
-1, 0, 1, 5
Let w(h) = -h - 8. Let v be w(-10). Suppose -9*x**3 + 5*x**4 + v*x**2 + 7*x**2 - 3*x - 2*x**4 = 0. What is x?
0, 1
Let y(q) be the third derivative of 0 - 1/150*q**5 - 4*q**2 - 1/20*q**4 + 0*q - 2/15*q**3. Suppose y(x) = 0. Calculate x.
-2, -1
Let g = 38 - 32. Let s = 32/5 - g. Suppose 0 - 2/5*w**5 + 0*w - 2/5*w**2 + 2/5*w**3 + s*w**4 = 0. Calculate w.
-1, 0, 1
Let m(n) be the third derivative of 1/90*n**5 - n**2 - 1/9*n**3 + 0*n + 0*n**4 + 0. Factor m(b).
2*(b - 1)*(b + 1)/3
Let d(b) be the first derivative of -1/900*b**6 + b**3 + 0*b - 1/30*b**4 + 1/100*b**5 + 1 + 0*b**2. Let y(a) be the third derivative of d(a). Factor y(v).
-2*(v - 2)*(v - 1)/5
Determine b, given that 10/7*b + 2/7*b**3 - 8/7*b**2 - 4/7 = 0.
1, 2
Let k(v) = v**2 - 15*v - 18. Let o(t) = 2*t**2 - 16*t - 18. Let n(f) = 4*k(f) - 3*o(f). Solve n(d) = 0 for d.
-3
Solve -2*p**2 - 8 + 8 = 0.
0
Let q(y) = -2*y**4 - 12*y**2 + 4*y + 6. Let x be 16/3 - 2/6. Let h(d) = 2*d**4 + d**3 + 11*d**2 - 3*d - 5. Let r(a) = x*q(a) + 6*h(a). Factor r(w).
2*w*(w + 1)**3
Suppose 0*f + 3/7*f**5 + 0*f**4 - 3/7*f**3 + 0 + 0*f**2 = 0. Calculate f.
-1, 0, 1
Let z(h) be the first derivative of -2*h**3/9 + 2*h**2 - 6*h - 12. Factor z(t).
-2*(t - 3)**2/3
Let l = -8 - 0. Let c be 8/(-30)*20/l. Factor -c - 1/3*k - 1/3*k**4 + 1/3*k**3 + k**2.
-(k - 2)*(k - 1)*(k + 1)**2/3
Factor -4/9*l**4 + 0*l**3 - 2/9*l + 4/9*l**2 + 2/9*l**5 + 0.
2*l*(l - 1)**3*(l + 1)/9
Let b = -293/4 + 243/4. Let p = -12 - b. Let 1/2*q**5 + 0 - q**2 + 0*q**3 - p*q + q**4 = 0. What is q?
-1, 0, 1
Let u(f) be the second derivative of 3*f - 24*f**3 + 48/7*f**2 + 261/35*f**6 + 0 - 81/98*f**7 + 276/7*f**4 - 894/35*f**5. Let u(x) = 0. Calculate x.
2/9, 2
Factor -12*j**2 - j**2 + 5*j**4 - 7*j**2.
5*j**2*(j - 2)*(j + 2)
Let d(x) = -x**2 - 7*x - 8. Suppose -11 = -a - 4*i, 4*a + 4 = i - 5*i. Let s be d(a). Find t such that 1/2*t**s + 0 - 1/2*t = 0.
0, 1
Let y be 15*2/6*1. Suppose y*n - 9 = 1. Suppose r - 1/4*r**n - 1 = 0. What is r?
2
Suppose -4 = -0*l - l, 4*v = 5*l - 20. Suppose 0 = -3*s + 12 - v. Determine u so that -1/3*u**s + 0*u**2 + 0 - 1/3*u**3 + 0*u = 0.
-1, 0
Suppose 5*v = -3*x + 21 + 6, -10 = -x - 2*v. Factor -4*z**2 - 12*z**x + 6*z**4 + 2*z**2 + 5*z**3 - 11*z**3 - 2*z**5.
-2*z**2*(z + 1)**3
Let a(i) be the second derivative of -5*i**4/18 - 5*i**3/18 - 16*i. Factor a(x).
-5*x*(2*x + 1)/3
Let i(m) = -7*m**2 + m. Let o(g) = 6*g**2 - g. Let l(k) = 5*i(k) + 6*o(k). Let p(u) = -5*u**2 + 8*u - 4. Let h(c) = -4*l(c) - p(c). Solve h(d) = 0 for d.
2
Let -95*j**2 - 5*j**4 + 35*j**2 + 20*j**3 + 40*j**2 = 0. Calculate j.
0, 2
Let g(x) be the third derivative of x**7/280 - 3*x**6/80 + 13*x**5/80 - 3*x**4/8 + x**3/2 + 32*x**2. What is k in g(k) = 0?
