 1
Let i = -115 + 119. Let t(w) be the third derivative of -3*w**2 + 0*w + 1/60*w**5 - 1/24*w**i - 1/3*w**3 + 0. Factor t(o).
(o - 2)*(o + 1)
Let u be ((-2)/(-6))/((-2)/12). Let k be (-4)/63 + u/(-7). Factor 0 - k*y**2 + 2/9*y.
-2*y*(y - 1)/9
Let c(n) be the second derivative of -n**4/3 + 2*n**3/3 - 19*n. Let z = 2 - -3. Let f(r) = 3*r**2 - 3*r. Let v(g) = z*c(g) + 7*f(g). Factor v(o).
o*(o - 1)
Let v(l) be the first derivative of 3*l**4/8 - l**3/2 + 3. Solve v(m) = 0 for m.
0, 1
Let w(r) be the second derivative of r**5/10 + 2*r**4/3 + 4*r**3/3 - 27*r. What is j in w(j) = 0?
-2, 0
Let p(s) be the third derivative of s**6/120 - s**5/30 - s**4/24 + s**3/3 + 7*s**2. Determine k so that p(k) = 0.
-1, 1, 2
Factor 3/2*b**2 + 6*b + 6.
3*(b + 2)**2/2
Suppose -r = 2*r - 12, 4*n - 2*r - 28 = 0. Let j = 9 - n. Determine d so that -4*d**2 - 2*d**3 - 4*d + j*d**2 + 2*d = 0.
-1, 0
Let x(c) be the third derivative of c**8/70560 - c**6/2520 + c**5/20 + 3*c**2. Let h(a) be the third derivative of x(a). Suppose h(g) = 0. What is g?
-1, 1
Factor -15*a**2 - 4 - 27*a**3 + 3 + 27*a + 21*a**4 - 1 - 4.
3*(a - 1)**2*(a + 1)*(7*a - 2)
Let i(d) = -2*d - 2. Let r be i(-2). Let b(l) = l**2 + 6*l + 3. Let v be b(-6). Solve -4*s**2 + v*s**2 + s**r + s**3 - s = 0.
-1, 0, 1
Let p(g) be the first derivative of 2*g**5/5 - 4*g**4/3 + 2*g**3/9 + 8*g**2/3 - 8*g/3 - 9. Find r, given that p(r) = 0.
-1, 2/3, 1, 2
Let f = 1376/15 - 274/3. Let t = 0 + 0. Solve 0*x + f*x**3 + 4/5*x**4 + 2/5*x**5 + t*x**2 + 0 = 0 for x.
-1, 0
Let v(f) = -f**5 + 5*f**4 - 4*f**3 + 5*f**2. Let t(q) = 2*q**5 - 8*q**4 + 6*q**3 - 8*q**2. Let g = 4 - -1. Let s(z) = g*t(z) + 8*v(z). Factor s(o).
2*o**3*(o - 1)*(o + 1)
Let u(w) be the third derivative of -1/480*w**6 + 1/96*w**4 + 0*w + 1/24*w**3 - 3*w**2 - 1/240*w**5 + 0. Determine c so that u(c) = 0.
-1, 1
Let t(j) be the second derivative of j**6/20 + 3*j**5/20 - j**4/2 - j**3/2 + 9*j**2/4 + 12*j. What is m in t(m) = 0?
-3, -1, 1
Let p(l) = -2*l**2 + 12*l + 2. Let v(s) = -4*s**2 + 25*s + 5. Let z(c) = 13*p(c) - 6*v(c). Factor z(r).
-2*(r - 2)*(r - 1)
Factor -8/3*r + 0 + 4/9*r**2.
4*r*(r - 6)/9
Let d = -121 - -124. Solve 8/9 + 0*z - 2/9*z**d - 2/3*z**2 = 0.
-2, 1
Let y(q) be the third derivative of q**5/100 + q**4/10 + 3*q**3/10 - q**2. Factor y(k).
