ulate r.
-1
Let j(m) be the third derivative of -m**6/540 + m**5/270 - 7*m**2. Let j(q) = 0. What is q?
0, 1
Suppose v - 4*p = 8, -6*v + 11*v - 2 = p. Suppose v = -4*y + 3*y. Suppose 6*t**4 - 3*t**5 + 0*t**2 - 6*t**2 + y*t**2 + 3*t = 0. Calculate t.
-1, 0, 1
Suppose -14 = -k - 0*k + 2*t, -4*k - 4*t = -20. Let q = 11 - k. Factor -y - 1/3*y**5 + 4/3*y**q + 0*y**4 + 2/3*y**2 - 2/3.
-(y - 2)*(y - 1)*(y + 1)**3/3
Let v(s) be the second derivative of -11*s**4/4 - 13*s**3/2 - 3*s**2 - 13*s. Factor v(r).
-3*(r + 1)*(11*r + 2)
Let y be -3 + 0 + 6*1. Let o be 3/1 + (y - 6). Factor -b**4 + o*b**2 + 2*b + 3*b**2 - b - 2 - 2*b + b**3.
-(b - 2)*(b - 1)*(b + 1)**2
Let f(z) be the third derivative of 5*z**8/672 - z**7/28 + z**6/16 - z**5/24 + 16*z**2. Let f(v) = 0. What is v?
0, 1
Suppose -10 - 65 = -5*m. Suppose m = 4*h + h. Factor s**2 - s**4 - 3*s**h - 4*s**2 + 2 + 3*s + 2*s**2.
-(s - 1)*(s + 1)**2*(s + 2)
Let o(s) = 2*s**5 + 5*s**4 + 2*s**3 - 4*s**2 - 4*s + 2. Let m(v) = v**5 + 4*v**4 + 2*v**3 - 4*v**2 - 3*v + 2. Let w(f) = 3*m(f) - 2*o(f). Factor w(u).
-(u - 2)*(u - 1)**2*(u + 1)**2
Let q(g) be the second derivative of 3*g**5/10 + 5*g**4/4 + g**3/2 - 3*g**2 - 5*g. Determine k so that q(k) = 0.
-2, -1, 1/2
Let a(v) = v**4 - v**3 - v. Let f(z) = -15*z**4 + 18*z**3 - 6*z**2 + 18*z + 3. Let t(n) = 18*a(n) + f(n). Suppose t(k) = 0. What is k?
-1, 1
Let v be -1*1*(-4 - 6). Suppose 2*n = 7*n - 2*x - 4, -2*n - 5*x - v = 0. Find o, given that -1/3*o + n + 2/3*o**2 - 1/3*o**3 = 0.
0, 1
Let s = 0 + 10. Let d = -10 + s. Determine b, given that -1/2*b**3 + d + 1/2*b**5 + 0*b + 1/2*b**2 - 1/2*b**4 = 0.
-1, 0, 1
Let n(f) = -f - 9. Let r be n(-11). Let q(a) = -a**3 - a**2 - a + 2. Let z be q(0). Factor -2*y - 2 + 0*y + z + r*y**2.
2*y*(y - 1)
Factor -r**3 - 2*r + r**3 + r**2 + r**3.
r*(r - 1)*(r + 2)
Factor 3/5*i**4 + 3/5*i**2 + 0*i + 0 + 6/5*i**3.
3*i**2*(i + 1)**2/5
Suppose -10/7*j**5 - 6/7*j**4 + 0 - 4/7*j + 2*j**3 + 6/7*j**2 = 0. Calculate j.
-1, 0, 2/5, 1
Let u be (-2)/3 + 3 - 2. Let v = u - -1/3. What is q in -2/3*q + v*q**3 + 2/3*q**2 - 2/3 = 0?
-1, 1
Suppose -6 = -3*y - 0*y. Solve -a + 3*a**2 - 4*a**y - a**2 - 3*a = 0 for a.
-2, 0
Factor -11 - 21*d - 39*d + 49 + 5*d**2 + 142.
5*(d - 6)**2
Let t(c) be the first derivative of c**4/12 - 5*c**3/9 + c**2/2 + 3*c + 1. Factor t(u).
(u - 3)**2*(u + 1)/3
Let k(f) be the second derivative of f**7/1680 + f**6/720 + f**3/6 + 3*f. Let p(w) be the second derivative of k(w). Find g, given that p(g) = 0.
-1, 0
Let w(o) be the second derivative of -2*o + 0 + 1/36*o**4 + 0*o**2 + 0*o**5 - 1/90*o**6 + 0*o**3. Factor w(s).
-s**2*(s - 1)*(s + 1)/3
Factor -8*g**5 - 6*g**3 + 2*g**2 + 6*g**4 + 12*g**5 - 6*g**5.
