1
Let n be (-26)/(-8) - (-3 + (-26)/(-8)). Let f(t) be the first derivative of 2*t + 13/6*t**3 - 3/4*t**4 - 5 - n*t**2 + 1/10*t**5. Factor f(d).
(d - 2)**2*(d - 1)**2/2
Let j(z) be the third derivative of -z**7/315 + z**6/60 + 2*z**5/45 - 101*z**2 - 1. Factor j(l).
-2*l**2*(l - 4)*(l + 1)/3
Let x(y) be the third derivative of 0 + 0*y**3 + 0*y**4 + 1/200*y**6 + 0*y + 1/100*y**5 - 14*y**2. What is s in x(s) = 0?
-1, 0
Factor -2/3*p**2 - 338/3 - 52/3*p.
-2*(p + 13)**2/3
Let p(l) be the second derivative of l**4/42 + 10*l**3/21 + 24*l**2/7 + 109*l + 3. Factor p(v).
2*(v + 4)*(v + 6)/7
Let z(i) be the second derivative of 0 + 0*i**4 + 1/9*i**3 - 1/90*i**5 - 2/9*i**2 - 6*i. Factor z(p).
-2*(p - 1)**2*(p + 2)/9
Let q(h) be the third derivative of 5*h**5/12 + 23*h**4/24 - h**3/3 - 11*h**2. Factor q(f).
(f + 1)*(25*f - 2)
Let v = 215/2 - 107. Factor 3*m**2 - 2*m - 2*m**3 + 1/2*m**4 + v.
(m - 1)**4/2
Let q(m) be the third derivative of m**5/36 + 7*m**4/36 - m**3/6 + 22*m**2 + 2. Factor q(x).
(x + 3)*(5*x - 1)/3
Let k(m) be the first derivative of -1/2*m**2 - 39 - 1/6*m**3 - 1/2*m. Factor k(j).
-(j + 1)**2/2
Let a be (-552)/80 - -7 - ((-1044)/(-520))/(-3). Factor a*l - 2/13*l**2 - 12/13.
-2*(l - 3)*(l - 2)/13
Let p(s) = 26*s**4 - 62*s**3 - 64*s**2 + 202*s + 14. Let i(u) = -9*u**4 + 21*u**3 + 22*u**2 - 67*u - 5. Let j(r) = 14*i(r) + 5*p(r). Factor j(l).
4*l*(l - 3)**2*(l + 2)
Let c(n) = 11*n**4 - 39*n**3 + 16*n**2 + 20*n + 4. Let l(j) = -54*j**4 + 195*j**3 - 81*j**2 - 102*j - 21. Let w(u) = 21*c(u) + 4*l(u). Factor w(a).
3*a*(a - 2)*(a - 1)*(5*a + 2)
Let j(y) be the first derivative of y**4/48 - y**3/12 + y**2/8 - 14*y - 5. Let a(r) be the first derivative of j(r). Find l, given that a(l) = 0.
1
Let i = 699878/75 - 9332. Let f = 1/25 - i. Determine o so that -o**2 + 0 - o**3 - f*o - 1/3*o**4 = 0.
-1, 0
Suppose -30 + 3159*y - 3180*y - y**2 - 2*y**2 = 0. Calculate y.
-5, -2
Let k be 2 - 4/7*(9 - 7). Suppose 10/7*m**2 - k*m - 4/7 = 0. Calculate m.
-2/5, 1
Let b(p) be the first derivative of -33*p**4/5 - 194*p**3/15 - 6*p**2 + 2*p/5 + 187. Let b(c) = 0. What is c?
-1, -1/2, 1/33
Suppose 3*u + 4 = 5*u. Let k = -5 - -11. Factor -z + k + 3*z + 3*z**u - 11*z.
3*(z - 2)*(z - 1)
Suppose -5*u = -3*l - 8, -3*l + 18 = 3*u - 6. Let m(j) be the second derivative of 2/9*j**3 + 2/3*j**2 + j - 1/12*j**l + 1/90*j**6 - 1/30*j**5 + 0. Factor m(q).
(q - 2)**2*(q + 1)**2/3
Factor r**3 + 239 + 244 + 12*r**2 - 4*r**3 - 3*r - 501.
-3*(r - 3)*(r - 2)*(r + 1)
Suppose 7*f - 2*f - 25 = 0. Factor f*m**3 - 6*m - 44 - 3*m**3 + 0*m**3 + 40.
2*(m - 2)*(m + 1)**2
Let n(y) = -3*y**3 - 14*y**2 - 11*y - 4. Let h(v) = 3*v**3 + 15*v**2 + 12*v + 3. Let t(o) = 4*h(o) + 3*n(o). Determine p, given that t(p) = 0.
