?
-3, 0, 1
Let h(p) be the third derivative of -p**7/525 + p**6/300 + p**5/150 - p**4/60 - p**2 + 252*p. Find q, given that h(q) = 0.
-1, 0, 1
Let o(i) be the second derivative of 0 + 1/15*i**4 + 4/15*i**3 + 0*i**2 + 7*i. Factor o(q).
4*q*(q + 2)/5
Let l(w) be the third derivative of -5*w**9/12096 - w**8/336 - w**7/224 - 7*w**3/3 - 2*w**2. Let o(d) be the first derivative of l(d). Factor o(s).
-5*s**3*(s + 1)*(s + 3)/4
Let m(z) = -2*z**2 + z + 3. Suppose 3*r - 5*r = 0. Let k be r + -3 + -1 - -9. Let v(h) = 3*h**2 - 2*h - 5. Let w(d) = k*v(d) + 8*m(d). Factor w(x).
-(x + 1)**2
Let z(c) = c**2 - 18*c - 23. Suppose 3*i = -j - 0*j + 16, 2*i = -j + 9. Let m(g) = 11 + 36 - g**2 + 20*g + 16*g. Let f(l) = i*z(l) + 4*m(l). Factor f(r).
3*(r + 3)**2
Let s be 3*(-2 - -1) - (-2 - 3). Factor -6/11*i + 0*i**s + 2/11*i**3 + 4/11.
2*(i - 1)**2*(i + 2)/11
Let y = -87/25 - -2183/225. Factor -16/9 - y*l + 4/9*l**2 + 14/9*l**3.
2*(l - 2)*(l + 2)*(7*l + 2)/9
Let o = -12676 + 12678. Let 0*a - 2/17*a**o + 8/17 = 0. Calculate a.
-2, 2
Let q(a) be the first derivative of -3 + 1/7*a - 1/21*a**3 + 0*a**2. Factor q(b).
-(b - 1)*(b + 1)/7
Suppose 6*m - 115 = -91. Let n(i) be the third derivative of m*i**2 + 1/240*i**6 + 0*i - 1/6*i**3 + 1/60*i**5 + 0 - 1/48*i**4. Factor n(l).
(l - 1)*(l + 1)*(l + 2)/2
Determine o so that 0*o**5 - 5*o**4 + 0*o**5 + 420 - 335*o**2 + 117*o**3 + 48*o**3 - 5*o**5 - 80*o = 0.
-7, -1, 2, 3
Determine t, given that 0*t**3 + 2*t - 2*t - 12*t**2 + 16*t - 4*t**3 = 0.
-4, 0, 1
Let i = 35964/89885 - 2/17977. Let a = 47 + -231/5. Solve -i*s**3 + 0 + 0*s**2 - a*s**5 - 6/5*s**4 + 0*s = 0 for s.
-1, -1/2, 0
Let j be ((-65178)/(-15))/(-6) - (1 - 1). Let h = -717 - j. Find p such that -4/5 + h*p**4 + 18/5*p**5 - 32/5*p**2 - 22/5*p + 4/5*p**3 = 0.
-1, -2/3, -1/3, 1
Let b be 504/9 + (0 - 1). Let 0 + 0 - 2*p**2 + 51*p - b*p + 6*p**3 = 0. What is p?
-2/3, 0, 1
Find k such that -115*k**4 + 37*k**4 - 100*k**2 - 5*k**5 + 43*k**4 + 140*k**3 = 0.
-10, 0, 1, 2
Let y(a) be the third derivative of 3*a**7/560 - 7*a**6/320 - 7*a**5/160 + 3*a**4/64 - 14*a**2. Determine t, given that y(t) = 0.
-1, 0, 1/3, 3
Let u(c) be the first derivative of 50 + 15*c**2 - 55/3*c**3 + 0*c + 5*c**4 + c**5. Factor u(f).
5*f*(f - 1)**2*(f + 6)
Suppose 2*t + 24 = 4*v, -76*v + 14 = -74*v. Factor -32/17 + 2/17*h**3 + 14/17*h**t + 16/17*h.
2*(h - 1)*(h + 4)**2/17
Let n = 72 + -143/2. Determine u so that 9/4*u**4 + 0 + 0*u - 7/4*u**5 - n*u**3 + 0*u**2 = 0.
0, 2/7, 1
Let c = -1 + 4. Let 4*n**c + n - 8*n**3 + 21*n - 12 - 4*n**2 - 2*n = 0. What is n?
-3, 1
Let f(n) = 4*n - 6. Let p be f(2). Factor 3*o**2 - 6*o**2 + o**4 - o + 0*o**4 + 2*o**p + o**3.
o*(o - 1)*(o + 1)**2
Let d(r) be the third derivative of r**8/4480 - r**7/3360 - 13*r**5/30 - 7*r**2 + 5*r. Let n(w) be the third derivative of d(w). Find i, given that n(i) = 0.