3*(k + 1)*(k + 3)/5
Let i(j) be the second derivative of 0 - 1/18*j**3 + 0*j**2 + 1/72*j**4 - 2*j. Factor i(y).
y*(y - 2)/6
Let r(k) be the third derivative of 1/240*k**6 + 1/48*k**4 + 0*k**3 + 0*k + 0 + 1/60*k**5 + k**2. Factor r(v).
v*(v + 1)**2/2
Solve -2*w**2 + 2*w**5 + 6*w**3 - 4*w**4 - 4*w**4 + 2*w**4 = 0 for w.
0, 1
Suppose 0 = k - 5*k + 24. Factor k - f**2 - 6 + f.
-f*(f - 1)
Let p(g) = g**3 - g**2 + 1. Let s(k) = -3*k**4 - 13*k**3 - k**2 - 4. Let x(n) = 5*p(n) + s(n). Solve x(d) = 0 for d.
-1, 1/3
Let c(i) = 12*i**4 + 6*i**3 - 12*i**2 - 22*i - 2. Let t(s) = -s**4 - s**3 + s. Let y(j) = 2*c(j) + 28*t(j). Let y(u) = 0. Calculate u.
-1
Let j(d) = 0*d**2 - 9 - 4*d**2 - 6*d**2 - 10*d. Let i(f) = -f**2 - f - 1. Let k(z) = 18*i(z) - 2*j(z). Suppose k(t) = 0. Calculate t.
-1, 0
Let z = 3 - 1. Let 2*y**3 - y**3 - z*y**4 + y**4 = 0. Calculate y.
0, 1
Suppose -8 - 23*v**3 + 12*v**2 + 7*v**3 + 10*v**3 + 10*v**3 - 4*v - 4*v**4 = 0. Calculate v.
-1, 1, 2
Let z(n) be the third derivative of n**10/151200 + n**9/20160 + n**8/6720 + n**7/5040 + n**5/30 + 3*n**2. Let h(m) be the third derivative of z(m). Factor h(o).
o*(o + 1)**3
Let z(o) = 3*o + 0*o + 2*o**2 + o. Suppose 4 = -0*q + 2*q. Let f(j) = -10*j**2 - 21*j. Let a(k) = q*f(k) + 11*z(k). Factor a(r).
2*r*(r + 1)
Let h(p) be the third derivative of -49*p**6/40 + 63*p**5/10 - 15*p**4/2 + 4*p**3 + 9*p**2. Solve h(y) = 0 for y.
2/7, 2
Let h(b) be the second derivative of 7*b**6/90 + b**5/12 - b**4/4 - 5*b**3/18 + b**2/3 + 11*b. Factor h(l).
(l - 1)*(l + 1)**2*(7*l - 2)/3
Factor -2*z**2 + z**4 - 2*z**3 + z - 8 + 2 + 7 + z**5.
(z - 1)**2*(z + 1)**3
Factor 8/3 - 8/3*z + 2/3*z**2.
2*(z - 2)**2/3
Suppose -7 - 9 = -4*o. Let b be 3 - (1 + (-678)/o). Factor b*l**5 - 67*l**2 + 196*l**4 + 34*l - 161/2*l**3 - 4.
(l + 1)**2*(7*l - 2)**3/2
Let t = 2 + 0. Let p be (-2)/2*(-2 - t). Suppose 2*f**4 + 6*f - 14*f**3 + 0*f**4 - 6*f**2 - 8*f**p + 4 = 0. Calculate f.
-1, 2/3
Let s(t) be the second derivative of -t**7/5040 - t**6/1440 - t**4/4 - 3*t. Let a(v) be the third derivative of s(v). Factor a(i).
-i*(i + 1)/2
Factor 2*q**3 - 4*q**3 - 3*q**2 - q**3 + 0*q**2.
-3*q**2*(q + 1)
Suppose q - 3*q = -8. Suppose -3 = -q*m + 3*m. Suppose -m*c - 1 + 4*c - c**2 - 3*c = 0. What is c?
-1
Let a(i) be the second derivative of -i**8/13440 + i**7/2520 + i**4/6 + 4*i. Let n(v) be the third derivative of a(v). Solve n(o) = 0 for o.
0, 2
Suppose -3*s = 4*s + s. Suppose s*z + 2/13*z**2 - 2/13 = 0. What is z?
