d(x) = 3*x**2 - 8*x - 5. Let h(g) = g**2 - g + 1. Let q(a) = -3*d(a) + 6*h(a). Determine s so that q(s) = 0.
-1, 7
Factor 13*j**2 + 3/2*j**4 + 3/2 - 8*j - 8*j**3.
(j - 3)*(j - 1)**2*(3*j - 1)/2
Let w be (1/(-3))/((-1)/3). Suppose -b + w = -1. Factor 2/5*p**b - 4/5*p + 2/5.
2*(p - 1)**2/5
Let j be 10/12*105/50. Let n = -5/4 + j. Factor -1/2*h**2 + 0*h - n*h**3 + 0 + 1/2*h**4 + 1/2*h**5.
h**2*(h - 1)*(h + 1)**2/2
Let r(a) be the first derivative of 16/15*a**3 + 4 - 8*a**4 - 4/5*a + 11/5*a**2. Factor r(x).
-2*(4*x - 1)**2*(5*x + 2)/5
Let p be (-3 - -2 - -3) + -7. Let g(k) = -k**2 - 5*k + 2. Let l be g(p). Factor -d**2 - 3*d**2 + 6*d**l.
2*d**2
Factor 8/7 + 0*o - 6/7*o**2 - 2/7*o**3.
-2*(o - 1)*(o + 2)**2/7
Let c(l) be the second derivative of -l**6/180 + l**5/45 - l**4/36 - l**3/3 + l. Let g(o) be the second derivative of c(o). Factor g(a).
-2*(a - 1)*(3*a - 1)/3
Let w(z) = -2*z**3 + 37*z**2 - 47*z + 22. Let k(f) = -3*f**3 + 75*f**2 - 93*f + 45. Let q(x) = 4*k(x) - 9*w(x). Factor q(h).
3*(h - 3)*(h - 2)*(2*h - 1)
Factor -24*w - 2*w**4 + 6*w**3 - 6*w**2 + 0*w**4 + 26*w.
-2*w*(w - 1)**3
Factor 2*w**3 + 5/2*w**2 + 0 + 1/2*w**4 + w.
w*(w + 1)**2*(w + 2)/2
Suppose -13*j = -7*j. Let p(x) be the third derivative of j + 0*x - x**2 - 1/12*x**3 - 1/32*x**4 - 1/240*x**5. Determine y, given that p(y) = 0.
-2, -1
Find d such that -8/3*d**3 + 4/3*d**5 + 4/3 + 4/3*d + 4/3*d**4 - 8/3*d**2 = 0.
-1, 1
Factor 1/7*m + 4/7 - 2*m**2.
-(2*m + 1)*(7*m - 4)/7
Let t = 2 + 0. Suppose -t*m + 5 + 1 = 0. What is q in -6*q**2 - 2*q**4 - 2*q + q**3 - 3*q**3 + 0*q**2 - 4*q**m = 0?
-1, 0
Find v, given that -1/2*v**4 + 1/2*v**2 - v + 0 + v**3 = 0.
-1, 0, 1, 2
Suppose 3*o = 5*v - 5, -5*v - 6 = -5*o - 1. Let a(s) be the second derivative of 2/9*s**3 + 1/18*s**v + 3*s + 0*s**2 + 0. Factor a(r).
2*r*(r + 2)/3
Let i = -3 + 3. Suppose 2*t - 4 = -i*t. Factor -2*n**t + 2*n**4 + n**5 - 5*n + 2*n**4 + 5*n**3 - n**3 - 2.
(n - 1)*(n + 1)**3*(n + 2)
Let -17*a**5 + 6*a**3 + 14*a**5 - 3*a**3 = 0. What is a?
-1, 0, 1
Let s(w) be the third derivative of 0*w**3 - 1/40*w**5 + 3*w**2 + 1/16*w**4 + 1/140*w**7 - 1/80*w**6 + 0 + 0*w. Factor s(n).
3*n*(n - 1)**2*(n + 1)/2
Factor -5*n**3 + 192*n**2 + 2*n**4 + 512 + 0*n + 512*n + 26*n**3 + 11*n**3.
2*(n + 4)**4
Let n(l) be the first derivative of -l**6/24 + 3*l**5/10 - 3*l**4/4 + 2*l**3/3 - 7. Suppose n(j) = 0. What is j?
0, 2
Suppose 0 = -k - 12 + 15. Let -7*m + 2*m + m**k + 5*m = 0. What is m?
0
Factor 0*o + 0 + 5/2*o**3 - o**4 + 3/2*o**2.
-o**2*(o - 3)*(2*o + 1)/2
Let v = 69/260 + -1/65. Factor 1/4*o**5 + 0*o**2 + 0*o + 0 - 1/2*o**4 + v*o**3.
o**3*(o - 1)**2/4
Let n(a) be the second derivative of 2*a**7/105 + a**6/20 + a**5/240 - a**4/16 + a**3/24 + 3*a**2 - 3*a. Let c(j) be the first derivative of n(j). Factor c(r).