-5, -1, 0
Let r = 272 + -270. Let m(c) be the second derivative of 0 + 0*c**3 - 1/54*c**4 + 4/9*c**r + 6*c. Suppose m(a) = 0. What is a?
-2, 2
Let k(g) be the third derivative of 0 + 0*g**4 + 0*g - 1/30*g**5 + 0*g**3 - 1/210*g**7 - 8*g**2 - 1/40*g**6. Determine b, given that k(b) = 0.
-2, -1, 0
Let r(z) be the second derivative of -11/2*z**2 + 1/390*z**5 + 0*z**3 - 4*z + 0 + 1/156*z**4. Let u(v) be the first derivative of r(v). Factor u(q).
2*q*(q + 1)/13
Factor 4*x**3 - 40*x**2 - 4*x + 10*x + 0*x - 6*x.
4*x**2*(x - 10)
Let o(r) be the third derivative of 0 + 1/120*r**6 + 1/6*r**3 + 1/40*r**5 + 3*r**2 + 0*r + 0*r**4. Let h(g) be the first derivative of o(g). Factor h(u).
3*u*(u + 1)
Let j be ((-6)/18)/((-1)/(-561)). Let v = -559/3 - j. Determine a, given that 2*a**4 + 16/3*a**2 + 1/3*a**5 + 3*a + v + 14/3*a**3 = 0.
-2, -1
What is m in 72*m - 56*m**4 + 159*m**5 - 163*m**5 - 240*m**3 + 23*m + 109*m - 200*m**2 + 296*m = 0?
-5, 0, 1
Let n(r) be the third derivative of -r**5/270 + 19*r**4/54 - 361*r**3/27 - 5*r**2 - 7. Suppose n(l) = 0. What is l?
19
Suppose -p**4 - 36 - 4*p**4 + 3*p**4 + 6*p**4 + 32*p**2 - 24*p + 24*p**3 = 0. Calculate p.
-3, -1, 1
Let b(w) be the first derivative of -w**5/4 - 5*w**4/4 + 5*w**3/6 + 15*w**2/2 - 11*w - 31. Let o(x) be the first derivative of b(x). Factor o(d).
-5*(d - 1)*(d + 1)*(d + 3)
Let j be (-2)/((1*-2)/((-52)/(-104))). Solve -j*f**2 - 5/2*f + 1/2*f**3 - 3/2 = 0 for f.
-1, 3
What is p in -171/5*p**4 - 144*p - 432*p**3 - 3/5*p**5 + 8088/5*p**2 - 2160 = 0?
-30, -1, 2
Let s(x) be the third derivative of -2/21*x**3 + 0*x**4 + x**2 + 1/105*x**5 + 0*x + 0. Determine d so that s(d) = 0.
-1, 1
Let h(f) = 5*f**3 + 55*f**2 - 52*f - 132. Let n(w) = 6*w**3 + 53*w**2 - 50*w - 132. Let q(k) = -7*h(k) + 6*n(k). Factor q(x).
(x - 66)*(x - 2)*(x + 1)
Suppose 472 = -11*i - 210. Let q = 122 + i. Solve 48*k + q*k**3 + 25/2*k**4 + 92*k**2 + 8 = 0.
-2, -2/5
Let f(i) be the third derivative of i**8/112 + 3*i**7/35 - 7*i**6/10 - 3*i**5/10 + 27*i**4/8 - 169*i**2. Solve f(b) = 0.
-9, -1, 0, 1, 3
Let h = 18842 + -18842. Suppose h - 24/5*q - 4/5*q**3 + 4*q**2 = 0. Calculate q.
0, 2, 3
Let a(w) be the second derivative of w**4/3 - 142*w**3/3 - 144*w**2 + 108*w - 2. Suppose a(f) = 0. Calculate f.
-1, 72
Let p(c) be the third derivative of c**6/160 - 9*c**5/40 + 15*c**4/8 + 25*c**3 + 2*c**2 - 13*c. Factor p(q).
3*(q - 10)**2*(q + 2)/4
Let i(n) be the second derivative of n**5/150 + 31*n**4/90 - n**3/45 - 31*n**2/15 - 168*n + 1. Let i(x) = 0. Calculate x.
-31, -1, 1
Let g(u) = -u + 5. Let t be g(3). Factor -9*w**3 + 16*w**3 - w**3 + 3*w + 2*w**2 - 11*w**t.
3*w*(w - 1)*(2*w - 1)
Let z = 161085/702548 - 12/2281. Let u = z + 2/77. Solve -u*g**2 - 3/4 + g = 0.
1, 3
Let r = 1286 - 1282. Factor -2/9*c**r + 0 - 4/9*c**3 + 0*c + 2/3*c**2.
