20 - b**3/15 + 9*b. Factor x(d).
-d*(d - 1)**2*(d + 2)/5
Let q(y) be the third derivative of y**7/210 + y**6/15 + 11*y**5/30 + y**4 + 3*y**3/2 - 5*y**2. Factor q(d).
(d + 1)**2*(d + 3)**2
Let j(p) = 34*p + 38. Let t be j(-1). Let 0*o**t + 0 + 0*o + 1/6*o**3 + 0*o**2 - 1/6*o**5 = 0. Calculate o.
-1, 0, 1
Suppose b - 3*b = -4. Determine t so that -t**2 - 4*t**2 - 5*t + 4*t + 4*t**b + 2 = 0.
-2, 1
Let f = 16 - 7. Factor 9*x**4 + 3*x + 12 - f*x**2 - 12 - 3*x**3.
3*x*(x - 1)*(x + 1)*(3*x - 1)
Let h(k) = k**2. Let j(y) = -5*y**2 + 4*y - 3*y**2 + 24 - 26. Let p(d) = -6*h(d) - j(d). Factor p(g).
2*(g - 1)**2
Suppose s = -4, -6*s = -h - s + 22. Suppose 8*x + 2*x**4 + 12*x**2 + 0*x**3 + 7*x**3 + x**3 + 0*x**3 + h = 0. What is x?
-1
Let s(o) be the second derivative of o**10/7560 + o**9/1890 + o**4/4 - 2*o. Let l(w) be the third derivative of s(w). Suppose l(f) = 0. Calculate f.
-2, 0
Solve 2*u**3 + 11*u**2 - u + 13*u**2 - 3*u**4 - 22*u**2 + 2*u**4 - u**5 - 1 = 0 for u.
-1, 1
Factor 60*c**2 - 4 + 4*c**3 + 12*c**3 + 2 + 32*c - 10.
4*(c + 1)*(c + 3)*(4*c - 1)
Let g be (-1)/2*30/(-3). Suppose 2*u - g = 3. Factor 0 + u - 16*d**3 - 6*d + 18*d**3.
2*(d - 1)**2*(d + 2)
Let l be 7/(28/24)*2/6. Factor 1/4*n**l + 0 + 0*n.
n**2/4
Let r(x) = -6*x - 2. Let o be r(-2). Suppose 0 = -5*g + 4*k + 2, -3*g - 3*k = -k - o. Find b such that -2/9*b**g + 0 - 2/9*b = 0.
-1, 0
Factor 5*g + 7*g - 20*g**3 + g + 10*g**2 + 2*g + 5*g**5 - 10*g**4.
5*g*(g - 3)*(g - 1)*(g + 1)**2
Let t(o) be the third derivative of o**7/840 - o**6/120 + o**5/40 - o**4/24 - o**3/6 + o**2. Let y(j) be the first derivative of t(j). Factor y(z).
(z - 1)**3
Let l(u) be the second derivative of -u**6/15 + 2*u**5/5 - 2*u**4/3 + u. Find z such that l(z) = 0.
0, 2
Factor -1/2*u**5 + 3/2*u + 0 + 3*u**3 - 4*u**2 + 0*u**4.
-u*(u - 1)**3*(u + 3)/2
Let t be (-115)/(-30) + (-1)/(-6). Let r be (12/14)/(t/14). Factor 1/3*s**4 + 0 + 0*s**r - 1/3*s**2 + 0*s.
s**2*(s - 1)*(s + 1)/3
Let f = -33 - -46. Determine p, given that -p**4 + 2*p**2 - 13*p**3 - p**4 + f*p**3 = 0.
-1, 0, 1
Suppose -4*d - m = m - 26, -4*d + m = -17. Suppose -5*v + 5 + d = 0. Determine n so that 36/7*n**v + 6/7*n**5 - 16/7*n**3 - 22/7*n + 4/7 - 8/7*n**4 = 0.
-2, 1/3, 1
Let k(g) be the second derivative of 5*g**4/12 + 3*g**3/2 - g**2 - 43*g. What is c in k(c) = 0?
-2, 1/5
Factor 21*p**3 - 6*p**3 + 12*p**4 + 3*p**2 + 3*p**2 + 3*p**5.
3*p**2*(p + 1)**2*(p + 2)
Let x(l) be the second derivative of -4/7*l**2 + 1/70*l**5 + 0 + 5*l - 5/42*l**4 + 8/21*l**3. Factor x(y).
2*(y - 2)**2*(y - 1)/7
Let y be (-12)/(-8)*8/(-426). Let r = y + 75/142. Factor 1/2*t**3 - 1/2*t - 1/2*t**2 + r.
(t - 1)**2*(t + 1)/2
Factor -5*o**2 + 3*o + 5*o**2 + o**2 + 2.
(o + 1)*(o + 2)
Let s(b) be the third derivative of -b**5/90 + b**4/8 + 5*b**3/18 - 12*b**2. Find r such that s(r) = 0.
