*(p - 1)/2
Factor 14/9*j**2 + 8 - 20/3*j - 1/9*j**3.
-(j - 6)**2*(j - 2)/9
Factor -2*l**3 + 0*l + 4*l**3 - 69 + l**4 + 68 - 2*l.
(l - 1)*(l + 1)**3
Let y be (-70)/63*(1 + 8/(-5)). Factor 2/9 + 2/9*z**3 + y*z**2 + 2/3*z.
2*(z + 1)**3/9
Factor -7*h**3 + 12*h**2 + 0*h**3 - h**3 + 4*h - 8*h**3.
-4*h*(h - 1)*(4*h + 1)
Let c(z) be the third derivative of -1/168*z**8 + 1/15*z**5 + 0 - 3*z**2 + 0*z**3 + 0*z**4 + 0*z + 1/20*z**6 + 0*z**7. Find k such that c(k) = 0.
-1, 0, 2
Find n, given that -3/4*n**5 - 3*n**2 - 9/2*n**3 - 3/4*n - 3*n**4 + 0 = 0.
-1, 0
Let w be (-6)/(-4) - 1/(-2). Suppose 2*m + 10*m**2 - 2*m**3 + w*m + 8*m**3 = 0. What is m?
-1, -2/3, 0
Let o(a) be the first derivative of 5*a**4/4 - 5*a**3 + 5*a**2 - 16. Find r, given that o(r) = 0.
0, 1, 2
Let f be 48/(-36)*21/(-2). Let w be (12/(-9))/(f/(-3)). Factor 2/7*x**5 - w*x**4 - 10/7*x**3 + 2/7*x**2 + 16/7*x + 8/7.
2*(x - 2)**2*(x + 1)**3/7
Suppose 2*f = h - 3 + 2, 4*f - 8 = 0. Factor 2*t**5 - 4*t**3 + 3*t + 0*t**h - t.
2*t*(t - 1)**2*(t + 1)**2
Let r = -46 + 66. Suppose p + 3*p - 12 = -l, -2*p + 3*l = -r. Let -m**2 + m**p + m**3 + m**2 = 0. What is m?
-1, 0
Let i(x) be the third derivative of -x**9/181440 + x**7/15120 - x**5/20 + 2*x**2. Let n(c) be the third derivative of i(c). Find p, given that n(p) = 0.
-1, 0, 1
Let o(x) be the third derivative of -x**7/630 + x**5/30 + x**4/8 + 6*x**2. Let n(j) be the second derivative of o(j). What is u in n(u) = 0?
-1, 1
Solve -1/4*n**2 + 1 - 1/4*n**3 + n = 0.
-2, -1, 2
Suppose 0*b - b = 0. Solve -5*w**2 + 4*w + b + 3*w**2 - 2 = 0 for w.
1
Factor 1/2*m + 0 + 0*m**2 - 1/2*m**3.
-m*(m - 1)*(m + 1)/2
Let y(h) be the first derivative of h**3/12 - h**2/4 + 15. Solve y(z) = 0.
0, 2
Let y(h) = 2*h**3 - 10*h**2 - 6*h + 8. Let t be -1*3/(6/(-14)). Let k(a) = 5*a**3 - 31*a**2 - 19*a + 24. Let l(s) = t*y(s) - 2*k(s). Factor l(p).
4*(p - 2)*(p - 1)*(p + 1)
Factor 0 + 0*r + 1/9*r**3 - 1/9*r**2.
r**2*(r - 1)/9
Let k(s) be the first derivative of -s**6/60 + s**5/10 - s**4/6 - 3*s**2/2 - 3. Let i(h) be the second derivative of k(h). Factor i(u).
-2*u*(u - 2)*(u - 1)
Let f = -408 - -1228/3. Solve -2/3 + 0*m**2 + 2/3*m**4 - 4/3*m + f*m**3 = 0.
-1, 1
Let p be 2 + (1 + 1 - -1). Let b = p - 5. Let 1/2*s**3 - 1/2*s**4 + 1/2*s**2 - 1/2*s**5 + b + 0*s = 0. Calculate s.
-1, 0, 1
Let q = -2049/7 + 293. Factor -2/7*f**4 + 2/7*f - q*f**3 + 2/7*f**2 + 0.
-2*f*(f - 1)*(f + 1)**2/7
Factor 1/7*l**3 - 2/7 - 1/7*l + 3/7*l**2 - 1/7*l**4.
-(l - 2)*(l - 1)*(l + 1)**2/7
Let l(j) = -2*j - 6. Let n be l(-5). Suppose -v - 9 = -n*v. Solve z**2 + 2*z**3 + 1 - 6*z + 5*z**2 + 1 - 4*z**v = 0 for z.
1
Suppose 2/5*o**4 + 2/5*o**3 + 0*o - 4/5*o**2 + 0 = 0. What is o?
