.
-a**3*(a - 1)**2/2
Factor 5*o**2 - 12*o - 14 + 6 - o**2 - 32.
4*(o - 5)*(o + 2)
Let k(b) be the first derivative of b**5/30 - 7*b**4/60 + 2*b**3/15 - b**2/2 + 3. Let c(s) be the second derivative of k(s). Factor c(r).
2*(r - 1)*(5*r - 2)/5
Let o(l) be the second derivative of -l**6/70 - 2*l. Factor o(g).
-3*g**4/7
Let p = 46/19 + -4121/1710. Let u(l) be the second derivative of 1/18*l**4 + 1/9*l**3 + 1/9*l**2 + 0 + 2*l + p*l**5. Factor u(z).
2*(z + 1)**3/9
Let j(g) be the second derivative of -25*g**7/14 - 13*g**6/3 + 31*g**5/2 + 10*g**4/3 - 115*g**3/6 - 15*g**2 - 11*g. Let j(p) = 0. What is p?
-3, -2/5, -1/3, 1
Suppose -42 = -2*h + 2. Suppose 4*q**4 + 21*q**5 - 21*q**3 + 16*q**2 - h*q**2 + 2*q**4 = 0. What is q?
-1, -2/7, 0, 1
Factor 1/2*v**2 + 5/2*v + 3.
(v + 2)*(v + 3)/2
Let k(d) be the first derivative of -d**4/16 - d**3/4 - 3*d**2/8 - d/4 + 1. Factor k(b).
-(b + 1)**3/4
Suppose b = 5*x - 13, 11 = -2*x + 3*x - 3*b. Solve -3/5*a**3 + 0 - a**x - 2/5*a = 0 for a.
-1, -2/3, 0
Let f = -1 + 5. Determine t, given that t**2 + f*t + 5*t - 10*t = 0.
0, 1
Let q(s) be the first derivative of s**4/6 - 8*s**3/9 + 4*s**2/3 - 17. Solve q(z) = 0.
0, 2
Suppose 0 - 8*g**2 + 20/3*g + 4/3*g**3 = 0. What is g?
0, 1, 5
Let g be (-80)/(-12) + -20 + 14. Factor 2*t + g*t**2 + 4/3.
2*(t + 1)*(t + 2)/3
Let y be (-7)/(-21) + (-1)/4. Let t(m) be the second derivative of 1/20*m**5 + y*m**4 - 1/6*m**3 + 0 - 2*m + 0*m**2 - 1/30*m**6. Factor t(q).
-q*(q - 1)**2*(q + 1)
Let u = -1026 + 7209/7. Factor u*g - 12/7*g**2 - 6/7.
-3*(g - 2)*(4*g - 1)/7
Suppose -6 = -0*q - 2*q + 4*z, 1 = q - 3*z. Suppose 0*n = n - 2*w - q, -n = -3*w - 9. Determine i, given that 0 - 1/4*i**4 + 0*i**n + 1/4*i**2 + 0*i = 0.
-1, 0, 1
Let w(x) = x + 10. Let n be w(-6). Factor 3*o**2 + 2*o**2 - 2*o - n*o**2.
o*(o - 2)
Let q be 3/((-36)/(-118)) + 3. Let m = q - 25/2. Factor -1/3*a**2 + 2/3 + m*a.
-(a - 2)*(a + 1)/3
Let t = -7 - -13. Let z(o) = 4*o - 9. Let i be z(t). Solve -15 - 3*j**4 + i + 3*j**3 = 0.
0, 1
Factor -2*w + 8 + 4 + 8*w**2 - 20*w.
2*(w - 2)*(4*w - 3)
Let r(m) be the first derivative of -2*m**3/27 + 2*m**2/9 - 29. Suppose r(k) = 0. Calculate k.
0, 2
Let j(u) be the first derivative of -u**6/2 - 36*u**5/25 + 33*u**4/20 + 26*u**3/5 - 18*u**2/5 - 24*u/5 + 1. What is l in j(l) = 0?
-2, -2/5, 1
Suppose 1/7*g**2 - 3/7*g + 2/7 = 0. What is g?
1, 2
Suppose -2*d = -4*d. Suppose x + 0 - 2 = d. Factor 2/3*v**x + 0*v + 0 + 2/3*v**3.
2*v**2*(v + 1)/3
Let n be -4 - -2 - 75/(-36). Let m(p) be the third derivative of -1/96*p**4 - p**2 - n*p**3 + 0 + 1/240*p**5 + 0*p. Factor m(u).
(u - 2)*(u + 1)/4
Let l(b) be the second derivative of -b**8/5880 + b**7/2940 + b**6/1260 - b**5/420 + 2*b**3/3 - 6*b. Let u(y) be the second derivative of l(y). Factor u(r).
