
-1, 0, 1/4
Let c(a) = -a**3 - 2*a**2 - 4*a - 5. Let h be c(-3). Let k = 18 - h. Find f such that -4*f**k - 2/3*f**3 - 8*f - 16/3 = 0.
-2
Let g(j) = j - 1 + 2*j + 8 - 4*j. Let l be g(7). Factor -2*n**2 - n**3 + 0*n**3 + l*n**3 - n.
-n*(n + 1)**2
Factor -3*d - 1/3*d**3 - 2*d**2 + 0.
-d*(d + 3)**2/3
Let b(i) = -i**5 + 6*i**4 + 4*i**3 + 2*i**2. Let u(c) = -c**5 + c**4 + c**2. Let h(j) = -b(j) + 2*u(j). What is m in h(m) = 0?
-2, 0
Let j = 18 - 26. Let b be (-3)/(-6) + (-44)/j. Find g, given that -69*g**4 - 7*g**3 + 4*g**3 - 48*g**5 - 12*g**5 + b*g**2 = 0.
-1, -2/5, 0, 1/4
Let n = -85 - -85. Factor 2/3*f**3 + 0*f - 1/6*f**2 - 1/2*f**4 + n.
-f**2*(f - 1)*(3*f - 1)/6
Suppose 253*w**2 + 256*w**2 - 524*w**2 + 12*w + 3*w**4 + 3*w**5 - 15*w**3 + 12 = 0. What is w?
-2, -1, 1, 2
Let a(i) be the second derivative of 3*i**5/70 - 5*i**4/14 + 3*i**3/7 + 27*i**2/7 + 8*i. Factor a(z).
6*(z - 3)**2*(z + 1)/7
Let q(o) be the third derivative of 135*o**8/28 + 552*o**7/35 - 8*o**6/15 - 112*o**5/15 - 8*o**4/3 - 3*o**2. Determine g, given that q(g) = 0.
-2, -2/9, 0, 2/5
Let n(h) be the first derivative of -h**5 + 5*h**4/4 + 5*h**3/3 - 5*h**2/2 - 2. Factor n(b).
-5*b*(b - 1)**2*(b + 1)
Let g(p) = -40*p**2 + 65*p - 25. Let n(y) = -5*y**2 + 8*y - 3. Let s(k) = -3*g(k) + 25*n(k). Factor s(t).
-5*t*(t - 1)
Let j be ((-8)/10)/((-2)/(-10)). Let m = 6 + j. Factor -2/3*r**m + 2/3*r + 0.
-2*r*(r - 1)/3
Let v(f) = -27 - 4*f**3 - 3*f**3 + 22. Let z(l) = 4*l**3 + 3. Suppose 6 = 3*j - j. Let y(n) = j*v(n) + 5*z(n). Determine p so that y(p) = 0.
0
Let s(y) be the first derivative of y**4/4 + 7*y**3/3 + 5*y**2/2 - 5*y + 2. Let t be s(-6). Factor 9*m**2 + 1 - m - 10*m**2 + t.
-(m - 1)*(m + 2)
Let 0*h**2 - 14/3*h + 2/3*h**3 - 4 = 0. Calculate h.
-2, -1, 3
Let l(o) = o**3 + o**2 - 1. Let c(z) = -6*z**3 - 5*z**2 + 5. Let t(p) = -c(p) - 5*l(p). Determine f, given that t(f) = 0.
0
Factor -65*x**2 - 20 - 22*x - x - 72*x - 45*x.
-5*(x + 2)*(13*x + 2)
Let o(t) be the first derivative of -t**5/20 - 3*t**4/16 - t**3/6 + 7. Factor o(v).
-v**2*(v + 1)*(v + 2)/4
Let d(h) = -2*h**2 + 18*h - 10. Let s(y) = y**2 - 19*y + 9. Suppose 6*p - p + 15 = 0. Let c(i) = p*d(i) - 2*s(i). Factor c(k).
4*(k - 3)*(k - 1)
Let n(w) be the second derivative of 1/120*w**6 + 0 + 1/80*w**5 - 1/4*w**2 - 5/24*w**3 - w - 1/16*w**4. Factor n(t).
(t - 2)*(t + 1)**3/4
Let t(w) be the third derivative of w**6/140 - 3*w**5/140 + w**3/14 + w**2. Factor t(b).
3*(b - 1)**2*(2*b + 1)/7
Let n(b) = b**5 - b**4 + 6*b**3 + b**2 + 7*b + 7. Let c(p) = 2*p**3 + 2*p + 2. Let w = 5 - -2. Let j(m) = w*c(m) - 2*n(m). Factor j(v).
-2*v**2*(v - 1)**2*(v + 1)
Factor 2/9*m**4 + 2/3*m**3 + 0 + 2/3*m**2 + 2/9*m.
2*m*(m + 1)**3/9
Let d = -1078 + 7549/7. Factor d*a**2 + 0 + 0*a.