-2, 0, 1
Let h(k) be the third derivative of -k**7/1680 - k**6/192 - 7*k**5/480 - k**4/64 - 3*k**2. Factor h(m).
-m*(m + 1)**2*(m + 3)/8
Let b(t) be the third derivative of t**7/42 - 7*t**5/12 + 5*t**4/4 - 2*t**2 + 6*t. Solve b(l) = 0.
-3, 0, 1, 2
Let g(l) be the second derivative of l**5/50 - 3*l**4/20 + 2*l**3/5 - 2*l**2/5 + 5*l. Let g(k) = 0. Calculate k.
1/2, 2
Let w(p) = 42*p**5 + 34*p**4 - 2*p**3 - 6. Let i(h) = -125*h**5 - 101*h**4 + 7*h**3 + 17. Let a(v) = -6*i(v) - 17*w(v). Solve a(u) = 0.
-1, 0, 2/9
Let r(p) be the first derivative of 4*p**5 - 18*p**4 + 68*p**3/3 - 16*p - 61. Factor r(f).
4*(f - 2)*(f - 1)**2*(5*f + 2)
Let x(o) be the third derivative of 0*o + 0*o**3 + 0 + 1/140*o**6 + o**2 + 0*o**4 - 8/735*o**7 + 1/105*o**5 + 1/392*o**8. Let x(t) = 0. What is t?
-1/3, 0, 1, 2
Factor 4/5*d**3 - 2/5*d**5 + 0*d**4 - 2/5*d + 0*d**2 + 0.
-2*d*(d - 1)**2*(d + 1)**2/5
Let h(n) be the first derivative of 2*n**3/21 + n**2/7 + 6. Suppose h(d) = 0. Calculate d.
-1, 0
Let l(i) be the second derivative of i**6/120 - 3*i**5/80 - i**4/48 + i**3/8 + 3*i - 9. Factor l(k).
k*(k - 3)*(k - 1)*(k + 1)/4
Suppose 0 = -2*t - 3*n + 76, -64 = -2*t + 2*n + n. Determine a, given that -t*a**2 + a**3 + 35*a**2 + a**4 = 0.
-1, 0
Let l(c) be the second derivative of c**4/66 - 2*c**3/11 + 9*c**2/11 - 2*c. Factor l(t).
2*(t - 3)**2/11
Let m(f) be the first derivative of f**7/35 + 2*f**6/15 + f**5/5 - f**3/3 - 3*f**2 + 2. Let u(i) be the second derivative of m(i). Factor u(c).
2*(c + 1)**3*(3*c - 1)
Factor 0 - 2/21*d**4 - 8/21*d**2 + 0*d + 10/21*d**3.
-2*d**2*(d - 4)*(d - 1)/21
Let w(p) be the first derivative of p**5/3 - 55*p**4/12 + 55*p**3/3 - 25*p**2/6 - 250*p/3 + 57. Suppose w(t) = 0. Calculate t.
-1, 2, 5
Suppose 2*t + t = 54. Suppose -3*j - 3 = -9. What is f in t*f - 2*f**j + 28 + 8 + 5*f**2 - 9 = 0?
-3
Let s = 10483/7 - 1493. Let q = s + -82/21. Factor 2/3*g**2 - 4/3*g + q.
2*(g - 1)**2/3
Let w(j) be the second derivative of 1/3*j**3 + 0*j**2 + 0*j**4 + 0 + 3*j - 1/10*j**5. Suppose w(y) = 0. What is y?
-1, 0, 1
Factor -2*n - 2/7*n**4 - 10/7*n**3 + 0 + 26/7*n**2.
-2*n*(n - 1)**2*(n + 7)/7
Factor 12*n**4 + 53*n**3 + 147*n**2 - 45*n + 61*n**2 + 35*n**3 + 36 + 213*n.
4*(n + 1)*(n + 3)**2*(3*n + 1)
Factor -1/5*g**3 - 2/5 + 0*g**2 + 3/5*g.
-(g - 1)**2*(g + 2)/5
Let a be 162/30 - (-2)/(-5). Factor a*f**3 + 2*f + 2 - 2 - 7*f**3.
-2*f*(f - 1)*(f + 1)
Let b(y) be the first derivative of -4 - 3/4*y**4 + 0*y + y**3 + 3*y**2. Suppose b(w) = 0. Calculate w.
-1, 0, 2
Factor -1/2*f**5 + 1/2*f**2 + 0*f + 0 - 3/2*f**3 + 3/2*f**4.
-f**2*(f - 1)**3/2
Find t such that -18*t**2 + 24*t**3 + 7*t + 10*t - 13*t - 10*t**4 = 0.
0, 2/5, 1
Suppose -5 + 1 = -h. Let j = h + -2. Factor 1/2*s**3 - 1/2*s + 1/2*s**4 - 1/2*s**j + 0.
s*(s - 1)*(s + 1)**2/2
Determine n, given that 4/3*n**4 + 128/3 - 20/3*n**3 - 8*n**2 + 128/3*n = 0.