(r + 1)**2*(4*r - 1)**2/4
Let y(q) = -11*q**3 - q**2. Let r be y(-1). Suppose 20 = 45*w - 41*w. Factor -3*o**w + 4*o**5 + 1 + 6*o**4 - 5*o - 10*o**3 + r*o**2 - 2*o**5 - o**4.
-(o - 1)**5
Let t be (-3)/3 - -2 - -1. Factor -8*u + 0*u**t - 2 + 4*u**2 - 2*u**2 + 10.
2*(u - 2)**2
Let y be 23/15 - -7*6/(-210). Factor 1/3*k**2 + 4/3*k + y.
(k + 2)**2/3
Suppose -g - 3*b - 13 = 0, 0 = -9*g + 7*g - 5*b - 21. Suppose -3*i = -2*i, -4*j = -i - 12. Let 1/2*z**j - z**g + 1/2*z + 0 = 0. What is z?
0, 1
Let d = -43 + 46. Let r(h) be the first derivative of -1/2*h**2 + d + 1/6*h**3 + 1/2*h. Factor r(b).
(b - 1)**2/2
Let c = -1384/3 + 466. Let b be 5 + 1/((-2)/2). Factor -4/3*f**2 + 2*f**3 + 0 + 8*f**b + c*f**5 + 0*f.
2*f**2*(f + 1)**2*(7*f - 2)/3
Let h(z) = -z**3 + 6*z**2 - 5. Let x be h(6). Let b be (2 - x/(-2))*-8. Solve 2 - 2*r**4 + 4*r + 3*r**4 - 3*r**4 - b*r**3 = 0.
-1, 1
Let h be 45/27 - (-2)/(-3). Let v(j) be the first derivative of 1/4*j**4 + h + 1/3*j**3 - 1/2*j**2 - j. Solve v(r) = 0.
-1, 1
Let s(m) = -3*m - 15. Let j be s(-5). Let l(k) be the first derivative of -1/2*k**4 + 1/3*k**6 + j*k - 2/5*k**5 - 2 + 2/3*k**3 + 0*k**2. Factor l(z).
2*z**2*(z - 1)**2*(z + 1)
Factor 15*r**2 + 4*r**4 - 7*r - r - 16*r**3 + 5*r**2.
4*r*(r - 2)*(r - 1)**2
Factor 24*t**2 - 18 - 11*t - 15*t**2 - 22*t - 18*t**2.
-3*(t + 3)*(3*t + 2)
Let p(g) be the first derivative of -2*g**5/45 - g**4/18 + 4*g**3/27 - 20. Let p(y) = 0. What is y?
-2, 0, 1
Let k(w) be the second derivative of -1/22*w**4 + 1/55*w**5 + 0*w**3 + 1/165*w**6 + 4*w + 0 + 0*w**2. Factor k(p).
2*p**2*(p - 1)*(p + 3)/11
Factor 0*v**2 + 0*v + 2/5*v**3 + 1/5*v**4 - 1/5*v**5 + 0.
-v**3*(v - 2)*(v + 1)/5
Solve -3*r**3 - 6*r**3 + 9*r - 6 - 5*r**2 + 4 + 7*r**4 = 0.
-1, 2/7, 1
Let h(u) = 10*u - 50. Let n be h(5). Let 5/6*x**3 + 1/6*x + 1/3*x**4 + 2/3*x**2 + n = 0. What is x?
-1, -1/2, 0
Let h(y) be the third derivative of -1/84*y**4 + 0*y**3 + 4*y**2 + 1/420*y**6 + 0*y + 0 - 1/210*y**5 + 1/735*y**7. Let h(x) = 0. Calculate x.
-1, 0, 1
Let w(l) be the third derivative of -l**9/52920 + l**8/7840 - l**7/2940 + l**6/2520 + l**4/24 - 3*l**2. Let h(d) be the second derivative of w(d). Factor h(c).
-2*c*(c - 1)**3/7
Suppose 5*u = 2*x + 20, 0*x - 2*x = 3*u - 12. Let i be (2/u)/(2/8). Factor 0 - 2/9*j**3 + 4/9*j**i - 2/9*j.
-2*j*(j - 1)**2/9
Let y(i) be the second derivative of i**4/6 - i**2 - 10*i. Factor y(t).
2*(t - 1)*(t + 1)
Let u(d) = -3*d**3 - 5 + 2 + 4 + d + 7*d**2 + 2*d**3. Let q be u(7). Suppose -q*k + 4*k - 5*k**2 - 4*k**3 + 3*k + 0*k**3 = 0. Calculate k.
-1, -1/4, 0
Let x(d) be the second derivative of 1/4*d**2 + 1/12*d**3 + 2*d - 1/12*d**4 + 0. Factor x(v).
