
Let d = -8 - -5. Let w = d + 6. Factor -2*q + w*q**2 - 1 - 7*q**2 + 3*q**2.
-(q + 1)**2
Let b(i) be the first derivative of 4/9*i**3 - 4/3*i + 0*i**2 - 2. Solve b(s) = 0 for s.
-1, 1
Suppose -2*r + 8 = -0. Let x(i) be the third derivative of 0*i**3 + 0*i**5 + 1/735*i**7 + 3*i**2 + 0*i**r + 1/420*i**6 + 0*i + 0. What is g in x(g) = 0?
-1, 0
Let b(l) be the second derivative of l**9/4032 + l**8/560 + l**7/224 + l**6/240 + l**3/2 + l. Let m(d) be the second derivative of b(d). Solve m(i) = 0.
-2, -1, 0
Let k(h) be the first derivative of -h**5/35 + 5*h**4/28 - 8*h**3/21 + 2*h**2/7 - 9. Factor k(t).
-t*(t - 2)**2*(t - 1)/7
Let t(i) be the second derivative of 8*i**7/105 - 2*i**6/15 - 11*i**5/25 + 23*i**4/15 - 26*i**3/15 + 4*i**2/5 + 24*i. Let t(a) = 0. What is a?
-2, 1/4, 1
Let r(i) = 10*i**4 + 19*i**3 + 15*i**2 + 13*i - 5. Let w(t) = -9*t**4 - 18*t**3 - 15*t**2 - 12*t + 4. Let q(m) = 5*r(m) + 6*w(m). Factor q(u).
-(u + 1)**3*(4*u + 1)
Find j such that -j**3 + 20*j - 8 - 25*j**4 - 14*j**2 - 19*j**4 + 48*j**4 - j**5 = 0.
-2, 1, 2
Let b(d) be the third derivative of -d**9/20160 + d**8/6720 + d**7/1680 - d**6/240 + d**5/12 - d**2. Let n(a) be the third derivative of b(a). Factor n(o).
-3*(o - 1)**2*(o + 1)
Suppose 0*n - 16 = -4*n. Let s be (-4)/(-2) - n/(-4). Factor 5*q**s - 2*q**2 - q**4 - q**3 - q**4.
-2*q**2*(q - 1)**2
Let r(m) be the first derivative of m**5/90 + m**4/18 + m**3/9 + m**2/9 + 8*m + 2. Let s(j) be the first derivative of r(j). Factor s(o).
2*(o + 1)**3/9
Let q be ((-2)/5)/(22/(-10)). Let r be 5/(-5) + (1 - 0). Solve 0 + r*b**3 + 0*b - q*b**4 + 2/11*b**2 = 0.
-1, 0, 1
Let a(f) be the third derivative of 3*f**2 + 0 - 4*f**3 - 11/10*f**5 + 61/40*f**6 - 25/112*f**8 + 0*f + 3/7*f**7 - 9/2*f**4. Determine w, given that a(w) = 0.
-1, -2/5, 1, 2
Let j(i) be the third derivative of 0 + 3*i**2 - 1/3*i**3 - 1/120*i**5 + 0*i + 1/12*i**4. Suppose j(n) = 0. What is n?
2
Let w(u) be the first derivative of -2*u**5/15 + u**4 - 26*u**3/9 + 4*u**2 - 8*u/3 + 11. Factor w(g).
-2*(g - 2)**2*(g - 1)**2/3
What is x in -52 - 12*x + 29 + 4*x**2 - 8*x**4 + 27 + 12*x**3 = 0?
-1, 1/2, 1
Let t(k) = 0*k**2 + k**3 - 2 + 2*k - 6*k**2 + 4*k. Let h be t(5). What is l in -l + l + l**h = 0?
0
Let -9*k**2 + 6*k - 57*k**3 + 54*k**3 - 3*k**5 + 0*k**5 + 9*k**4 = 0. Calculate k.
-1, 0, 1, 2
Let q(r) = -2*r**3 + 62*r**2 - r + 36. Let h be q(31). Find b, given that 1/3*b**2 + 1/3*b**3 - 1/6 - 1/6*b**h - 1/6*b - 1/6*b**4 = 0.
-1, 1
Determine y so that 9 - 6*y**2 - 9 + 4*y**2 + 2*y = 0.
0, 1
Factor -n**2 + 3*n**2 - 19 + 2*n + 15.
2*(n - 1)*(n + 2)
Let z = -10/11 + 72/55. Let 24/5*b + 12/5*b**2 + 16/5 + z*b**3 = 0. Calculate b.
-2
Let p(y) be the second derivative of 4*y**7/105 + y**6/20 - y**5/6 - y**4/4 + y**3/3 - 3*y**2/2 + 5*y. Let g(i) be the first derivative of p(i). Factor g(m).