-2*g**2*(g - 1)**3
Suppose -3*p = -8*p + 10. Suppose p*l - 5*l = 0. What is s in s**2 + 0*s - s**4 + l*s = 0?
-1, 0, 1
Let n = 51/26 - 713/390. Suppose 2/5*b + 4/15 + n*b**2 = 0. What is b?
-2, -1
Suppose 1 = -5*h + 41. Let w = -6 + h. Factor -v - v**3 + 4*v**w - 2*v - v.
-v*(v - 2)**2
Let z(x) = -5*x + 2. Let c be z(2). Let o = c - -11. Factor -o + d**2 + 5 - 5*d**2 - d + 3*d**3.
(d - 1)**2*(3*d + 2)
Let a(b) be the second derivative of b**6/480 - b**4/32 - b**3/12 - b**2/2 + 3*b. Let l(w) be the first derivative of a(w). Find m, given that l(m) = 0.
-1, 2
Let v = 1493/4 - 373. Solve -1/4 - 1/4*u**3 + v*u**2 + 1/4*u = 0.
-1, 1
Let z(l) be the second derivative of -l**7/21 + l**6/10 + l**5/20 - l**4/4 + l**3/6 + 9*l. What is t in z(t) = 0?
-1, 0, 1/2, 1
Let v(q) be the first derivative of 0*q**4 + 0*q - 1 + 1/20*q**5 - 1/12*q**3 + 0*q**2. Factor v(x).
x**2*(x - 1)*(x + 1)/4
Factor 0 - 2/13*g**5 - 14/13*g**4 - 36/13*g**3 - 40/13*g**2 - 16/13*g.
-2*g*(g + 1)*(g + 2)**3/13
Let s(f) be the first derivative of -f**4/2 - 4*f**3/3 - 3. What is p in s(p) = 0?
-2, 0
Let w = 13 + -15. Let s be (-8)/(-21) - w/7. Factor -1/3*a**2 + s*a**3 + 0*a + 7/3*a**4 + 0 + 4/3*a**5.
a**2*(a + 1)**2*(4*a - 1)/3
Let r be (-2 + 2)*(-6 - 91/(-14)). Find f, given that 2/3*f**3 + 2/9*f**5 + 0 + r*f + 2/3*f**4 + 2/9*f**2 = 0.
-1, 0
Let z(o) = -o**3 + 3*o**2 + 6*o - 6. Let t be z(4). Let y be 9/t*8/12. Factor 0*i + 0 + 2/11*i**4 + 4/11*i**y + 2/11*i**2.
2*i**2*(i + 1)**2/11
Factor 2/7*j**2 + 0*j - 8/7.
2*(j - 2)*(j + 2)/7
Let s be (-2)/6*(-12)/24. Let g(z) be the first derivative of 1 - 2/3*z - 1/3*z**2 + 2/9*z**3 + s*z**4. Suppose g(v) = 0. Calculate v.
-1, 1
Let v(l) be the third derivative of -3*l**2 + 0 + 0*l - 1/6*l**4 - 1/6*l**3 - 1/15*l**5. Let v(j) = 0. Calculate j.
-1/2
Let y(v) = 3*v**2 - 44*v + 28. Let l be y(14). Factor 3/2*g - 3/4*g**2 + l.
-3*g*(g - 2)/4
Let u(h) be the first derivative of 2*h**3/3 - 36*h**2 + 648*h + 71. Solve u(a) = 0.
18
Let z(c) be the second derivative of c**5/40 + 3*c**4/16 + c**3/2 + 11*c**2/2 + 2*c. Let n(q) be the first derivative of z(q). Factor n(x).
3*(x + 1)*(x + 2)/2
Let g(p) be the first derivative of -7*p**5/25 + p**4/4 + 16*p**3/15 + 2*p**2/5 - 10. Find x such that g(x) = 0.
-1, -2/7, 0, 2
Let y be (-26)/(-45) - (66/(-27))/11. Factor 0 - 2*m**4 + 14/5*m**3 + 0*m - y*m**2.
-2*m**2*(m - 1)*(5*m - 2)/5
Let g(p) be the third derivative of 0*p**4 + 0*p + 0*p**3 + 0 - 1/210*p**7 + 1/60*p**5 + 1/336*p**8 - 1/120*p**6 - p**2. Factor g(t).
t**2*(t - 1)**2*(t + 1)
Factor 162/7 - 18*t - 34/7*t**2 - 2/7*t**3.
-2*(t - 1)*(t + 9)**2/7
Find q such that 1/5*q + 1/10 + 1/10*q**2 = 0.
-1
Let j(p) be the second derivative of -2/15*p**6 - 2/3*p**4 - 2*p + 0 - 1/2*p**5 - 1/3*p**3 + 0*p**2. Solve j(h) = 0.
