-1, 0, 1
Let y(b) = b**3 - b. Suppose -2 = z - 3*z. Let m(i) = -3*i**3 + 3*i. Suppose -3*k = 4*s - 35, 4*k + 4*s + 7 = 47. Let l(r) = k*y(r) + z*m(r). Factor l(a).
2*a*(a - 1)*(a + 1)
Suppose 2*z + 4 = 3*z. Let r(f) be the second derivative of f - 1/21*f**3 + 0*f**2 + 0 + 1/42*f**z. Factor r(b).
2*b*(b - 1)/7
Let j(o) = -o**3 + 3. Let s be j(0). Factor 1/2*u**s + 0*u**2 + 0*u - 5/4*u**4 + 0.
-u**3*(5*u - 2)/4
Let i(n) = n**2 + n + 1. Let o(m) = -m - 3. Let c be o(-4). Let q(u) = 6*u**2 + 8*u + 7. Let b(j) = c*q(j) - 5*i(j). Determine d so that b(d) = 0.
-2, -1
Let m(d) be the third derivative of -d**6/24 + d**5/3 - 2*d**2 - 14*d. Find c, given that m(c) = 0.
0, 4
Let u = 165 - 823/5. Let -1/5*i**5 + 3/5*i**3 + 1/5*i**2 - u*i - 1/5*i**4 + 0 = 0. Calculate i.
-2, -1, 0, 1
Let z(p) be the third derivative of -p**8/336 - 2*p**7/105 - p**6/30 + 20*p**2. Determine d so that z(d) = 0.
-2, 0
Let t(k) = -6*k**4 - 4*k**3 + 34*k**2 - 32*k. Let r(i) = i**4 - i**3 - i**2 + i + 1. Let a be (-4)/(-3)*(7 - 1). Let n(y) = a*r(y) + t(y). Factor n(d).
2*(d - 2)**2*(d - 1)**2
Let d(z) be the second derivative of z**7/336 + z**6/240 - 3*z**5/40 - 7*z**4/24 - z**3/3 - 37*z. Find f, given that d(f) = 0.
-2, -1, 0, 4
Let y(x) = 5*x**3 + 85*x**2 - 195*x + 95. Let v(d) = 3*d**3 + 42*d**2 - 97*d + 48. Let j(f) = -5*v(f) + 2*y(f). Factor j(n).
-5*(n - 1)**2*(n + 10)
Let j(p) = p**2 + 15*p - 13. Let y be j(-16). Let n(k) be the first derivative of 2 - 1/3*k**2 + 2/9*k**y + 2/9*k - 1/18*k**4. Solve n(c) = 0 for c.
1
Factor -4/3*u + 0 + 2/3*u**2.
2*u*(u - 2)/3
Let h(s) = 10*s**3 - 10*s**2 - 50*s - 25. Let t(y) = -5*y**3 + 5*y**2 + 25*y + 13. Let d(w) = -2*h(w) - 5*t(w). Factor d(a).
5*(a - 3)*(a + 1)**2
Let w(j) be the third derivative of -j**6/200 + 3*j**5/100 + j**4/10 - 42*j**2. Let w(a) = 0. What is a?
-1, 0, 4
Let p(n) = 5*n**2 + n. Let l be p(-1). Let 3*j + j**l - 2 + 9*j + 15*j**3 - 7*j**4 + 5*j**3 - 24*j**2 = 0. What is j?
1/3, 1
Let l(h) be the first derivative of -h**3/3 - 2*h**2 - 4*h - 3. What is d in l(d) = 0?
-2
Let v(m) = 5*m**2 + 2*m. Let d(u) = 11*u**2 + 5*u. Let r(n) = -4*d(n) + 9*v(n). Let r(k) = 0. What is k?
0, 2
Let b(x) be the third derivative of -x**5/12 - 5*x**4/24 + 5*x**3/3 - 22*x**2. Factor b(a).
-5*(a - 1)*(a + 2)
Let h(w) = w**2 - 9*w + 11. Let y be h(8). Suppose -3*v = -9 + y. Solve 6*k**2 - 3*k - v*k**2 + 1 - 2*k**2 = 0.
1/2, 1
Let k be 10/4*360/225. Factor 0*y**k + 16/3*y + 0*y**2 + 0 - 8/3*y**3 + 1/3*y**5.
y*(y - 2)**2*(y + 2)**2/3
Factor -c**4 + 3*c**4 - c**5 - 1 + 2*c**3 + 3 - c - 4*c**2.
-(c - 2)*(c - 1)**2*(c + 1)**2
Let b(i) = 2*i**5 + 6*i**4 - 4*i**3 - i. Let m = 2 + 0. Let l(t) = -t**5 - t**4 + t**3 - t**2 + t. Let z(k) = m*b(k) + 6*l(k). Determine r, given that z(r) = 0.