-2*r*(r - 1)**2*(r + 1)/7
Let u = -30 + 30. Factor 2/5*z + 0 - 2/5*z**3 + u*z**2.
-2*z*(z - 1)*(z + 1)/5
Suppose r + 4 = -2*v, -5*r = -3*v + 30 + 29. Let s = r - -14. Solve -k**s + k**3 + 0*k - 1/3*k**2 + 0 + 1/3*k**5 = 0 for k.
0, 1
Let f(j) = -j + 4*j + 1 + 0*j. Let n be f(1). Suppose -2*a - n*a**2 + a**2 + 5*a**2 = 0. Calculate a.
0, 1
Find l, given that 13*l**3 - 2*l**4 + 0*l**4 - 3*l**3 + 9*l**2 + 2*l + 5*l**4 = 0.
-2, -1, -1/3, 0
Let z(w) = -2*w - 12. Let p be 1*3*(-40)/15. Let o be z(p). Find d such that 2*d + d**3 - 7*d**3 - 4*d**o + 0*d**3 = 0.
-1, 0, 1/2
Let r be (-35)/2 - (-1)/(-2). Let p be -2 + 0 - r/7. Factor -6/7*t + 2/7*t**2 + p.
2*(t - 2)*(t - 1)/7
Suppose 0*k + k = 0. Suppose -5*r + r = k. Factor 8/7*w**2 - 8/7*w - 2/7*w**3 + r.
-2*w*(w - 2)**2/7
Suppose -3*p + 8*p = 0. Let h(l) be the second derivative of -1/5*l**2 - 2/15*l**3 + 1/25*l**5 + 1/75*l**6 + l + 0 + p*l**4. Factor h(n).
2*(n - 1)*(n + 1)**3/5
Let w be (1 - 1)/(12/(-4)). Let 12*y + 0 - 12*y**2 + 5*y**3 - 2*y**3 + w = 0. Calculate y.
0, 2
Let s(h) be the first derivative of h**3 + 0*h**2 - 1/50*h**5 + 0*h - 2 - 1/10*h**4 - 1/600*h**6. Let y(f) be the third derivative of s(f). Factor y(n).
-3*(n + 2)**2/5
Let -21*p**3 + 60*p + 4 - p**3 + 16 + 15*p**2 - 3*p**3 = 0. Calculate p.
-1, -2/5, 2
Let h(c) be the first derivative of 5*c**6/6 + 2*c**5 - 10*c**3/3 - 5*c**2/2 - 3. Let h(o) = 0. Calculate o.
-1, 0, 1
Let k(o) = -o - 7. Let t be k(-5). Let u be (t + 2)/(2/1). Suppose u*n**2 + 1/4*n - 1/4*n**3 + 0 = 0. What is n?
-1, 0, 1
Let u be (-2)/4*0/11. Let t(h) be the second derivative of 2*h + u*h**2 + 0*h**3 + 1/4*h**4 + 0. Factor t(s).
3*s**2
Let l(k) be the first derivative of -k**4/19 + 10*k**3/57 - 4*k**2/19 + 2*k/19 + 24. Factor l(p).
-2*(p - 1)**2*(2*p - 1)/19
Suppose 3*k = k + 4. Let r(a) be the second derivative of 0 + 0*a**k + 1/12*a**4 + 0*a**3 + a. Factor r(z).
z**2
Let m(k) = 2*k. Let g be m(-7). Let d be (-6)/21*g/6. Let -2/3*a**5 + 0*a + 2/3*a**3 + 0 - d*a**4 + 2/3*a**2 = 0. Calculate a.
-1, 0, 1
Let l be (-2)/((-210)/27 + (-4)/18). Solve 1/4*u**4 + 0 + l*u**3 + 0*u + 0*u**2 = 0.
-1, 0
Let h = 38 + -34. Let 6/7*q**3 - 2/7*q**h - 6/7*q**2 + 2/7*q + 0 = 0. What is q?
0, 1
Factor -7/5*s**2 + 0 + 4/5*s**3 + 3/5*s.
s*(s - 1)*(4*s - 3)/5
Let p(i) = -5*i**2 - 23*i + 11. Let t(c) = 3*c**2 + 12*c - 6. Let n(v) = 3*p(v) + 7*t(v). Factor n(f).
3*(f + 3)*(2*f - 1)
Let u be 1/4*2*8. Factor -w**3 + 6*w**3 - 8*w**3 + 2*w**4 + u*w**3.
w**3*(2*w + 1)
Determine b so that 0 - 1/6*b**4 + 1/6*b**2 - 1/6*b**5 + 0*b + 1/6*b**3 = 0.
-1, 0, 1
Let x(p) = 87*p - 672. Let u(z) = z**2 - 175*z + 1345. Let r(c) = -3*u(c) - 5*x(c). Find b such that r(b) = 0.