-1, -1/2, 0
Let y be (1/(-6))/((-9)/27). Let n(l) be the first derivative of -3 + y*l + 1/16*l**4 - 1/6*l**3 - 1/8*l**2. Let n(c) = 0. What is c?
-1, 1, 2
Let c(i) be the third derivative of -i**6/24 + i**5/12 + 5*i**4/12 - 12*i**2. Factor c(p).
-5*p*(p - 2)*(p + 1)
Let d(h) = -23*h**4 - 8*h**3 + 17*h**2 + 8*h - 3. Let i(n) = -22*n**4 - 7*n**3 + 18*n**2 + 7*n - 2. Let p(w) = 2*d(w) - 3*i(w). Let p(v) = 0. Calculate v.
-1, -1/4, 0, 1
Let t(y) = -3*y**2 - y - 4. Let d(w) = 6*w**2 + w + 7. Suppose -4*f + 2*k + k + 16 = 0, -k = -5*f + 20. Let b(r) = f*d(r) + 7*t(r). Factor b(c).
3*c*(c - 1)
Let s(y) = -y - 1. Let z be s(-3). Find i such that 16 - 2*i**z + 3*i**2 - 19 + 2*i**2 = 0.
-1, 1
Suppose -11*q + 3 = -10*q. Solve 8/3*z + 0 - 4/3*z**q + 4/3*z**2 = 0.
-1, 0, 2
Let d = 427 - 12809/30. Let s(u) be the first derivative of -1/5*u - 3/10*u**2 + 1/10*u**4 + 1 - 2/15*u**3 + d*u**6 + 3/25*u**5. Factor s(o).
(o - 1)*(o + 1)**4/5
Let c = 0 - 0. Suppose 0 = -4*m - 2*h - 3*h + 11, c = -5*m + 4*h + 24. Find j such that -13/4*j**2 + 3/2*j**3 - 1 - 1/4*j**m + 3*j = 0.
1, 2
Suppose 0 = -4*q - 15 + 3, -5*y = q - 12. Let h(x) be the first derivative of 0*x**y - 2*x + x**4 + 2/5*x**5 + 1 - 2*x**2. Factor h(o).
2*(o - 1)*(o + 1)**3
Let y(o) be the first derivative of o**5/90 - o**3/9 + 3*o**2/2 - 2. Let q(g) be the second derivative of y(g). Factor q(x).
2*(x - 1)*(x + 1)/3
Determine a, given that 0*a**2 - 4/7 + 4/7*a**4 - 10/7*a + 10/7*a**3 = 0.
-2, -1, -1/2, 1
Let z be -10 - -7 - (1 + -3). Let q(f) = f**3 + f**2. Let x be q(z). Factor 1/2*b**2 - 1/4*b**3 + x - 1/4*b.
-b*(b - 1)**2/4
Let p = -268319/480 - -559. Let l(x) be the third derivative of -1/24*x**3 + 0*x - 1/32*x**4 + 0 - p*x**6 - 1/80*x**5 + 2*x**2. Factor l(v).
-(v + 1)**3/4
Let j be (-9*(-1)/4)/6. Let p(t) be the first derivative of -1/4*t**2 + 1/2*t - j*t**4 - 5/6*t**3 + 2. Factor p(z).
-(z + 1)**2*(3*z - 1)/2
Let c(k) be the third derivative of -k**7/4095 - k**6/1560 + k**5/780 + k**4/3 + k**2. Let m(z) be the second derivative of c(z). Solve m(p) = 0.
-1, 1/4
Let l(i) be the first derivative of i**4/8 + 2*i**3/3 + i**2 - 22. Factor l(t).
t*(t + 2)**2/2
Let z(s) be the second derivative of s**7/21 + s**6/15 - 3*s**5/10 - 5*s**4/6 - 2*s**3/3 + 22*s. Factor z(q).
2*q*(q - 2)*(q + 1)**3
Let n(y) be the first derivative of 2*y**6/21 - 12*y**5/35 + 2*y**4/7 + 29. Factor n(g).
4*g**3*(g - 2)*(g - 1)/7
Let p(b) be the first derivative of b**6/360 - b**4/72 + b**2/2 + 2. Let i(o) be the second derivative of p(o). What is s in i(s) = 0?
-1, 0, 1
Let c be (5/5)/(2/16). Let a(q) be the first derivative of -c*q - 10/3*q**3 - 8*q**2 - 1/2*q**4 - 2. Determine s so that a(s) = 0.
-2, -1
Suppose 0 = 2*k + 5*j + 21, -6 = -3*k + j + 5. Determine c so that 0*c**k + 0 + 0*c + 1/4*c**4 + 0*c**3 = 0.
0
S