*m