-1/2, 5
Let p(h) = 8*h**2 + 6*h - 2. Let s(i) = -4*i**2 - 3*i + 1. Let m(n) = -6*p(n) - 15*s(n). Suppose m(d) = 0. What is d?
-1, 1/4
Suppose 6 = c + 2*c. Factor 1/5*m**4 + 1/5*m**3 + 0 - 1/5*m - 1/5*m**c.
m*(m - 1)*(m + 1)**2/5
Let q be (21/147)/(9/42*2). Factor x**2 + 1/3 + x + q*x**3.
(x + 1)**3/3
Suppose j = w - 4, -9*j = -4*w - 10*j + 6. Suppose 2*d**w - 4/3*d - 2/3 = 0. Calculate d.
-1/3, 1
Let f = -2383/9 - -265. Solve f*v**3 + 0*v**2 - 2/9*v + 0 = 0 for v.
-1, 0, 1
Suppose -3*j - 2*c + 7*c = 5, 13 = 5*j - 3*c. Let u(p) be the second derivative of 0 + p**3 + 2*p - 3/20*p**j + 0*p**2 + 1/4*p**4. Factor u(s).
-3*s*(s - 2)*(s + 1)
Let o(m) = -7*m**3 + 7*m**2 - 5*m - 1. Let l(v) = 13*v**3 - 13*v**2 + 9*v + 2. Let c = -12 - -18. Let j(g) = c*l(g) + 11*o(g). Factor j(d).
(d - 1)**2*(d + 1)
Suppose b**2 - 5/4*b + 1/2 - 1/4*b**3 = 0. Calculate b.
1, 2
Let c be 166/91 - 16/(-56). Let f = -20/13 + c. Factor 2/7*s**2 + 0 + f*s.
2*s*(s + 2)/7
Let t be (-12)/(-9) - (1 + 2). Let i = t - -7/3. Factor 2/3*p + 0 + i*p**4 - 2/3*p**3 - 2/3*p**2.
2*p*(p - 1)**2*(p + 1)/3
Factor 5*o**3 + 57*o + 142 - 2*o**3 - 115 + 33*o**2.
3*(o + 1)**2*(o + 9)
Let v be -3*((-64)/(-36) + -2). Determine a so that 0 - v*a + 1/3*a**2 = 0.
0, 2
Suppose 5*x + 1 = 16. Solve -x + 1 + 0*p**3 + p**3 - 2*p - p = 0 for p.
-1, 2
Let t(q) be the third derivative of q**6/1440 - q**5/480 - q**4/48 - q**3/6 - 2*q**2. Let n(p) be the first derivative of t(p). Suppose n(k) = 0. Calculate k.
-1, 2
Let s(v) be the first derivative of -v**6/45 + 4*v**5/75 - 4*v**3/45 + v**2/15 + 11. Factor s(n).
-2*n*(n - 1)**3*(n + 1)/15
Factor -24*t - 17*t**2 + 0*t + 3*t + 9*t**4 + 33*t**3 - 7 + 3.
(t - 1)*(t + 4)*(3*t + 1)**2
Find c, given that 40*c**3 - 13*c**3 + 3*c**5 + 0*c - 18*c**4 + 0*c = 0.
0, 3
Let t(o) be the second derivative of 3*o**5/100 - 2*o**4/5 + 21*o**3/10 - 27*o**2/5 + o + 2. Let t(f) = 0. What is f?
2, 3
Let q = 13 + -9. Solve -2*f**5 + q*f**4 + 0*f**5 + 6*f**3 + 2*f**2 - 4*f**3 - 6*f**4 = 0.
-1, 0, 1
Let l be (-2)/(-5)*(-60)/(-48). Determine q, given that 1/2*q**2 + 0*q + 0 - l*q**3 = 0.
0, 1
Let m(o) be the second derivative of o**7/420 - o**6/180 + o**3/3 + 5*o. Let c(s) be the second derivative of m(s). Factor c(x).
2*x**2*(x - 1)
Let i(z) be the second derivative of -z**5/30 - z**4/3 - 11*z**3/9 - 2*z**2 - 13*z + 4. What is x in i(x) = 0?
-3, -2, -1
Factor 12 + 3/4*s**2 - 6*s.
3*(s - 4)**2/4
Find h such that 25/3*h**3 + 10/3 + 15*h**2 + 35/3*h + 5/3*h**4 = 0.
-2, -1
Factor 4*f**3 - 5*f**2 - f**2 + 2*f**2.
4*f**2*(f - 1)
Let t(r) be the first derivative of r**3/3 - r**2/2 + 15. Factor t(y).
y*(y - 1)
Let g(f) be the third derivative of f**6/780 + 2*f**5/195 + f**4/39 + 4*f**2. Factor g(l).
