t p(n) be the first derivative of n**7/2940 - n**5/140 + n**4/42 + 2*n**3 + 8. Let h(w) be the third derivative of p(w). Factor h(a).
2*(a - 1)**2*(a + 2)/7
Let v(f) = 1. Let o be 1 + -1 - 21 - 3. Let c(d) = 12*d - 24. Let x(y) = o*v(y) - c(y). Let n(h) = h**2 - 13*h. Let i(k) = -4*n(k) + 5*x(k). Solve i(m) = 0.
-2, 0
Let f be 4 - (-1 + 0) - 1. Let x be 2/(-6)*(-13 + f). Factor 3*w - 4*w**2 + 19 + 2*w**x - 5*w - 15.
2*(w - 2)*(w - 1)*(w + 1)
Suppose 35 = -0*u + 7*u. What is x in 9*x**2 + 5*x**4 - u*x + 5*x**3 - 34*x**2 + 20*x**2 = 0?
-1, 0, 1
Let y(f) be the first derivative of 0*f**3 + 10 + 9*f - 1/10*f**5 + 0*f**4 + 0*f**2. Let z(d) be the first derivative of y(d). Factor z(j).
-2*j**3
Let x(r) = 5*r**2 + 5*r + 9. Let p be x(-2). Factor 36*m + 33*m**2 + p*m**2 + 48 - 12*m**3 + 76*m.
-4*(m - 6)*(m + 1)*(3*m + 2)
Let q(a) = a + 3. Let w be q(4). Suppose 0 = 4*m - 231 + w. Suppose m + 4*f**3 - 56 - 4*f = 0. Calculate f.
-1, 0, 1
Let v(k) be the second derivative of -16*k + 0 + 0*k**2 - 1/2*k**3 + 1/8*k**4. Determine c so that v(c) = 0.
0, 2
Suppose -2*k + 5*j = 2*k + 3, 0 = -3*k - 5*j + 24. Let 20 - 3*a**3 + 11*a**3 - a**3 - 2*a**k - 15*a**2 = 0. Calculate a.
-1, 2
Let m be 28*3*4/8. Let p = m + -40. Factor 6/5 - p*r + 2/5*r**2 + 2/5*r**3.
2*(r - 1)**2*(r + 3)/5
Suppose 0 = 4*a - 3*h + 6, -2 = -2*h + 2. Suppose -2*c - 6*t + 2*t - 14 = 0, 24 = 3*c - 3*t. Let -4*s**c + 7*s**3 + 12*s + 12*s**2 + a*s = 0. Calculate s.
-2, 0
Determine d, given that -4*d**5 - 92*d**3 + 27*d**4 - 14*d**4 + 9*d**4 + 18*d**4 + 56*d**2 = 0.
0, 1, 2, 7
Let x(c) be the third derivative of c**5/48 - 5*c**4/24 - 35*c**3/8 - 47*c**2 + 2. What is g in x(g) = 0?
-3, 7
Factor 0*k - 92/5*k**2 + 2/5*k**3 + 0.
2*k**2*(k - 46)/5
Let j(c) be the first derivative of c**5/80 + c**4/32 - 3*c**2/2 + 8*c + 37. Let k(i) be the second derivative of j(i). Let k(u) = 0. Calculate u.
-1, 0
Let p(k) = -16*k**3 + 8*k**2 + 4*k + 4. Let u(f) = -13*f**3 + 8*f**2 + 3*f + 3. Let w(c) = 3*p(c) - 4*u(c). Find y such that w(y) = 0.
0, 2
Let t(m) be the second derivative of -m**5/100 + m**4/10 - 3*m**3/10 - 73*m. Factor t(c).
-c*(c - 3)**2/5
Suppose -3*t + 56 = 26. Suppose 152 = t*m - 6*m. Find x, given that -2*x**2 + 40 - m + 0*x**2 = 0.
-1, 1
Let c be -5 + 5/10*10. Let c + 8 + 3*g + 19*g + 5*g**2 + 0 = 0. What is g?
-4, -2/5
Let t(q) be the first derivative of q**5/15 + 2*q**4/3 + 8*q**3/3 + 13*q**2/2 + 11. Let c(z) be the second derivative of t(z). Factor c(r).
4*(r + 2)**2
Factor -92/19*m**3 - 292/19*m - 288/19*m**2 - 98/19 + 2/19*m**4.
2*(m - 49)*(m + 1)**3/19
Solve -2*a**2 + 2*a**4 + 0*a**5 - 4454*a + 4453*a + a**5 = 0.
-1, 0, 1
Let o be 948/(-3318)*21/(-2). Let k = 1/3 + 1/3. Factor 2/3*d**o + 2/3*d**4 - k*d - 2/3*d**2 + 0.