3*a**2/7
Let g = -6 - -9. Suppose -2*f = 4*k - 12, f + g*f = -k + 3. Factor f + 0*p + 0*p**3 - 1/3*p**2 + 1/3*p**4.
p**2*(p - 1)*(p + 1)/3
Let w(b) = 24*b**3 - 36*b**2 + 16*b. Let p(u) = -u**3 + u**2. Let v(n) = 20*p(n) + w(n). Factor v(t).
4*t*(t - 2)**2
Suppose 0*j**4 - 88 + j**4 - 2*j**2 + 89 = 0. What is j?
-1, 1
Let v be ((-5)/10)/((-1)/(-14)). Let w = -4 - v. Factor 2*l**3 - 4*l**w + 4*l**3.
2*l**3
Let j(y) be the third derivative of -y**5/90 - y**4/12 - 5*y**2. Factor j(d).
-2*d*(d + 3)/3
Let j(x) be the first derivative of -4*x**5/5 + 11*x**4 - 60*x**3 + 162*x**2 - 216*x - 52. Factor j(d).
-4*(d - 3)**3*(d - 2)
Let a = 14 - 9. Let m(k) = 22*k**2 - k - 5. Let j(q) = -21*q**2 + 6. Let s(x) = a*j(x) + 6*m(x). Factor s(p).
3*p*(9*p - 2)
Suppose 13 - 3 = 5*f. Let n(b) be the third derivative of -f*b**2 - 1/105*b**7 + 1/15*b**5 + 0*b**4 - 1/3*b**3 + 0 + 0*b + 0*b**6. Factor n(k).
-2*(k - 1)**2*(k + 1)**2
Let z(l) be the first derivative of l**6/6 + 3*l**5/5 + 25. Factor z(w).
w**4*(w + 3)
Let l(i) be the third derivative of 0*i**3 + 0*i**4 - i**2 + 0 + 1/1344*i**8 + 1/160*i**6 + 0*i + 1/280*i**7 + 1/240*i**5. Determine y, given that l(y) = 0.
-1, 0
Suppose -1/2*g**3 + 1/4*g**5 + 0*g**4 + 1/4*g + 0 + 0*g**2 = 0. Calculate g.
-1, 0, 1
Let l = -944 + 947. Let -3/2 - 9/2*y - 3/2*y**l - 9/2*y**2 = 0. What is y?
-1
Let r(g) be the second derivative of -g**5/60 - g**4/18 + 16*g. Factor r(i).
-i**2*(i + 2)/3
Determine c, given that -15*c - 25*c**2 - 12*c + 9*c**5 + c**2 - 6 + 30*c**4 + 18*c**3 = 0.
-2, -1, -1/3, 1
Let v(r) = r**3 - 3*r**2 + 3*r. Let w(n) = 1 - n**3 + n - 1 + n**2. Let t(q) = -v(q) + w(q). Factor t(l).
-2*l*(l - 1)**2
Let g(h) = -h**2 - 6*h - 5. Let w(o) = 3*o**2 + 24*o + 21. Let n(f) = 9*g(f) + 2*w(f). Determine a, given that n(a) = 0.
-1
Let 4/5*r**2 - 11/5*r + 6/5 + 1/5*r**3 = 0. Calculate r.
-6, 1
Let x(v) be the first derivative of 2*v**3/3 - 2*v**2/5 + 7. Factor x(y).
2*y*(5*y - 2)/5
Let d(s) = s**3 - 6*s**2 + 4*s + 7. Let c be d(5). Factor -j**3 + 32 - 3*j**c - 32 - 2*j.
-j*(j + 1)*(j + 2)
Let a(o) be the second derivative of -o**4/66 - 8*o**3/33 - 16*o**2/11 + 2*o. Factor a(t).
-2*(t + 4)**2/11
Let l(n) = 7*n**2 - 10*n - 5. Let w(o) = -o**2 + o + 1. Let g(h) = -3*l(h) - 24*w(h). Suppose g(y) = 0. What is y?
-3, 1
Let m(i) = -35*i - 171. Let y be m(-5). Suppose j + 15 = -3*d, 5*j - j - 20 = 4*d. Let 2/7*u**y + 2/7*u**2 + 0*u - 4/7*u**3 + j = 0. What is u?
0, 1
Let v(u) = -4*u**5 - 40*u**4 + 112*u**2 + 4*u - 72. Let k(r) = -3*r**5 - 27*r**4 + 75*r**2 + 3*r - 48. Let i(d) = -8*k(d) + 5*v(d). Suppose i(a) = 0. What is a?
-3, -2, -1, 1
Let p = -17 - -18. Let v be p*(-3 - 3/(-1)). Factor v + 0*c - 2/7*c**2.
-2*c**2/7
Suppose 101*l - 3 = 100*l. Determine g, given that -6*g**2 + 0 - 14/3*g**l - 4/3*g = 0.