-1, 0, 1, 2
Let a(r) be the second derivative of -r**6/120 + r**4/16 - r**3/12 + 3*r. Factor a(m).
-m*(m - 1)**2*(m + 2)/4
Factor 1 + 5 + 2*u**2 - 8*u + 0*u.
2*(u - 3)*(u - 1)
Let j be (-1 + -1)*6/(-4). Factor -j*f**2 + f**2 + 2 + 4*f**2 - f - 3*f.
2*(f - 1)**2
Let j(t) be the first derivative of 2*t**6/15 - 4*t**5/25 - 2*t**4/5 - 70. Factor j(r).
4*r**3*(r - 2)*(r + 1)/5
Factor 1 - 5*y + y - 5*y - 4 - 9*y**2 - 3*y**3.
-3*(y + 1)**3
Let q(j) be the third derivative of -j**5/100 + 3*j**4/40 - j**3/5 + 5*j**2. Factor q(u).
-3*(u - 2)*(u - 1)/5
What is q in -1/5*q**2 + 12/5*q - 36/5 = 0?
6
Let g be 32/(-176) + (-16)/308*-9. Let 0*f - 2/7*f**4 - g*f**5 + 0*f**2 + 0 + 0*f**3 = 0. Calculate f.
-1, 0
Let m(j) be the second derivative of -j**5/20 + j**4/4 + 2*j**3/3 + 3*j**2/2 - 3*j. Let q be m(4). Factor -3*s - 2*s + 4*s**2 - s**3 + 5 - q.
-(s - 2)*(s - 1)**2
Let y(f) = -f. Let k be (-2)/7 + (-32)/(-14). Let b(q) = -5 + 2*q**2 + 5 - k*q. Let u(a) = b(a) - 4*y(a). Let u(o) = 0. What is o?
-1, 0
Let m(y) be the third derivative of y**10/680400 + y**9/136080 + y**8/90720 - y**5/30 - 5*y**2. Let u(r) be the third derivative of m(r). Factor u(d).
2*d**2*(d + 1)**2/9
Suppose 2*a - 2 = 4. Suppose -5*s + 3 + 6 = -d, -3*d = -3*s + a. Factor 6*n**2 + n**s - 7*n**2 + 3*n - 3*n**2.
-3*n*(n - 1)
Suppose 28 = 3*s - 4*o, 7*s = 2*s - 5*o + 105. Suppose 0 = -2*d - 2*d + s. Suppose -4*h**5 + h**d + h**4 + 2*h**4 + 2*h**5 - 2*h**3 = 0. Calculate h.
0, 1
Suppose 2*q - 4*u = -2*u - 2, 2*u = -4*q + 26. Suppose q*w = w. Find s such that 1/2*s**3 + w + 1/2*s**2 - 1/2*s**4 + 0*s - 1/2*s**5 = 0.
-1, 0, 1
Let s(q) = q + 13. Let t be s(-10). Suppose 1 = -y + t. Solve -9 + 3*l - 6*l**3 + 3*l**y + 9 = 0.
-1/2, 0, 1
Let h(s) be the third derivative of 2*s**2 + 0*s - 1/18*s**4 + 1/90*s**5 + 0*s**3 + 0. Find i such that h(i) = 0.
0, 2
Let o be (-730)/(-560) - 3/(-24). Factor o*f + 8/7*f**2 + 2/7.
2*(f + 1)*(4*f + 1)/7
Let o = -35787706/1505 + 118894/5. Let t = -2/301 - o. Factor t*c**2 - 2/5*c**3 + 0*c + 0.
-2*c**2*(c - 1)/5
Let h = 160 - 156. Factor 2*t**2 + 24/13*t + 8/13 + 12/13*t**3 + 2/13*t**h.
2*(t + 1)**2*(t + 2)**2/13
Let a(v) be the first derivative of -7*v**4/6 - 22*v**3/3 - 6*v**2 + 16*v/3 + 18. Factor a(r).
-2*(r + 1)*(r + 4)*(7*r - 2)/3
Let f be 1*-3*(-4)/6. Let s be f/4 - 18/(-4). Find l, given that -l**3 - 5*l**2 - l**4 + s*l**2 = 0.
-1, 0
Let z(s) be the first derivative of -s**4/14 - 10*s**3/21 - 8*s**2/7 - 8*s/7 - 1. Find o such that z(o) = 0.
-2, -1
Let u(c) be the second derivative of -c**5/50 + 2*c**4/5 - 12*c**3/5 - 26*c. Let u(z) = 0. What is z?
0, 6
Let w(f) be the third derivative of -f**8/2688 - f**7/420 - f**6/240 + f**5/240 + 5*f**4/192 + f**3/24 - 17*f**2. What is s in w(s) = 0?
