. Let p(y) be the first derivative of t(y). Factor p(c).
-2*(7*c + 2)**3
Let w(t) = t**3 - 15*t**2 + 17*t - 42. Let y be w(14). Factor 2/3*o**2 + y*o - 2/3.
2*(o - 1)*(o + 1)/3
Let c(z) be the first derivative of -z**5/35 - z**4/7 - 5*z**3/21 - z**2/7 - 5. Factor c(h).
-h*(h + 1)**2*(h + 2)/7
Let a = -507 - -511. Factor 1/2*z**a + 1/2*z**3 - 1/2*z + 0 - 1/2*z**2.
z*(z - 1)*(z + 1)**2/2
Let m(n) = 14*n + 32. Let u be m(-2). Factor -3/5*w**u + 0*w**2 + 6/5*w + 3/5 - 6/5*w**3.
-3*(w - 1)*(w + 1)**3/5
Let h(v) be the third derivative of -v**6/60 - 7*v**5/30 - 11*v**4/12 - 5*v**3/3 + 27*v**2. Find c, given that h(c) = 0.
-5, -1
Let r be (-4 - 510/(-72)) + -3. Let h(z) be the first derivative of -1/9*z**3 + r*z**4 + 1/3*z - 4 - 1/6*z**2. Factor h(i).
(i - 1)**2*(i + 1)/3
Let v = -29 - -33. Let a be (3 - v)*1 + 1. Suppose 0 + a*j - 2/7*j**2 = 0. What is j?
0
Let r(x) be the third derivative of x**7/1260 - x**6/60 + 3*x**5/20 - 3*x**4/4 + 9*x**3/4 - 10*x**2. Factor r(d).
(d - 3)**4/6
Let b(w) be the first derivative of -5*w**6/6 + 15*w**4/2 - 40*w**3/3 + 15*w**2/2 - 16. Factor b(d).
-5*d*(d - 1)**3*(d + 3)
Let n = 6 - 6. Let -2*o + o**3 - 3*o**2 + 3*o**4 - o**3 + n*o**3 + 2*o**3 = 0. Calculate o.
-1, -2/3, 0, 1
Let s(y) be the third derivative of -y**6/780 - y**5/65 - 3*y**4/52 - 4*y**3/39 + 12*y**2. Suppose s(p) = 0. What is p?
-4, -1
Let a(z) be the first derivative of -2*z + 4 - 2*z**2 - 2/3*z**3. Determine p so that a(p) = 0.
-1
Suppose f = -5, 5*f + 3 = 5*k - 32. Determine l, given that -16/7*l**2 - k*l - 6/7*l**3 - 4/7 = 0.
-1, -2/3
Let q(s) = -s**4 + s**3 - s**2 + s + 1. Let a(m) = -19*m**4 - 17*m**3 + 5*m**2 + 25*m + 10. Let n(i) = -a(i) + 4*q(i). Find f, given that n(f) = 0.
-1, -2/5, 1
Let p(h) be the first derivative of -2*h**3/3 - 1. Factor p(d).
-2*d**2
Suppose -7 = 5*x + 2*o - 26, 4*o - 14 = -2*x. Suppose z = -3*u - x*z + 25, 5*z = 3*u + 11. Factor -u*h**3 + 2*h + h**4 + 5 + h**3 - 6.
(h - 1)**3*(h + 1)
Factor -5*i**5 + 2*i**4 + i**5 - 14*i**4 + 16*i**2.
-4*i**2*(i - 1)*(i + 2)**2
Let h(t) be the third derivative of -t**5/10 - t**4/6 + t**3/3 + 5*t**2. Factor h(k).
-2*(k + 1)*(3*k - 1)
Let l(x) be the first derivative of 3/2*x**2 + 0*x - 3/4*x**4 + 3 + x**3 - 3/5*x**5. Factor l(k).
-3*k*(k - 1)*(k + 1)**2
Let s(f) be the first derivative of -f**3/36 + f**2/24 - 23. Solve s(r) = 0.
0, 1
Factor -6*f**3 + 2*f**4 - 5*f**4 - 3*f**3 + 7*f**3 - f**5.
-f**3*(f + 1)*(f + 2)
Let u = -9 - -15. Let y be u/8 - 2/4. Suppose y*i**2 - 1/4 + 0*i = 0. Calculate i.
-1, 1
What is r in -1/2*r**2 + 0*r + 0 + 5/4*r**3 - 3/4*r**4 = 0?
0, 2/3, 1
Let k(s) = -s + 13. Let d be k(6). Let f = 3 + 0. What is b in 11*b**2 + 30*b**f + 81*b**5 + 10*b**3 - d*b**2 + 117*b**4 = 0?