2*(m - 1)*(m + 1)**2*(4*m - 1)
Let s(u) be the first derivative of -1/4*u**4 + 1/6*u**6 + 0*u + 0*u**2 + 0*u**3 + 0*u**5 - 2. What is l in s(l) = 0?
-1, 0, 1
Let k(f) = 28*f**4 - 88*f**3 + 156*f**2 - 160*f + 64. Let w(y) = -9*y**4 + 29*y**3 - 52*y**2 + 53*y - 21. Let d(s) = -5*k(s) - 16*w(s). Factor d(v).
4*(v - 2)**2*(v - 1)**2
Let p be 2/3*(3 - 0). Factor -3*w**2 + 6*w**2 + 8*w + 0*w**p - 2*w.
3*w*(w + 2)
Factor -3/2*q**4 + 0 + 0*q + 0*q**2 - q**3 - 1/2*q**5.
-q**3*(q + 1)*(q + 2)/2
Let p(b) be the second derivative of b**6/6 - 9*b**5/4 + 10*b**4 - 40*b**3/3 - 28*b. Factor p(j).
5*j*(j - 4)**2*(j - 1)
Suppose 0 = -7*b + 4*b + 6. Factor -15 + 3*l**b + 9*l + 15.
3*l*(l + 3)
Let x(a) be the first derivative of 30*a**6 + 312*a**5/5 + 44*a**4 + 32*a**3/3 - 1. What is u in x(u) = 0?
-2/3, -2/5, 0
Let j be (3 - (0 + 1)) + 0. Factor 9*d - d**j + 2 - 6*d - 4*d.
-(d - 1)*(d + 2)
Let i(u) = -u - 7. Let y be i(-7). Let j be -1 - -9 - (2 + 0). Determine a, given that -6 - 6*a**2 + y*a**3 + a**3 + j*a + 4 + a**3 = 0.
1
Let a be ((-2)/6)/((-5)/30). Let t(z) = 4*z**a + z**2 - 3*z**2 + z**3 + 2 - z. Let p(j) = -2*j**3 - 2*j**2 + j - 3. Let r(m) = -2*p(m) - 3*t(m). Factor r(y).
y*(y - 1)**2
Let i = -119/3 - -41. Determine o so that 2/9 - 8/9*o**3 + 2/9*o**4 + i*o**2 - 8/9*o = 0.
1
Let g(h) be the second derivative of -h**9/3024 + h**7/420 - h**5/120 + h**3/6 + h. Let b(l) be the second derivative of g(l). Factor b(k).
-k*(k - 1)**2*(k + 1)**2
Let a(m) be the second derivative of -m**5/10 - m**4/2 - 2*m**3/3 - 12*m. Factor a(d).
-2*d*(d + 1)*(d + 2)
Let l be -10*(2 - 20/8). Let g(w) be the third derivative of 0*w + 0 + 1/18*w**3 + 1/360*w**6 + 2*w**2 - 1/180*w**l - 1/72*w**4. Factor g(x).
(x - 1)**2*(x + 1)/3
Let s(r) be the second derivative of -1/30*r**5 + 0 + r**2 - 1/3*r**3 + 3*r - 1/6*r**4. Let w(i) be the first derivative of s(i). Solve w(u) = 0 for u.
-1
Let j(z) = 10*z**3 - 6*z**2 + 16. Let b(q) = 2*q**3 - q**2 + 3. Let t(m) = -16*b(m) + 3*j(m). Solve t(w) = 0 for w.
-1, 0
Let u(j) be the second derivative of j**5/20 + 13*j**4/60 - 13*j**3/15 + 4*j**2/5 + 3*j. Determine x so that u(x) = 0.
-4, 2/5, 1
Let u be (-47)/(-4)*(13 - 11). Let d = u - 23. Let -d*r**2 + 3*r**3 + 0*r - 5/2*r**4 + 0 = 0. What is r?
0, 1/5, 1
Let v = 7 - 9. Let f be (-21)/v + (-1)/2. Factor -10*j + f*j**4 + 0*j**5 + 14*j**3 - 4*j**2 - 6*j**3 - 2*j**4 - 4 + 2*j**5.
2*(j - 1)*(j + 1)**3*(j + 2)
Let m(y) be the third derivative of y**7/1120 - y**6/360 - y**5/96 + y**4/48 + y**3/3 + y**2. Let c(h) be the first derivative of m(h). Factor c(p).
(p - 2)*(p + 1)*(3*p - 1)/4
Suppose 0 = 5*c + 2*j - 13 + 5, -c + j = -3. Let a(s) be the third derivative of 1/240*s**5 + 0*s + 1/48*s**4 + 1/24*s**3 + 0 + s**c. Find n such that a(n) = 0.