-1, -2/7, 0
Let g(q) be the first derivative of 14*q**5/115 - q**4/23 - 14*q**3/69 + 2*q**2/23 - 56. What is s in g(s) = 0?
-1, 0, 2/7, 1
Let u(c) = -4*c**3 - 3*c**2 - 3*c - 4. Let o(t) = -3*t**3 - 3*t**2 - 3*t - 3. Let p(h) = 6*o(h) - 4*u(h). Find s such that p(s) = 0.
-1
Let o(n) = 1. Let k(w) = 2*w**2 - 4*w + 5. Let c(h) = -k(h) + 3*o(h). Let c(y) = 0. What is y?
1
Let k be ((-2)/1)/(75/(-60)). Factor k*z**2 + 2/5 - 2*z.
2*(z - 1)*(4*z - 1)/5
Let x(l) be the second derivative of l**6/30 - l**5/4 + 3*l**4/4 - 7*l**3/6 + l**2 + 11*l. Factor x(u).
(u - 2)*(u - 1)**3
Suppose 5 = 5*g - 5. Suppose 6*p - g*p = 12. What is d in -1/2*d**p + 0 - d**2 - 1/2*d = 0?
-1, 0
Let a(u) be the second derivative of 2/9*u**3 + 1/63*u**7 + 0*u**2 + 0 + 1/18*u**4 - 1/10*u**5 - 1/45*u**6 + u. Solve a(c) = 0 for c.
-1, 0, 1, 2
Suppose -z = -0*o - 3*o - 18, 5*z + 3*o = 0. Let s = 3 - z. Factor 1/5 + s*j - 1/5*j**2.
-(j - 1)*(j + 1)/5
Let b(l) be the second derivative of l**6/10 + 9*l**5/10 + 13*l**4/4 + 6*l**3 + 6*l**2 - 10*l. Factor b(w).
3*(w + 1)**2*(w + 2)**2
Let i(f) = 9*f**5 - 28*f**4 + 52*f**3 - 30*f**2 - 9*f + 10. Let o(v) = -v**5 - v**3 + v**2 + v - 1. Let t(z) = -i(z) - 4*o(z). Find q such that t(q) = 0.
-2/5, 1, 3
Let s(i) = -3*i**3 - 2*i**2 - i. Let u be s(-1). Suppose 3*n = u*n + 2. Factor 2/7*r**n + 0 + 4/7*r**3 + 0*r + 2/7*r**4.
2*r**2*(r + 1)**2/7
Let i(v) be the first derivative of -3*v**3/5 + v**2/2 + 4*v/5 + 26. Find o such that i(o) = 0.
-4/9, 1
What is x in -x**3 - 6*x**2 - 11*x**3 + x**2 + 20*x + 20 + 7*x**3 = 0?
-2, -1, 2
Suppose 0 = -2*o + 10, 18 = -s + 2*s + 3*o. Factor 10*f**3 - 5*f**4 - 12*f**3 + s*f**5 + 4*f**5.
f**3*(f - 1)*(7*f + 2)
Let c = -3 - -6. Factor -y + 3*y**c + 4*y - 6*y**2 + 2*y**2 - 2*y**2.
3*y*(y - 1)**2
Suppose -10*o = -0*o + 6*o. Factor -2/3*a**3 - 2/3*a**5 + 4/9*a + 2/3*a**2 - 14/9*a**4 + o.
-2*a*(a + 1)**3*(3*a - 2)/9
Let k = 5 - 3. Suppose -2*v + v**2 - v**3 - 1 + v + k*v**3 = 0. What is v?
-1, 1
Factor 5/2*a**2 + 10 + 25/2*a.
5*(a + 1)*(a + 4)/2
Let i be (0 - 3)/((-18)/12). Factor -3*n**4 + 4*n + 6*n**3 - 10*n**2 + i*n**3 + n**4.
-2*n*(n - 2)*(n - 1)**2
Suppose -3 = s, -2*d = 3*d + 4*s - 13. Factor -4*i**4 - i**d + 5*i**4 + 6*i**3 + 3*i**5 + 2*i**2 + 5*i**4.
2*i**2*(i + 1)**3
Let t = -6 - -8. Suppose 4 + 11 = -2*s + 5*w, -2*s - 4*w = -12. Find j such that s + 2/5*j - 2/5*j**t = 0.
0, 1
Let r(f) be the third derivative of -f**6/40 - f**5/15 - f**4/24 + 6*f**2. Factor r(c).
-c*(c + 1)*(3*c + 1)
Let s(g) be the first derivative of 5*g**4/4 + 20*g**3/3 + 25*g**2/2 + 10*g + 18. Factor s(m).
5*(m + 1)**2*(m + 2)
Let p(u) be the first derivative of 3 + 1/6*u**6 + 0*u**2 + 0*u**3 + 0*u - 2/5*u**5 + 1/4*u**4. Factor p(d).
d**3*(d - 1)**2
Facto