0, 1/3
Let s(x) be the first derivative of 2 - 15*x - 2 + 8*x**3 + 9*x**2 + 5 - 9*x**3. Factor s(o).
-3*(o - 5)*(o - 1)
Let l be (-64)/(-84) + (-9)/21. Let u(f) be the second derivative of -4*f + l*f**4 + 0 + 0*f**2 + 2/3*f**3. Factor u(a).
4*a*(a + 1)
Determine t so that 4*t - 2*t + 24*t - 200 + 14*t - 2*t**2 = 0.
10
Let a(z) be the first derivative of -2*z**3/3 + 5*z**2 - 8*z - 136. Solve a(y) = 0 for y.
1, 4
Suppose 2*m + 0*m + n - 8 = 0, 3*m - 12 = 5*n. Let -2*y**2 + m*y**2 - 2*y**3 - 2*y**3 + 2*y**3 = 0. Calculate y.
0, 1
Suppose 10*x - 25 + 7*x**3 + 4*x**4 + 21 - 17*x**3 = 0. Calculate x.
-1, 1/2, 1, 2
Let q(r) = 44*r**2 - 8*r + 26. Let u(c) = 5*c**2 - c + 3. Let z be 1320/25 - (-4)/(-5). Let a(j) = z*u(j) - 6*q(j). Find v, given that a(v) = 0.
-1, 0
Let l(k) = -k - 7. Let a be l(-11). Suppose 0 = a*j - 2 - 10, -f + j - 1 = 0. Suppose -5*s + 0*s + 8 + 4*s**f - 7*s = 0. Calculate s.
1, 2
Factor 12*t + 3/2*t**2 + 18.
3*(t + 2)*(t + 6)/2
Let g(b) be the first derivative of -b**3/3 + 5*b**2 + 14*b - 7. Let x(p) = -2*p**2 + 11*p + 13. Let k(t) = 3*g(t) - 2*x(t). Suppose k(h) = 0. What is h?
-4
Let w(z) be the second derivative of -z**4/90 + z**3/9 + 2*z**2/5 + 55*z. Determine i so that w(i) = 0.
-1, 6
Factor 4*g**5 + 4021*g**3 - 2010*g**3 - 2011*g**3 + 12*g**4.
4*g**4*(g + 3)
Let q be (8 + 2 + -8)/(-4)*(-7 - 1). Determine o so that -q*o + 7/2 + 1/2*o**2 = 0.
1, 7
Let s(j) be the second derivative of 3/5*j**5 + 2/21*j**7 + 0*j**2 + 21*j + 0*j**3 + 1/3*j**4 + 2/5*j**6 + 0. Find d such that s(d) = 0.
-1, 0
Let t(o) = -o**3 + 6*o**2 - 4*o - 3. Let y be t(5). Let i(q) = -17*q + 54. Let d be i(3). Factor -3*x**2 + y*x**2 - 2*x**3 - 3*x**2 - 3*x + x**d.
-x*(x + 1)*(x + 3)
Let f(r) be the second derivative of 1/72*r**4 - r - 1/180*r**5 + 0 + 0*r**3 - 1/2*r**2. Let l(n) be the first derivative of f(n). Factor l(m).
-m*(m - 1)/3
Let v be (144/40)/((-6)/(-40)). Factor 10*t**2 + v*t - 24*t + 5*t**3.
5*t**2*(t + 2)
Let h(o) = o**3 - 15*o**2 + 13*o + 14. Let b be h(14). Let l be (-2 + b)*(-15)/6. Factor -1 + 2*i**l + 0*i**2 - 5*i**2 + 5*i**4 + i**2 - 4*i + 2*i**3 + 0*i**5.
(i - 1)*(i + 1)**3*(2*i + 1)
Factor -16/3 - 38/9*v**2 + 8/9*v**3 - 92/9*v + 2/9*v**4.
2*(v - 4)*(v + 1)**2*(v + 6)/9
Suppose 0 = -3*k + 5 + 109. Factor 10*z**2 + 38 - k + 15*z**3 + 5*z**4.
5*z**2*(z + 1)*(z + 2)
Let l(x) = x**2 + 29*x + 192. Let c be l(-10). Let v(r) be the first derivative of -3/2*r**c - 3 + 3/4*r**4 + 2*r**3 - 6*r. Factor v(q).
3*(q - 1)*(q + 1)*(q + 2)
Let y(z) be the third derivative of -z**6/1140 - 17*z**5/570 - 31*z**4/228 - 5*z**3/19 - 6*z**2 + 29. Factor y(h).
-2*(h + 1)**2*(h + 15)/19
Factor 392 - 23/2*o**3 + 30*o**2 + 434*o + 1/2*o**4.