15
Suppose 0 = -0*i - i. Let u = 2 - i. What is w in 0*w**4 - 2*w**3 + 2*w**u - 7*w**3 + 9*w**4 = 0?
0, 1/3, 2/3
Factor 3/7*x**2 + 0*x - 3/7.
3*(x - 1)*(x + 1)/7
Let o(w) = -31*w**2 + 20*w - 8. Let s(n) = -n**2 - n - 1. Let t(i) = o(i) - 4*s(i). Find a, given that t(a) = 0.
2/9, 2/3
Let u(j) be the first derivative of 2*j**6/9 - 16*j**5/15 + 5*j**4/3 - 8*j**3/9 - 10. Factor u(q).
4*q**2*(q - 2)*(q - 1)**2/3
Let p(g) = -g**3 + 4*g**2 + 2*g - 4. Let q be p(4). Suppose -f**q + 4*f**4 - 3 + 3 = 0. What is f?
0
Suppose -1024/15 - 128/5*z - 16/5*z**2 - 2/15*z**3 = 0. Calculate z.
-8
Let b(k) be the first derivative of -4*k**5/15 + 4*k**3/9 + 9. Determine r, given that b(r) = 0.
-1, 0, 1
Let r(a) = 11*a**3 + 3*a**2 - 2*a + 1. Let g be r(3). Let i = 983/3 - g. Suppose 2/3 + 8*y**2 - i*y**4 - 2/3*y**3 + 5*y**5 - 13/3*y = 0. What is y?
-1, 1/3, 2/5, 1
Let d(x) be the third derivative of -1/160*x**6 + 0*x**4 - 1/40*x**5 - 9*x**2 + 0 + 0*x + 0*x**3. Factor d(v).
-3*v**2*(v + 2)/4
Let v(g) be the first derivative of -5*g**3/3 + 10*g**2 - 15*g + 5. Factor v(t).
-5*(t - 3)*(t - 1)
Let f(h) be the third derivative of 0 + 1/120*h**6 + 0*h + 3*h**2 + 0*h**3 + 0*h**5 + 0*h**4. Factor f(g).
g**3
Suppose x = 6*x + 65. Let i be 9/3 + x/5. Find k such that -3/5*k**4 + 1/5*k**2 - k**3 + i + k = 0.
-1, -2/3, 1
Factor 0 + 2/5*z**3 - 2/5*z + 0*z**2.
2*z*(z - 1)*(z + 1)/5
Factor 1/2*k**2 + k**4 + 0 - 7/4*k**3 + 1/4*k.
k*(k - 1)**2*(4*k + 1)/4
Let h(t) be the second derivative of -3/2*t**2 + 1/10*t**6 + t + 0*t**4 + 0 - t**3 + 3/10*t**5. Determine f, given that h(f) = 0.
-1, 1
Solve -157 + 2*n**2 + 157 - 2*n**3 = 0 for n.
0, 1
Let p(f) be the second derivative of -2*f**4/5 + 11*f**3/15 - 2*f**2/5 - 16*f. Let p(m) = 0. What is m?
1/4, 2/3
Let q(a) be the first derivative of a**6/600 - a**5/50 + a**4/10 + a**3/3 + 1. Let i(j) be the third derivative of q(j). Let i(p) = 0. What is p?
2
Let u = -47/6 - -8. Let 0*t - 1/3*t**2 + 0 + u*t**3 = 0. Calculate t.
0, 2
Factor -2*l - 8/11 - 14/11*l**2.
-2*(l + 1)*(7*l + 4)/11
Let n(j) = -3*j**2 + 27*j. Let r(v) = 2*v**2 - 14*v. Let d(l) = -6*n(l) - 11*r(l). Factor d(g).
-4*g*(g + 2)
Let m(v) be the second derivative of -1/35*v**6 + 0 - 1/70*v**5 + 0*v**2 + 0*v**3 + 0*v**4 - 3*v. Determine h, given that m(h) = 0.
-1/3, 0
Let g(f) = 4*f**2 + 2*f + 2. Let y(t) = 20*t**2 + 9*t + 11. Let u(s) = -11*g(s) + 2*y(s). Factor u(p).
-4*p*(p + 1)
Let c be (-1*4/(-192))/(5/4). Let b(m) be the second derivative of -1/4*m**2 - 1/4*m**4 - 1/3*m**3 - c*m**6 + 0 - 1/10*m**5 + m. Factor b(z).
-(z + 1)**4/2
Suppose -1/8*p**3 + 0*p + 1/4*p**2 - 1/8*p**4 + 0 = 0. What is p?
-2, 0, 1
Let v(f) = -f**3 + f**2 + 2. Let w(g) = -5*g**3 + 5*g**2 + 11. Let a = -52 + 77. Suppose -a = 3*m + 8. Let r(p) = m*v(p) + 2*w(p). Factor r(x).
x**2*(x - 1)
Let z(w) = -3*w**5 - 15*