-2, -1, 1
Let s be 10/(-45) - (-50)/(-45) - -2. Factor s - 2/3*n**2 - 1/3*n + 1/3*n**3.
(n - 2)*(n - 1)*(n + 1)/3
Let f(s) = 2*s**2 + 2*s + 3. Let m(i) = -i**2 - i - 2. Let w(y) = 4*f(y) + 6*m(y). Factor w(u).
2*u*(u + 1)
Let v = -566/9 + 5416/99. Let p = v - -652/77. Factor -2/7*b - p + 10/7*b**2 - 6/7*b**3.
-2*(b - 1)**2*(3*b + 1)/7
Let i(n) be the second derivative of -n**4/4 - n**3 + 9*n**2/2 - 5*n. Let i(d) = 0. Calculate d.
-3, 1
Let w(p) = p**5 + p**3 - p + 1. Let a(t) = 18*t**5 - 80*t**4 + 52*t**3 - 20*t**2 + 16*t - 14. Let r(m) = -2*a(m) - 28*w(m). Factor r(l).
-4*l*(l - 1)**2*(4*l - 1)**2
Let a(n) = 3*n**3 + n**2. Let x(b) = 7*b**3 + b**2 - b. Let v(j) = 5*a(j) - 2*x(j). Determine t, given that v(t) = 0.
-2, -1, 0
Let p(j) = -j**2 - 9*j - 18. Let v be p(-5). What is n in 9/4*n**v + 0 - 3/2*n = 0?
0, 2/3
Let k(l) be the first derivative of -1/6*l**3 + 3*l + 1/6*l**2 + 1/20*l**5 + 2 - 1/36*l**4. Let x(f) be the first derivative of k(f). Factor x(z).
(z - 1)*(z + 1)*(3*z - 1)/3
Let n(j) be the second derivative of 0*j**4 - 2*j + 0 + 3/2*j**2 - 1/40*j**6 - 1/20*j**5 + 0*j**3. Let h(p) be the first derivative of n(p). Factor h(r).
-3*r**2*(r + 1)
Suppose 4*f = 5*b + 17 - 0, -19 = -5*f + 4*b. Factor 22*j**3 + j**2 - 23*j**f - 4*j + 2*j + 4*j.
-j*(j - 2)*(j + 1)
Factor -25*c**4 + 0*c**2 + 17*c**4 - 4*c**2 - 2*c**5 - 10*c**3.
-2*c**2*(c + 1)**2*(c + 2)
Suppose f + 2*f = 3. Let h = -11 + 7. Let l(n) = -n**2 + n - 1. Let z(t) = t**2 + 3*t - 4. Let u(v) = f*z(v) + h*l(v). Determine k so that u(k) = 0.
0, 1/5
Let b = 45 + -26. Factor 10*x + 13*x**4 + 7*x**2 + 4*x**5 + 10*x + 15*x**3 - b*x.
x*(x + 1)**3*(4*x + 1)
Let f(p) = -p**2 + 7*p + 9. Let r be f(8). Suppose -a + 0*a = -r. Solve -1 + 2*g**2 - 8*g + 11*g - a = 0 for g.
-2, 1/2
Factor 5 - 21*x + 0*x**3 + 5*x + 10*x**2 - 2*x**3 + 3.
-2*(x - 2)**2*(x - 1)
Let q(n) be the first derivative of 0*n**4 - 1/25*n**5 + 2 + 0*n + 0*n**2 + 1/15*n**3. Find h such that q(h) = 0.
-1, 0, 1
Let v be 5/(-10) - (-21)/18. Solve v - 8/3*w**3 + 2/3*w**4 - 8/3*w + 4*w**2 = 0.
1
Factor 51*d**2 - 79*d**2 + 12 + 20*d - 4.
-4*(d - 1)*(7*d + 2)
Let u(b) be the first derivative of -b**7/525 + b**6/150 + b**5/150 - b**4/30 - b**2 - 6. Let d(m) be the second derivative of u(m). Factor d(k).
-2*k*(k - 2)*(k - 1)*(k + 1)/5
Let a(z) be the second derivative of -z**4/28 - 3*z**3/14 - 3*z**2/7 - z. Factor a(y).
-3*(y + 1)*(y + 2)/7
Let w(c) be the first derivative of c**7/2940 - c**5/420 - c**3 - 1. Let p(a) be the third derivative of w(a). Factor p(i).
2*i*(i - 1)*(i + 1)/7
Let s = 65/96 + -1/96. Factor -1/2*p**2 - s*p + 2/3*p**3 + 2/3 - 1/6*p**4.
-(p - 2)**2*(p - 1)*(p + 1)/6
Let c(v) = -v**3 + v**2 - v. Let z(h) = -h**5 - 5*h**3 + 6*h**2 - 6*h. Let n(t) = 6*c(t) - z(t). Suppose n