-1, -2/9, 0
Factor -4*p - 8 - 103*p**2 + 0*p + 4*p**3 + 115*p**2 - 4*p**4.
-4*(p - 2)*(p - 1)*(p + 1)**2
Let q = 5 - 3. Determine k, given that -8 + q*k + 7*k - 2*k**2 - k = 0.
2
Solve 2*r**2 - 4/3*r + 0 = 0.
0, 2/3
Let t(u) be the third derivative of u**6/90 + u**5/10 + u**4/3 - 2*u**3/3 - 2*u**2. Let b(d) be the first derivative of t(d). Find q such that b(q) = 0.
-2, -1
Let b(h) be the first derivative of 7*h**6/4 + 39*h**5/5 + 51*h**4/4 + 8*h**3 - 3*h**2/4 - 3*h - 8. Factor b(u).
3*(u + 1)**4*(7*u - 2)/2
Let s(z) be the third derivative of z**7/70 - z**6/20 + z**5/20 - 8*z**2. What is g in s(g) = 0?
0, 1
Suppose 4*t = 3 + 13. Find q such that -q**t - 7/4*q**3 - 1/2 + 3/2*q**2 + 7/4*q = 0.
-2, -1, 1/4, 1
Let u(g) be the first derivative of -g**4/24 + g**2/4 - 2*g - 2. Let l(x) be the first derivative of u(x). Factor l(k).
-(k - 1)*(k + 1)/2
Let j be (14/(-9) + 2)/2. Let t = -3/16 + 59/144. Solve -j*o**3 + 0*o + 0 + 2/9*o**4 + 2/9*o**5 - t*o**2 = 0.
-1, 0, 1
Suppose -4*r = 1 - 17. Suppose 4*p = r*m + 8, -5*m - 2*p = 2*p - 35. Solve 2 - 2*o**2 + 0 + 2*o**m + 2*o - 4*o = 0.
-1, 1
Let a(m) = m**2 + 3*m + 1. Let v be a(-2). Let w be (2 - 0)*v/(-6). Factor 1/3*h + 1/3*h**4 + 0 - w*h**3 - 1/3*h**2.
h*(h - 1)**2*(h + 1)/3
Solve 14/9 + 8/9*n**3 + 4*n**2 - 2/9*n**4 + 40/9*n = 0 for n.
-1, 7
Let b = 337 - 335. Determine j, given that 1/2*j**b - 1/4*j**3 - 1/4*j + 0 = 0.
0, 1
Let p(r) be the first derivative of -r**3 + 3*r - 2 + 9/4*r**2. Find a such that p(a) = 0.
-1/2, 2
Factor -5 - 2*l + 5*l + 5*l**2 - 3*l**3 - 2*l**3 + 2*l.
-5*(l - 1)**2*(l + 1)
Let a = -31 + 21. Let n = a + 14. What is h in n*h + 3*h**2 + 4/3 = 0?
-2/3
Let m(l) = 125*l**3 + 350*l**2 + 217*l + 40. Let p(f) = -125*f**3 - 350*f**2 - 218*f - 40. Let y(s) = -2*m(s) - 3*p(s). Suppose y(n) = 0. What is n?
-2, -2/5
Find i such that 0 + 6/5*i**4 + 0*i + 18/5*i**3 - 8/5*i**5 + 4/5*i**2 = 0.
-1, -1/4, 0, 2
Let i = -1/325 + 979/1300. Suppose -i*a**4 + 0 + 0*a**2 - a + 7/4*a**3 = 0. What is a?
-2/3, 0, 1, 2
Let m(h) be the second derivative of h**9/30240 + h**8/2688 + h**7/630 + h**6/360 + 2*h**4/3 - 8*h. Let c(b) be the third derivative of m(b). Factor c(t).
t*(t + 1)*(t + 2)**2/2
Let h = 13 - 10. Factor 4*a - 3 - 3*a + 3*a**2 - 7*a + 6*a**h.
3*(a - 1)*(a + 1)*(2*a + 1)
Let m be ((-5)/((-20)/8))/(-2). Let o(f) = -1. Let k(b) = b**2 - b + 5. Let l(g) = m*k(g) - 5*o(g). Find z, given that l(z) = 0.
0, 1
Let l be 28/4 - (2 - 0). Suppose -l*f + 46 = 1. Solve 4*d + 4*d + 6 - f*d**3 - 2 - 3*d**2 = 0 for d.
-2/3, 1
Let w(p) be the second derivative of -p**5/300 - p**4/120 + 5*p**2/2 + 3*p. Let b(x) be the first derivative of w(x). Solve b(y) = 0 for y.
-1, 0
Let y(g) be the second derivative of g**8/10080 + g**7/945 + g**6/270 - g**4/6 + g. Let m(l) be the third derivative of y(l). Factor m(d).