-(v - 1)*(2*v + 1)/2
Let v(b) = 4*b - 48. Let n be v(12). Let q(j) be the third derivative of -1/70*j**7 - 1/20*j**5 + n + 0*j + 3/40*j**6 + 3*j**2 - 3/8*j**4 + j**3. Factor q(s).
-3*(s - 2)*(s - 1)**2*(s + 1)
Let f(d) = -7*d**3 + 11*d**2 + 19*d - 29. Let s(x) = 13*x**3 - 21*x**2 - 37*x + 59. Let b(w) = -5*f(w) - 3*s(w). What is y in b(y) = 0?
-2, 2
Solve 2/5*h - 1/5*h**2 + 0 - 1/5*h**3 = 0.
-2, 0, 1
Let b(o) = -o**3 - 12*o**2 - 12*o - 11. Let j be b(-11). Let k(l) be the second derivative of 4/3*l**3 + 2*l - 4*l**2 + j - 1/6*l**4. Let k(i) = 0. What is i?
2
Let t = 9 + -6. Let w = 387/4 - 96. Find p, given that 0 - 1/4*p**t - 1/2*p + w*p**2 = 0.
0, 1, 2
Let l be 4 - 6 - (-1 - 4). Suppose 2*d**l - 4*d**3 - 2*d**5 - d**5 + 5*d**4 = 0. What is d?
0, 2/3, 1
Let d(f) be the third derivative of -f**5/150 - f**4/30 - f**3/15 + 6*f**2. Let d(i) = 0. Calculate i.
-1
Determine w, given that 4*w + 62 - 62 - 2*w**2 + 2*w = 0.
0, 3
Let q(u) = u**3 + 9*u**2 + 8*u. Suppose -1 = 2*c - 5*z, -3*c - 4*z - 16 = 20. Let s be q(c). Determine y, given that -4/5*y - 81/5*y**3 - 36/5*y**2 + s = 0.
-2/9, 0
Let y(c) be the first derivative of c**5/40 + 3*c**4/32 + c**3/12 + 27. Factor y(m).
m**2*(m + 1)*(m + 2)/8
Let g(a) be the first derivative of -a**6/24 - 7*a**5/20 - a**4/2 + 4*a**3/3 + 51. Determine c, given that g(c) = 0.
-4, 0, 1
Let x(f) be the first derivative of 1/10*f**5 + 6 + 0*f**3 - 1/16*f**4 + 1/8*f**6 + 0*f**2 + 0*f. Factor x(m).
m**3*(m + 1)*(3*m - 1)/4
Suppose -4 = 4*h, 5*f = f - 2*h - 26. Let v be (0 - f)/(3 - 1). Factor i**2 - 15*i**2 - 3*i - 8*i**v + 7*i.
-2*i*(i + 2)*(4*i - 1)
Let c(d) = 11*d**2 - 5*d - 6. Let r(y) = -y**2 + y. Let p(f) = c(f) - 4*r(f). Factor p(q).
3*(q - 1)*(5*q + 2)
Let d(p) be the third derivative of p**8/1176 - p**7/735 + p**2 - 24. Factor d(l).
2*l**4*(l - 1)/7
Let h be ((-2)/(-3) + -1)*-9. What is m in 16*m**3 - 5*m**2 + 5 - 1 + m - 14*m**h - 2 = 0?
-1/2, 1, 2
Suppose 4*l + 8 = 2*p, 0 = -l - 0*p - 4*p + 16. Suppose 14 = 2*z + 2*t, l = -t - 3 + 6. Factor 13*g**3 + 5*g**4 - g**3 + 4*g**2 + 0*g**2 + z*g**4.
g**2*(3*g + 2)**2
Let t(z) = 9*z**4 - 4*z**3. Let r(p) = 2*p**3 + 0*p**3 - 8*p**3 + 13*p**4. Let q = -24 - -17. Let y(o) = q*t(o) + 5*r(o). Solve y(f) = 0.
0, 1
Let a be ((-11)/66)/(2/(-3)). Let 1/2*q + 1/4*q**2 + a = 0. What is q?
-1
Let m(d) = 5*d - 4. Let n be m(2). What is k in n*k**2 - 3*k - 3*k**4 + 3*k**3 + k**2 - 3*k**2 - k**2 = 0?
-1, 0, 1
Let a(c) be the first derivative of c**4/10 - 2*c**3/15 - 2*c**2/5 + 28. Factor a(l).
2*l*(l - 2)*(l + 1)/5
Suppose 5*k - 2*k - 5*z = 28, 0 = 5*z + 10. Let x be (-21)/(-15) + k/10. Let 5/3*r**4 + 10/3*r**3 + 1/3*r**5 + 1/3 + 5/3*r + 10/3*r**x = 0. What is r?
-1
Let d(o) be the second derivative of o**7/21 - 7*o**6/15 + 19*o**5/10 - 25*o**4/6 + 16*o**3/3 - 4*o**2 - 26*o. Factor d(b).
2*(b - 2