1, 2
Let a = -186/13 + 662/39. Factor -2*m + 0 + a*m**2 - 2/3*m**3.
-2*m*(m - 3)*(m - 1)/3
Let k(q) be the second derivative of 0 + 1/3*q**4 - 1/2*q**3 - 1/2*q**2 - 3*q. Determine f, given that k(f) = 0.
-1/4, 1
Suppose 0 = 3*d - 2*b - 12, b + 1 = 2*d - 3*d. Factor -v + v**d + 2*v + 0*v**2.
v*(v + 1)
Let v be 1/((-22)/14) - -1. Let w(s) = -s**3 + 12*s**2 - 18*s - 18. Let t be w(10). Determine r, given that -2/11*r**4 - 4/11*r**3 + 0*r**t + v*r + 2/11 = 0.
-1, 1
Let k(y) be the first derivative of -2*y**3/15 - y**2 - 8*y/5 + 20. Factor k(q).
-2*(q + 1)*(q + 4)/5
Let 0 - 2*f**4 + 4/3*f - 8/3*f**3 + 10/3*f**2 = 0. Calculate f.
-2, -1/3, 0, 1
Let a = -16 + 20. Let l be -4 - -2*(a + 0). Factor 1/3*w**l - 4/3*w - 5/3*w**3 + 8/3*w**2 + 0.
w*(w - 2)**2*(w - 1)/3
Let o(n) be the second derivative of -n**9/30240 - n**8/6720 - n**7/5040 - n**4/12 - 3*n. Let p(v) be the third derivative of o(v). Factor p(s).
-s**2*(s + 1)**2/2
Let p(x) be the second derivative of 0*x**2 - 1/2*x**3 + 0*x**4 - 1/180*x**5 + 0 - 2*x + 1/1080*x**6. Let h(j) be the second derivative of p(j). Solve h(q) = 0.
0, 2
Let p(i) = i**2 - 2*i + 3. Let h be p(2). Suppose -4*z**3 + 12*z + 12*z**h + 3 + 4*z - 30*z**2 + 3 = 0. What is z?
-1/4, 1, 3
Let z(u) = -u**3 + 6*u**2 + 30*u - 19. Let x be z(9). Solve 194/9*d**2 + 8/9 - 16*d**3 - x*d + 32/9*d**4 = 0 for d.
1/4, 2
Solve 5/2*r**2 - 2*r**3 - 3/2*r**4 + 0 + r = 0 for r.
-2, -1/3, 0, 1
Let k(h) be the first derivative of -h**4/12 + 2*h**3/3 - 3*h**2/2 - 9. What is c in k(c) = 0?
0, 3
Factor 0*a + 9/2*a**3 + 0 + 0*a**2 - 3/2*a**4.
-3*a**3*(a - 3)/2
Let o(f) be the third derivative of 0 - 1/80*f**5 + 0*f - 1/32*f**4 - 1/24*f**3 - 7*f**2 - 1/480*f**6. Factor o(x).
-(x + 1)**3/4
Let -2/3 + 2/3*a**2 - 2/9*a**3 + 2/9*a = 0. Calculate a.
-1, 1, 3
Let z(j) be the second derivative of 0*j**3 + 1/6*j**4 - j**2 + 0 - j. Factor z(v).
2*(v - 1)*(v + 1)
Let h(f) be the second derivative of -f**5/100 + 9*f. Solve h(d) = 0.
0
Let p(t) be the second derivative of 1/12*t**4 + 1/2*t**2 + 1/3*t**3 + 0 + 1/120*t**5 + 2*t. Let s(g) be the first derivative of p(g). Solve s(j) = 0 for j.
-2
Let i(o) = -31*o**3 + 20*o**2 + 69*o - 91. Let w(h) = -6*h**3 + 4*h**2 + 14*h - 18. Let x(a) = 2*i(a) - 11*w(a). Factor x(n).
4*(n - 2)*(n - 1)*(n + 2)
Let s(v) be the second derivative of -v**6/285 - 3*v**5/190 - v**4/114 + v**3/19 + 2*v**2/19 - 33*v. Suppose s(p) = 0. Calculate p.
-2, -1, 1
Let u(o) be the second derivative of -o**7/42 + 2*o**6/45 + o**5/30 - o**4/9 + o**3/18 - 4*o. Let u(w) = 0. What is w?
-1, 0, 1/3, 1
Let o = 56/45 - 2/45. Factor 9/5 + 3*m + o*m**2.
3*(m + 1)*(2*m + 3)/5
Let k(c) = c. Let a be k(3). Suppose m**3 - 4*m**4 + 0*m**4 + a*m**4 = 0. Calculate m.
0, 1
Suppose -4*m = -12 + 4, 2*w + 5*m = 10. Suppose -1/2*i**2 + w + i = 0. Calculate i.