2*d*(d + 2)**2/3
Let m(d) be the first derivative of -3/8*d**2 - 3/20*d**5 + 4 + 3/16*d**4 + 0*d + 1/4*d**3. Determine c so that m(c) = 0.
-1, 0, 1
Let n(f) be the third derivative of f**9/15120 + f**8/6720 - f**7/2520 - f**6/720 + f**4/24 - 4*f**2. Let q(b) be the second derivative of n(b). Solve q(y) = 0.
-1, 0, 1
Let j(l) be the third derivative of -2/3*l**3 + 0*l + 2*l**2 + 7/12*l**4 + 1/15*l**5 - 7/60*l**6 + 0. Factor j(f).
-2*(f - 1)*(f + 1)*(7*f - 2)
Let v(k) be the first derivative of -k**4/60 + k**3/30 + k**2/5 + 3*k - 1. Let i(q) be the first derivative of v(q). Suppose i(n) = 0. What is n?
-1, 2
Suppose -46*j + 120 = -22*j. Find d such that 0*d - 1/4*d**j + 1/4*d**3 + 0 + 1/4*d**2 - 1/4*d**4 = 0.
-1, 0, 1
Let u(b) be the third derivative of -b**7/210 - b**6/30 - b**5/30 + b**4/6 + b**3/2 - 26*b**2. Solve u(w) = 0 for w.
-3, -1, 1
Let q(z) = z**5 + z**2 - z. Let h(t) = -59*t**5 - 175*t**4 - 160*t**3 - 29*t**2 + 19*t + 5. Let j(u) = h(u) - q(u). Find p such that j(p) = 0.
-1, -1/4, 1/3
Factor -285*d - 16*d**2 + 4*d**3 - 282*d + 567*d.
4*d**2*(d - 4)
Suppose -4*q - 5*d + 23 = 0, -q + 0 = -2*d + 4. Let u(j) be the first derivative of 6*j**q - 31/6*j**3 + 2 - 2*j + 7/2*j**5 - 3*j**4. What is t in u(t) = 0?
-1, 2/7, 2/5, 1
Let u(j) be the third derivative of 2/21*j**3 + 4/105*j**5 - 2/735*j**7 + 0 - 1/12*j**4 + 0*j + 1/1176*j**8 + 9*j**2 - 1/210*j**6. Solve u(r) = 0.
-2, 1
Let h(q) be the second derivative of -1/27*q**3 + 1/18*q**4 + 0 + 0*q**2 - q + 1/135*q**6 - 1/30*q**5. Find a, given that h(a) = 0.
0, 1
Let k be ((-3)/(-5))/((-3)/(-2)). Let o(m) = -2*m**2 + 14*m - 9. Let z be o(6). Solve 6/5*n**2 + 1/5*n - 3/5*n**5 - n**4 - 1/5 + k*n**z = 0 for n.
-1, 1/3, 1
Suppose 3*s + 0*r + 2*r = 4, 0 = -5*s + 2*r + 12. Factor -23 - 2*z - 3*z**s + 25 - 3*z.
-(z + 2)*(3*z - 1)
Determine i so that -59*i**3 + 120*i**3 - 4*i**4 - 2*i**5 - 63*i**3 = 0.
-1, 0
Let q(b) be the third derivative of 0*b**4 + 0*b**3 + 0*b + 1/480*b**6 + 2*b**2 - 1/120*b**5 + 1/840*b**7 + 0. Factor q(z).
z**2*(z - 1)*(z + 2)/4
Let y be 1*4/8 - 2/12. Factor -4/3*b + 1 + y*b**2.
(b - 3)*(b - 1)/3
Let s = 1 + 2. Suppose 5*k = 5*p + 25, 2*k = s*p - 0*p + 13. Factor 3*o + 12*o**2 - o**3 + 2*o**4 + k + 9*o**3 + 5*o.
2*(o + 1)**4
Let b(n) = 6*n**5 + 16*n**4 + 4*n**3 - 42*n**2 - 16*n + 30. Let z(j) = j**5 - j**2 - 1. Let q(f) = -b(f) + 2*z(f). Factor q(s).
-4*(s - 1)**2*(s + 2)**3
Let d be 2/(12/(-9)) + (-38)/(-24). Let u(n) be the second derivative of 3*n - d*n**4 + 0 - 5/12*n**3 + 1/8*n**5 + 1/2*n**2. Factor u(w).
(w - 1)*(w + 1)*(5*w - 2)/2
Let r = 12/13 + -10/13. Solve -4/13*z - r*z**3 + 0 - 6/13*z**2 = 0.
-2, -1, 0
Let a = 38 + -3. Suppose -3*y = -a + 8. Find j, given that -y*j**3 + 7*j**4 - 2*