-1
Let j(c) be the third derivative of -3*c**2 + 1/36*c**5 + 0 + 0*c + 1/9*c**3 - 7/72*c**4. Factor j(a).
(a - 1)*(5*a - 2)/3
Determine m, given that 3*m**3 - 3*m**4 + 10*m**3 - 4*m**2 - 5*m**3 - m**4 = 0.
0, 1
Let x(t) be the first derivative of 3*t**4/14 - 10*t**3/21 + t**2/7 + 2*t/7 + 4. Let x(m) = 0. Calculate m.
-1/3, 1
Let m be 4/6 - (-32)/(-12). Let w be (4/3)/(m/(-3)). Factor -2*y**2 + 1 + w*y**4 + 0 - y**4.
(y - 1)**2*(y + 1)**2
Factor -162*d**2 + 81*d**3 - 11 - 13 + 0*d + 108*d.
3*(3*d - 2)**3
Let z(q) = q - 1. Let d be z(6). Suppose -4*i + 14 = -a, d*a + 5*i - 31 = -1. Solve -4/3 + 2/3*x + 2/3*x**a = 0 for x.
-2, 1
Let f(n) = -n**3 - n**2 - n + 8. Let x be f(0). Suppose 0 = -w - 5*y + 10, 5*w - x = 2*w - 4*y. What is l in 3/5*l**2 + w*l - 3/5 = 0?
-1, 1
Suppose -4*t - 3*l + 15 = 2*l, -3*t = 4*l - 11. Suppose 4*f = 3*v - t, 4*v + f - 11 = 2*f. Factor 2/3*k**5 + 0*k + 0 + 2/3*k**2 - 2/3*k**4 - 2/3*k**v.
2*k**2*(k - 1)**2*(k + 1)/3
Let g(a) be the third derivative of a**5/120 - a**4/48 - a**3/6 - 12*a**2. Factor g(d).
(d - 2)*(d + 1)/2
Let k(o) be the third derivative of 0*o**4 + 1/30*o**5 + 1/105*o**7 + 0 - 2*o**2 + 0*o**3 + 1/30*o**6 + 0*o. Factor k(f).
2*f**2*(f + 1)**2
Let n = 199 - 197. Let 0 - 2/11*f**n - 2/11*f = 0. Calculate f.
-1, 0
Determine p so that -4/3 + 4*p - 5/3*p**2 = 0.
2/5, 2
Let y(h) be the third derivative of -h**5/20 - h**4/4 - h**3/2 - 11*h**2. Determine k, given that y(k) = 0.
-1
Suppose 7*t - 10*t = 0. Factor t*f - f**2 - 6*f + 4*f**2.
3*f*(f - 2)
Let l(w) = w**3 - 5*w**2 + 4*w + 2. Let u be l(4). Suppose -1 = -u*h + 3. Factor 2 - 2 - h*x**3.
-2*x**3
Let k be (27/(-18))/(10/11). Let s = k + 419/60. Suppose s*z - 2*z**2 - 8/3 = 0. What is z?
2/3, 2
Let i(g) = 4*g**2 - g + 3. Let y(r) be the second derivative of 2*r**4/3 - r**3/6 + 5*r**2/2 - 4*r. Let m(v) = 7*i(v) - 4*y(v). Factor m(t).
-(t + 1)*(4*t - 1)
Let x(t) be the second derivative of t**6/30 + 3*t**5/20 + t**4/4 + t**3/6 - 2*t. Factor x(s).
s*(s + 1)**3
Let q(l) be the first derivative of 2 + 1/12*l**4 - 1/6*l**3 + 3*l - l**2. Let i(k) be the first derivative of q(k). Find u, given that i(u) = 0.
-1, 2
Let f(r) = r**2 + 8*r - 9. Let a(k) = -k + 1. Let c(v) = -a(v) - f(v). Determine b so that c(b) = 0.
-8, 1
Let z be (-1)/((-1)/4) - -1. Suppose z*t + 11 + 9 = 0, -2*d = -t - 8. Factor -2 + 2 + 0 - x**3 - x**d.
-x**2*(x + 1)
Let v = 4/35 - -17/35. Factor 6/5 - v*s**3 + 3*s - 3/5*s**4 + 9/5*s**2.
-3*(s - 2)*(s + 1)**3/5
Let a(i) be the second derivative of 3*i**5/20 - i**4/2 - i**3/2 + 3*i**2 - 28*i. Factor a(w).
3*(w - 2)*(w - 1)*(w + 1)
Suppose -2*w - 1 - 1 = 2*y, 0 = 5*y - 5*w - 25. Let -275*n**4 - 6*n + 33*n**y + 40*n**