-2, -1, 4
Suppose -3*x = -5 + 35. Let j be (8 + x)*2/(-10). Suppose 6/5*f**2 + 0 + j*f = 0. Calculate f.
-1/3, 0
Factor 5/4 + f - 1/4*f**2.
-(f - 5)*(f + 1)/4
Let w = -64 - -706/11. Factor 2/11 - w*p**2 + 0*p.
-2*(p - 1)*(p + 1)/11
Let u be (-11)/(-2) + (66/12 - 6). Let b be 21/12 - (-2)/8. Find a, given that -3 - 2*a**2 + 3*a - 3*a**3 + 0 + u*a**b = 0.
-1, 1
Let f(j) = 40*j**3 - 11*j**2 - 20*j + 1. Let i(p) = -p**3 - 1. Let r(m) = -3*f(m) - 15*i(m). Factor r(g).
-3*(g - 1)*(5*g + 2)*(7*g + 2)
Let m(i) be the third derivative of i**7/350 + i**6/200 - i**5/50 + 4*i**2. Factor m(p).
3*p**2*(p - 1)*(p + 2)/5
Suppose 3*r = -0*n + 2*n - 38, -34 = -2*n + r. Suppose 0 = -2*p - 2*p + n. Let -9*i + 0*i**p - 2*i**3 - 3*i**4 + 1 + 12*i + 2*i**2 - i**5 = 0. What is i?
-1, 1
Let z(r) = 3*r**5 + 3*r**4 + r**3 + r**2 - 2*r. Let v(u) = 16*u**5 + 16*u**4 + 6*u**3 + 6*u**2 - 11*u. Let d(n) = 4*v(n) - 22*z(n). Factor d(o).
-2*o**2*(o - 1)*(o + 1)**2
Let z(h) be the second derivative of -h**5/130 - 5*h**4/78 - h**3/13 + 9*h**2/13 + 12*h. Factor z(f).
-2*(f - 1)*(f + 3)**2/13
Let m(b) = 16*b**3 - 59*b**2 + 84*b - 36. Let h(o) = 48*o**3 - 176*o**2 + 252*o - 108. Let a(l) = -5*h(l) + 16*m(l). Factor a(z).
4*(z - 1)*(2*z - 3)**2
Let v(s) be the first derivative of s**7/105 + s**6/25 + 3*s**5/50 + s**4/30 - 2*s + 5. Let d(b) be the first derivative of v(b). Let d(y) = 0. Calculate y.
-1, 0
Let p(a) = a**2 + 15*a + 26. Let g be p(-13). Factor 0*v + 2/9*v**3 + 8/9*v**4 + 0*v**2 + g.
2*v**3*(4*v + 1)/9
Let l(i) = 12*i**4 + 21*i**3 - 52*i**2 + 24*i + 5. Let o(m) = -12*m**4 - 20*m**3 + 52*m**2 - 24*m - 4. Let h(k) = 4*l(k) + 5*o(k). Factor h(u).
-4*u*(u - 1)*(u + 3)*(3*u - 2)
Factor 2/13*t**3 - 2/13*t**2 + 0*t - 2/13*t**5 + 2/13*t**4 + 0.
-2*t**2*(t - 1)**2*(t + 1)/13
Factor 10/3*a - 8/3*a**2 - 2/3.
-2*(a - 1)*(4*a - 1)/3
Let j be (3 - (-63)/(-24))*(-3)/(-9). Let l(k) be the first derivative of j*k**2 + 1/12*k**3 + 0*k - 1/16*k**4 - 4 - 1/20*k**5. Find q, given that l(q) = 0.
-1, 0, 1
Let n be 5*((-6)/5 - -2). Suppose -f + n*f = 6. Determine r so that r**f + 1/2*r**3 + 1/2*r + 0 = 0.
-1, 0
Let p(c) be the first derivative of -10 - 2*c**2 + 0*c - 9*c**4 + 16/5*c**5 + 8*c**3. Suppose p(v) = 0. Calculate v.
0, 1/4, 1
Let -5 + 33*a**3 - 24*a**3 - 65*a**2 + 21*a**3 + 60*a - 5*a**4 - 15 = 0. Calculate a.
1, 2
Let n(t) = t + 3. Let s be n(-4). Let v(o) = -o**2. Let p(r) = -r**2. Let i(w) = s*v(w) + 3*p(w). Determine h so that i(h) = 0.
0
Let n(s) = -s**3 - 3*s**2 - s + 1. Let t be n(-3). Suppose -1 + 2 + 5*u - u**t - u**5 + 1 - 4*u**3 + 2*u**2 - 3*u**4 = 0. What is u?
-2, -1, 1
Let r(w) be the second derivative of -w - 1/16*w**4 - 27/8*w**2 + 3/4*w**3 + 0. Factor r(o).
-3*(o - 3)**2/4
Let y = 