0, 2
Let f be 306/18*(-4)/(-34). Let -5/3*o**4 + 0*o + 0 + 2/3*o**f + o**3 = 0. What is o?
-2/5, 0, 1
Factor -1 + 53*s**2 - 83*s**2 + 34*s**3 + 18*s - 7 - 90*s.
2*(s - 2)*(s + 1)*(17*s + 2)
Factor 45*a - 20*a**2 - 25*a - 25*a**3 + 16*a**4 - a**4.
5*a*(a - 2)*(a + 1)*(3*a - 2)
Let y(t) be the first derivative of 6 + 4/3*t**3 - 4/5*t**2 - 12/5*t. Factor y(g).
4*(g - 1)*(5*g + 3)/5
Let p(i) be the first derivative of -3*i**4/22 - 4*i**3/33 + 3*i**2/11 + 4*i/11 - 25. Determine m so that p(m) = 0.
-1, -2/3, 1
Let t = 1/66 + 127/330. Let f = -510 + 512. Factor -t*a**3 - 6/5*a**f + 0*a + 8/5.
-2*(a - 1)*(a + 2)**2/5
Factor -33*k + 0 + 39*k - 3 - 3*k**2.
-3*(k - 1)**2
Let u(o) be the third derivative of -o**5/120 - o**4/48 + 13*o**2. Factor u(f).
-f*(f + 1)/2
Suppose -16*x = -14*x - 4. Let w(s) be the second derivative of 0*s**6 - 1/21*s**7 + 2*s + 0*s**3 + 0*s**4 + 0*s**x + 0*s**5 + 0. Let w(v) = 0. What is v?
0
Determine i, given that 1/4*i**3 - 1/2*i**2 - 3/4*i + 0 = 0.
-1, 0, 3
Let s be (-27)/18 - (-7)/2. Factor -2*k**4 + k**2 - 2*k**s + 6*k**2 - 3*k**2 + 2*k - 2*k**3.
-2*k*(k - 1)*(k + 1)**2
Let q be (-3)/(-4)*4 - 0. Let y(x) be the second derivative of 1/10*x**5 + x**2 + 1/2*x**4 + 2*x + x**q + 0. Factor y(f).
2*(f + 1)**3
Suppose 2 - 2/3*p**3 - 14/3*p + 10/3*p**2 = 0. What is p?
1, 3
Let o(l) be the second derivative of -l**5/80 - l**4/24 + l**3/24 + l**2/4 + 16*l. Factor o(x).
-(x - 1)*(x + 1)*(x + 2)/4
Factor 1/2*g**2 + 0*g - 1/2.
(g - 1)*(g + 1)/2
Let a(y) = -4*y + 1. Let h be a(-2). Solve -t**5 - 2*t**3 - 9*t + h*t + 3*t**5 = 0 for t.
-1, 0, 1
Determine z so that 4*z - 4*z**4 + 0*z - 4*z**3 + 0*z**4 + 4*z**2 = 0.
-1, 0, 1
Suppose 6*d - o = -3*o + 18, 0 = 5*d - 2*o - 4. What is u in -1/3*u**3 + 0*u**d - 1/6*u**4 + 0 + 0*u = 0?
-2, 0
Let c(p) be the second derivative of -p**7/840 - p**6/120 - p**5/40 - p**4/24 + p**3/3 - 3*p. Let v(n) be the second derivative of c(n). Factor v(q).
-(q + 1)**3
Let p = -1/108 + 661/1404. Factor p*r - 2/13*r**3 - 4/13 + 0*r**2.
-2*(r - 1)**2*(r + 2)/13
Let p = 132 + -3959/30. Let n(y) be the third derivative of -2*y**2 - 1/12*y**4 + 1/12*y**5 + 0*y**3 + 0 + 1/210*y**7 - p*y**6 + 0*y. Factor n(f).
f*(f - 2)*(f - 1)**2
Let c be 16/6*(-72)/(-42) + -4. What is u in 2*u + c + 10/7*u**2 = 0?
-1, -2/5
Let x = -10 + 13. Factor -3*m**x - 3*m**2 + 3*m + 24 + 0*m**3 - 21.
-3*(m - 1)*(m + 1)**2
Let t(b) be the third derivative of -b**8/10080 - b**7/630 - b**6/120 + b**5/12 - b**2. Let p(o) be the third derivative of t(o). Factor p(k).
-2*(k + 1)*(k + 3)
Let h(l) be the third derivative of 0*l**5 + 0*l**4 + 0*l**3 + 1/180*l**6 + 4*l**2 + 0 + 0*l. Let h(z) = 0. Calculate z.
0
Suppose 0 = -l - 5*j - 21, -6*l = -3*l + 2*j - 2. Suppose 18 = -0*f +