2*d*(d - 1)*(d + 1)**2/3
Let p(b) be the first derivative of -9*b**3 - 3/4*b**4 - 81*b - 81/2*b**2 - 9. Suppose p(f) = 0. What is f?
-3
Let f = -4 - -10. Let b be 9/(-6)*(-28)/f. Solve b*w**2 - w + 7*w - 3*w**2 - 4*w = 0.
-1/2, 0
Let u(k) be the first derivative of k**3/3 - 3*k**2 + 8*k + 196. Factor u(h).
(h - 4)*(h - 2)
Let a(d) be the first derivative of d**4/12 + 19*d**3/9 + 33*d**2/2 + 27*d - 61. Factor a(s).
(s + 1)*(s + 9)**2/3
Let z(b) be the second derivative of b**10/30240 - b**9/5040 + b**8/2240 - b**7/2520 + 5*b**4/6 + 16*b. Let k(s) be the third derivative of z(s). Factor k(d).
d**2*(d - 1)**3
Suppose 0 = 635*z - 642*z. Solve -16/9*i**2 + 8/3*i**3 - 4/3*i**4 + z + 2/9*i**5 + 0*i = 0 for i.
0, 2
Let h be ((-110)/(-8) + 2/8)/2. Solve -168*q**3 - h*q**3 + 4*q - 54*q**2 - 14*q - 31*q**2 = 0 for q.
-2/7, -1/5, 0
Let u(j) be the first derivative of j**6/42 - j**5/7 - 13*j**4/28 - j**3/3 - 110. Factor u(x).
x**2*(x - 7)*(x + 1)**2/7
Let u be (220/1650)/((-1)/(-36)). Factor u*b + 8/5 + 18/5*b**2.
2*(3*b + 2)**2/5
Suppose 5*l + 193*t - 192*t = 2, 5*t + 38 = -l. Factor 0*m**l + 0 + 2/5*m**3 - 2/5*m.
2*m*(m - 1)*(m + 1)/5
Suppose 5*j - 11 = 9. Factor 0*n**2 + 0*n**2 - 8*n**2 + 4*n**2 + j*n.
-4*n*(n - 1)
Let n(y) be the second derivative of y**4/4 + 51*y**3 - y + 413. What is p in n(p) = 0?
-102, 0
Let f = -10 - -14. Factor -10 + c**2 - c - f*c + 4*c**2.
5*(c - 2)*(c + 1)
Let a(d) be the first derivative of 126*d - 4 + 4*d**2 + 0*d**3 + 25 - 127*d - 5*d**3. Solve a(u) = 0 for u.
1/5, 1/3
Let i(y) be the first derivative of -2*y**6/3 - 4*y**5/5 + y**4 + 4*y**3/3 - 73. Factor i(r).
-4*r**2*(r - 1)*(r + 1)**2
Let d be (-11 - -5) + 4 + 7. Let p(y) be the second derivative of -9/40*y**d + 0*y**2 - 1/28*y**7 - 1/8*y**4 + 0 - 12*y + 0*y**3 - 3/20*y**6. Factor p(v).
-3*v**2*(v + 1)**3/2
Let v(h) be the first derivative of h**8/112 + h**7/35 - h**5/10 - h**4/8 - 17*h**2/2 - 12. Let q(f) be the second derivative of v(f). Factor q(u).
3*u*(u - 1)*(u + 1)**3
Find z, given that -295/4*z**3 + 355/4*z**2 + 75/4*z**4 - 125/4*z - 5/2 = 0.
-1/15, 1, 2
Let h(s) = -2*s**3 - 13*s. Let l(g) = g**3 + g**2 + 6*g. Let u(z) = 2*h(z) + 5*l(z). Let u(y) = 0. What is y?
-4, -1, 0
Let m(s) = s. Let w(f) = -2178*f**4 - 4224*f**3 - 1916*f**2 + 124*f - 2. Let n(g) = -4*m(g) - w(g). Find c such that n(c) = 0.
-1, 1/33
Let y(p) be the second derivative of p**6/660 + p**5/330 + 3*p**2 + 8*p. Let h(b) be the first derivative of y(b). Let h(k) = 0. Calculate k.
-1, 0
Factor 0 + 3/2*m**5 + 3*m**4 + 0*m**2 + 3/2*m**3 + 0*m.
3*m**3*(m + 1)**2/2
Let v be (-7)/(-3) + 24/(-72). Factor 9/4*k - 3/4*k**v + 0.
-3*k*(k - 3)/4
Suppose s - p = 38, -3*p = 5*s - s - 180. Suppose 40 + 31*n**2 - 7*n**3 + 5*n**4 - 7*n**2 + s*n**3 + 100*n + 66*n**2 = 0. Calculate n.