-2*c**2*(c - 1)*(c + 3)/9
Let u be ((-30)/(-630))/((-46)/12 + 4). Factor 0 - 10/7*l**2 + u*l.
-2*l*(5*l - 1)/7
Suppose -1 + 1/2*z**2 - 1/2*z = 0. Calculate z.
-1, 2
Let r(x) be the third derivative of -x**6/360 + x**5/20 + x**4/2 - x**2 - 49. Suppose r(j) = 0. Calculate j.
-3, 0, 12
Let d(r) = r**3 - 2*r**2 + r - 1. Let m(z) = -9*z**3 + 18*z**2 + 3*z + 6. Let y(j) = 6*d(j) + m(j). Factor y(h).
-3*h*(h - 3)*(h + 1)
Let j(t) be the second derivative of -t**6/105 - 4*t**5/35 - 5*t**4/14 + 8*t**3/21 + 16*t**2/7 + 11*t + 5. Suppose j(n) = 0. Calculate n.
-4, -1, 1
Let -2*u**2 - 2*u**3 - 12 - 16 + 0*u - 34*u - 12*u - 18*u**2 = 0. Calculate u.
-7, -2, -1
Let k(y) = y**2 + 9*y + 7. Let p be k(-9). Suppose -3*w = -z - 7, -p = 3*z - 4. Factor -5*h**3 + 2*h + h**3 + 0*h**3 + w*h**3.
-2*h*(h - 1)*(h + 1)
Let o(b) be the first derivative of 1/4*b**4 - 1/2*b**2 + 4/3*b**3 - 4*b - 16. Let o(t) = 0. What is t?
-4, -1, 1
Let l(b) be the first derivative of -b**5 - 5*b**4 - 20/3*b**3 + 0*b**2 - 5 + 0*b. Suppose l(j) = 0. Calculate j.
-2, 0
Suppose -42*c**2 + 27/4*c**3 + 63*c - 12 = 0. Calculate c.
2/9, 2, 4
Let k(m) = m**2 + 16*m + 2. Let b be k(-17). Solve 20*d**2 - b*d + 0*d + 34*d = 0 for d.
-3/4, 0
Let o(i) be the second derivative of -i**4/54 - i**3/27 + 2*i**2/3 + 3*i + 7. Solve o(f) = 0 for f.
-3, 2
Let x = -28 + 36. Suppose -5*y + 8 = 5*v - 7, -3*y = 2*v - x. Let 0*s**y + 0*s - 1/3*s**3 + 0 = 0. What is s?
0
Let g = 49/148 + 31/74. Solve g*b**2 + 0 + 0*b = 0 for b.
0
Let a(l) = l**2 + 7*l - 5. Suppose -4*n - 32 = -4*r, 4*r + 8 = -3*n - 16. Let g be a(n). Factor -4*c**3 - 20*c - 2*c**3 + 16*c**2 + 8 + 2*c**g.
-4*(c - 2)*(c - 1)**2
Let y be (-2 + 35/10)/(702/(-8)). Let x = 244/585 + y. Determine l so that 0*l + x*l**3 + 0 - 2/5*l**2 = 0.
0, 1
Let m be (8 - 10 - -12) + -8. Factor 4/3*p**m + 0 - 1/3*p**4 - 4/3*p + 1/3*p**3.
-p*(p - 2)*(p - 1)*(p + 2)/3
Let r(v) be the third derivative of -5*v**8/336 + v**6/6 + v**5/6 - 5*v**4/8 - 5*v**3/3 - 46*v**2. Factor r(f).
-5*(f - 2)*(f - 1)*(f + 1)**3
Determine v, given that 31*v**2 - 5*v**5 - 50*v**4 + 34*v**2 - 15*v**2 - 98*v**3 + 105*v - 2*v**3 = 0.
-7, -3, -1, 0, 1
Let j(i) be the third derivative of 0*i + 1/90*i**6 - 11/18*i**4 - 4/3*i**3 + 2 + 12*i**2 - 4/45*i**5. Find m, given that j(m) = 0.
-1, 6
What is k in -117*k**2 + 56*k**3 - 151*k**2 + 107 + 28*k**4 + 49 - 8*k**5 - 12 + 144*k = 0?
-3, -1/2, 2, 3
Let a(t) be the third derivative of -1/100*t**5 + 1/5*t**3 + 0 - 20*t**2 + 0*t + 1/40*t**4. Let a(p) = 0. Calculate p.
-1, 2
Let n(l) be the first derivative of 0*l + 2/39*l**3 - 28 + 4/13*l**2. What is c in n(c) = 0?
-4, 0
Let l(m) be the first derivative of m**7/168 - m**5/8 - 5*m**4/12 + 2*m**3 - 10. Let j(c) be the third de