(o - 14)**2*(o + 1)*(o + 4)/2
Let r(t) = -3*t**5 + t**4 - t**2 + 3*t - 5. Let i(w) = 3*w**5 - 3*w + 6. Let z = 36 + -30. Let v(s) = z*r(s) + 5*i(s). What is c in v(c) = 0?
-1, 0, 1
Let m(u) be the second derivative of u**7/336 + u**6/48 - 5*u**4/12 - 5*u**3/3 - 3*u**2 + 390*u. Factor m(w).
(w - 3)*(w + 2)**4/8
Let i(k) be the second derivative of -k**5/60 - k**4/2 + 7*k**3/6 + 19*k**2/3 - 112*k. Factor i(r).
-(r - 2)*(r + 1)*(r + 19)/3
Suppose 0 = 2*h - 5*i - 13, 2*h = 4*i + 5 + 5. Let n = 2 - h. Suppose 3 + 3*d**2 + n*d - 8*d - d = 0. Calculate d.
1
Let x(y) be the third derivative of -y**7/490 + y**6/280 + y**5/28 + 3*y**4/56 - 6*y**2 + 3*y. Find c such that x(c) = 0.
-1, 0, 3
Let v(n) = -n**5 - n**3 - n. Let p(a) = -6*a**2 - 6*a - 3*a + 3*a - 2*a**2 + 4*a**4 + 4 + 6*a**3 - 6*a**5. Let u(d) = p(d) - 2*v(d). Factor u(b).
-4*(b - 1)**3*(b + 1)**2
Let s be ((-120)/(-504) - (-2)/(-6))*(8 - 53). Determine l, given that -86/7*l**3 + 116/7*l**2 + 16/7 + s*l**4 - 72/7*l - 4/7*l**5 = 0.
1/2, 1, 2
Let v = -6944 + 6947. Let 1/2*j**v + 1/2*j**2 + 0 - j = 0. What is j?
-2, 0, 1
Let u be (-63)/(-14)*4/6. Determine f, given that -2*f**5 - 20*f**u + f + 20*f**2 + 10*f**4 - 9*f - 2*f + 2 = 0.
1
Let p(x) be the second derivative of x**5/20 + 13*x**4/36 + 4*x**3/9 - 2*x**2 + 1033*x. Solve p(w) = 0 for w.
-3, -2, 2/3
Let x(l) be the first derivative of 2*l**5/95 + 2*l**4/19 + 10*l**3/57 + 2*l**2/19 - 12. Solve x(v) = 0.
-2, -1, 0
Let t(o) be the second derivative of 1/12*o**3 + o + 1/24*o**4 + 0 + 0*o**2. Factor t(i).
i*(i + 1)/2
Let p(q) be the third derivative of -q**7/105 + 11*q**6/60 - q**5/2 - 175*q**4/12 + 500*q**3/3 - 267*q**2. Factor p(w).
-2*(w - 5)**3*(w + 4)
Let d(n) = -n**3 - 11*n**2 - 12*n + 1. Let b be d(-1). Suppose 0*q**2 + 0 - 1/2*q**4 + 0*q + 1/2*q**b = 0. What is q?
0, 1
Let f(p) be the third derivative of p**5/40 - 161*p**4/8 + 25921*p**3/4 + 7*p**2 - 20. Factor f(t).
3*(t - 161)**2/2
Let g(c) = c**2 - 14*c + 29. Let r be g(12). Factor -20*u**2 + 5*u**3 - 15*u - 14*u + r*u**4 + 9*u.
5*u*(u - 2)*(u + 1)*(u + 2)
Let i be 3/((8/12)/1). Let h = 32 - 29. Find l, given that 23*l**h - 17*l**4 + 1 + i*l**5 + 1/2*l - 12*l**2 = 0.
-2/9, 1
Let q(u) be the third derivative of -u**6/240 - 3*u**5/5 - 36*u**4 - 1152*u**3 + 3*u**2 + 13*u. Factor q(l).
-(l + 24)**3/2
Let b(w) = -3*w**4 - 19*w**3 - 15*w**2 - 13*w + 7. Let p(l) = 3*l**4 + 18*l**3 + 15*l**2 + 12*l - 6. Let o(k) = -6*b(k) - 7*p(k). Factor o(y).
-3*y*(y + 1)**2*(y + 2)
Let g(u) be the second derivative of -u**5/80 + 11*u**4/48 + u**3/24 - 11*u**2/8 + 2*u + 150. Let g(o) = 0. What is o?
-1, 1, 11
Let r = 507 - 507. Let j(x) be the second derivative of 7*x + 1/84*x**7 + 1/8*x**4 + 1/40*x**5 - 1/6*x**3 - 1/20*x**6 + 