-2, -1
Suppose 4*r - 12 = 0, 0*o = -3*o + 4*r - 9. Factor -6*z**2 + o + 3 + 8 - 13*z - z.
-2*(z + 3)*(3*z - 2)
Factor -4*a**2 - 5300*a**3 + 4*a**4 + 2*a**5 - 5302*a**3 + 10600*a**3.
2*a**2*(a - 1)*(a + 1)*(a + 2)
Suppose -2*f = -t - 2 + 4, -2*t + 4 = 5*f. Let -1/5*j**4 + f - 2/5*j + 0*j**3 + 3/5*j**2 = 0. What is j?
-2, 0, 1
Let l(o) be the third derivative of o**5/24 - 145*o**4/48 - 25*o**3/2 - 16*o**2 - 2. Factor l(k).
5*(k - 30)*(k + 1)/2
Let x = -1158 + 13897/12. Let q(z) be the second derivative of 0*z**4 + z + 1/30*z**6 - x*z**3 + 3/40*z**5 + 0 + 0*z**2. Factor q(h).
h*(h + 1)**2*(2*h - 1)/2
Suppose 0 = 2*j - 4. Suppose 4 = -0*n + 2*n. Solve n*z**j + 4 - 7 + 3 = 0.
0
Let c(p) be the third derivative of -1/24*p**6 - 10/3*p**3 + 5/6*p**4 - 17*p**2 + 1/12*p**5 + 0*p + 0. Factor c(z).
-5*(z - 2)*(z - 1)*(z + 2)
Factor -34/21*u**2 - 10/7*u + 4/21.
-2*(u + 1)*(17*u - 2)/21
Let o(v) be the third derivative of v**7/18900 - v**6/2700 - v**5/300 + v**4/24 + 10*v**2. Let y(b) be the second derivative of o(b). Factor y(a).
2*(a - 3)*(a + 1)/15
Let v(d) = d**3 - 23*d**2 + 41*d + 28. Let u be v(21). Let r = u - 7. Solve 0 + 0*p - 2/13*p**3 + r*p**2 + 2/13*p**4 = 0 for p.
0, 1
Factor 7 - 42*r**3 - 8*r**3 - 4*r**5 + 18*r**3 + 12*r**4 + 36*r - 36*r**4 + 8*r**2 + 9.
-4*(r - 1)*(r + 1)**3*(r + 4)
Let h(o) be the first derivative of -o**8/840 - o**7/140 + o**5/15 + 11*o**3/3 - 2. Let f(u) be the third derivative of h(u). Factor f(j).
-2*j*(j - 1)*(j + 2)**2
Let k be (20 - 8 - 2) + -4. Let s(p) be the first derivative of -4/3*p**3 + 1/2*p**4 + 4*p + k - p**2. Solve s(h) = 0 for h.
-1, 1, 2
Let z = -105 - -109. Suppose -23 = -z*j - 7. Factor 0*v - 24/5*v**3 + 0 + 3*v**j - 12/5*v**2.
3*v**2*(v - 2)*(5*v + 2)/5
Let j(z) be the first derivative of -1/10*z**4 + 12 + 0*z**2 + 2/25*z**5 + 0*z - 4/15*z**3. Determine b, given that j(b) = 0.
-1, 0, 2
Factor -16 + 7*n**2 - 6*n**4 + 12*n**5 + 16 + n**2 - 10*n**5.
2*n**2*(n - 2)**2*(n + 1)
Let a = 9 - 6. Let c = -89 - -92. Find v, given that a*v + 0*v**3 + 2*v**2 + 2*v**3 - c*v = 0.
-1, 0
Suppose 4*x = 3*m - 9, 0*m - x - 12 = -4*m. Find z, given that 402*z - 457*z + 10 - 13*z**m + 65*z**2 - 7*z**3 = 0.
1/4, 1, 2
Let o be (30/25)/(-1 - (-548)/560). Let q be (-42)/o*20/6. Factor -3/2*d**4 + 0 - d**2 + 0*d - q*d**3.
-d**2*(d + 1)*(3*d + 2)/2
Let r(m) = 8*m**4 + 42*m**3 + 148*m**2 + 198*m + 90. Let a(d) = 55*d**4 + 295*d**3 + 1035*d**2 + 1385*d + 630. Let p(t) = -3*a(t) + 20*r(t). Factor p(g).
-5*(g + 1)*(g + 2)*(g + 3)**2
Let x(i) = -1. Let t be (2/4)/((-1)/(4 + -2)). Let d(f) = 5*f**2 - 3. Let r = -6 + 4. Let b(z) = r*x(z) + t*d(z). What is l in b(l) = 0?
-1, 1
Suppose 40 = -5*c - 2*k, 0*c + 3 = 2*c - 3*k. Let w be 64/c*(-5 + 2). Factor 38*q**3 