2*l*(l + 2)**2/13
Find p, given that 1/3*p**3 + 0*p + 0 - 1/3*p**5 + 1/3*p**2 - 1/3*p**4 = 0.
-1, 0, 1
What is o in -208 - 80 - 2*o**2 - 12*o - 36*o = 0?
-12
Let a = -1 - -6. Suppose -3 - 1 = y, k - 20 = a*y. Solve k - 1/3*p + 4/3*p**2 - 2*p**3 - 1/3*p**5 + 4/3*p**4 = 0 for p.
0, 1
Let p(d) be the first derivative of -d**6/132 - d**5/165 - d**2/2 + 2. Let k(c) be the second derivative of p(c). Suppose k(m) = 0. What is m?
-2/5, 0
Suppose -17 - 1 = -2*y. Let b = -6 + y. Factor 1/3*k**4 - 2/3*k**b + 1/3*k**2 + 0 + 0*k.
k**2*(k - 1)**2/3
Let q = 5 - 2. Let h be -3 - (-6 - -3 - q). Factor -16*z**5 + 4*z**3 - 4*z**3 - z**h + 8*z**4.
-z**3*(4*z - 1)**2
Let q(k) = k**5 + k**4 - k**3 + k + 1. Let b(c) = 5*c**5 + 4*c**4 - 5*c**3 + 4*c + 4. Let g(x) = -b(x) + 4*q(x). Factor g(r).
-r**3*(r - 1)*(r + 1)
Let v = 207 - 204. Determine n, given that 0 - 15/4*n**v - 2*n**4 + 2*n**2 - 1/4*n + 4*n**5 = 0.
-1, 0, 1/4, 1
Suppose -12 = -3*p - 2*p - 3*u, 0 = p - 3*u - 6. Suppose 0 = 5*l - 18 + p. Factor 0*f + 0 + 0*f**2 + 0*f**4 + 1/3*f**l - 1/3*f**5.
-f**3*(f - 1)*(f + 1)/3
Let i(g) = -g**2 + 7*g + 4. Let h be i(7). Factor -3*k**4 + 0 + 5*k**h - 2*k**3 + 0.
2*k**3*(k - 1)
Factor 1/4*b**2 + 2*b - 1 - 1/2*b**3.
-(b - 2)*(b + 2)*(2*b - 1)/4
Let r(w) = w**2 - 8. Let u be r(4). Determine s so that -s - s**2 - 1 + u - 5 = 0.
-2, 1
Let z(b) = -b**3 - 9*b**2 - 5. Let m be z(-9). Let d = m - -7. Let 3/2*i + 1/2*i**3 + 3/2*i**d + 1/2 = 0. What is i?
-1
Suppose -5*c + 4*x = -c, 0 = -5*c + x. Let p = 1/2 - 1/4. Factor 1/4*r - p*r**3 - 1/4*r**4 + c + 1/4*r**2.
-r*(r - 1)*(r + 1)**2/4
Let -18 + 64*s**3 + 9*s**4 + 33*s**2 - 4*s - 11*s - 25*s**3 = 0. What is s?
-3, -1, 2/3
Let h be -30*(0 - (-1)/(-3)). Factor 4 - 8*p + 30*p**2 - p + p - h.
2*(3*p + 1)*(5*p - 3)
Let n(z) be the third derivative of z**5/90 - 7*z**4/36 + 2*z**3/3 + 11*z**2. Factor n(h).
2*(h - 6)*(h - 1)/3
Let t(y) be the third derivative of -y**7/945 + y**6/540 + y**5/270 - y**4/108 - 19*y**2. Find x such that t(x) = 0.
-1, 0, 1
Suppose 3*q - 2*i - 5 = 5, -5*q + 3*i + 16 = 0. Determine h so that 0*h**q + 3/4*h + 1/2 - 1/4*h**3 = 0.
-1, 2
Let o(y) = 3*y**4 - 20*y**2. Let q = 10 + -16. Let a(u) = u**4 - 7*u**2. Let g(m) = q*o(m) + 17*a(m). Let g(v) = 0. What is v?
-1, 0, 1
Let q be ((-18)/15)/((-6)/20). Let m = q - 4. Suppose m + 2/7*n**4 + 0*n + 0*n**3 - 2/7*n**2 = 0. What is n?
-1, 0, 1
Let u(n) = -n**5 + n**4 + n**3 + n**2. Let q(l) = -32*l**5 + 46*l**4 + 14*l**3 + 2*l**2 + 18*l - 4. Let r(s) = -2*q(s) + 44*u(s). Solve r(k) = 0 for k.
-1, 2/5, 1
Let g(n) be the first derivative of -3/2*n**2 + 4/5*n**3 - 2 + 6/5*n - 3/20*n**4. Factor g(y).
-3*(y - 2)*(y - 1)**2/5
Factor 8/7 - 8/7*v + 2/7*v**2.
2*(v - 2)**2/7
Let i(p) = -p**2 + p