-1, 1
Let s(d) be the second derivative of 1/10*d**5 + 1/15*d**6 - 5*d + 0 - 1/3*d**3 - 1/6*d**4 + 0*d**2. Factor s(j).
2*j*(j - 1)*(j + 1)**2
Let u(y) = 2*y + 11. Let d be u(-3). Let l(c) be the first derivative of -c**2 + 2*c - 1 - 4/3*c**3 + 2/5*c**d - 1/3*c**6 + c**4. Suppose l(w) = 0. Calculate w.
-1, 1
Let o(j) be the second derivative of -1/6*j**4 + 4/105*j**6 - 2*j + 0 + 11/21*j**3 - 11/70*j**5 + 3/7*j**2. Determine r, given that o(r) = 0.
-1, -1/4, 1, 3
Let t be (-325)/(-78) + (-2)/(-6). Let o(q) be the first derivative of t*q**4 + 14/3*q**3 + 0*q - 1 - 2*q**2. Factor o(r).
2*r*(r + 1)*(9*r - 2)
Factor 2*g**3 + 0*g**3 - g - 2*g**2 - g**3 + 2*g.
g*(g - 1)**2
Factor 0 - 2/5*x - 4/5*x**2 - 2/5*x**3.
-2*x*(x + 1)**2/5
Let o = 12 + -12. Find m such that -3*m**4 + 2*m + 3*m**4 + o*m**4 + 4*m**4 - 6*m**3 = 0.
-1/2, 0, 1
Let k(a) = a**2 + 8*a + 2. Let m be k(-8). Let -t**3 - 5*t**m - t - 4 - t - 6*t = 0. What is t?
-2, -1
Let u be (3 - (-212)/(-60))*12/(-16). Solve 2/5*q**4 + 6/5*q**2 + 6/5*q**3 + 0 + u*q = 0 for q.
-1, 0
Let z be (2/(-3))/((-442)/3). Let w = 437/1105 + z. Factor -w*s**2 - 4/5 - 6/5*s.
-2*(s + 1)*(s + 2)/5
Let b(s) be the first derivative of -7*s**3/2 + 3*s**2/4 + 20. Factor b(t).
-3*t*(7*t - 1)/2
Let w = -127 + 130. Let u(p) be the first derivative of -1/16*p**4 + 0*p - 1/4*p**w - 1 - 1/4*p**2. Factor u(f).
-f*(f + 1)*(f + 2)/4
Let f = -13 - -15. Let b be 1 - f*(-5)/6. What is x in 8/3*x + b + 2/3*x**2 = 0?
-2
Solve -4/11 - 4/11*c**4 + 10/11*c - 20/11*c**3 + 8/11*c**2 + 10/11*c**5 = 0.
-1, 2/5, 1
Let j(a) be the third derivative of 0*a + 0 + 1/300*a**6 + 2*a**2 + 1/300*a**5 - 1/30*a**3 - 1/60*a**4. Solve j(m) = 0.
-1, -1/2, 1
Let z(g) be the second derivative of -g**6/105 + g**4/7 + 8*g**3/21 + 3*g**2/7 + 4*g. Find t such that z(t) = 0.
-1, 3
Let m(z) be the second derivative of -z**6/150 + 2*z**5/25 - z**4/4 - 4*z**3/15 + 8*z**2/5 + 18*z. Factor m(o).
-(o - 4)**2*(o - 1)*(o + 1)/5
Let k(y) be the third derivative of -y**8/10080 + y**7/3780 + y**6/540 - 5*y**4/24 - 2*y**2. Let p(s) be the second derivative of k(s). Factor p(r).
-2*r*(r - 2)*(r + 1)/3
Let k(y) be the first derivative of -3*y**5/5 - 27*y**4/4 - 21*y**3 - 57*y**2/2 - 18*y + 47. Factor k(q).
-3*(q + 1)**3*(q + 6)
Suppose -9*c**4 - 12*c**4 + 42*c**3 + 12 - 16*c**2 + 36*c**3 + 12*c - 65*c**2 = 0. Calculate c.
-2/7, 1, 2
Let q(b) be the second derivative of b**7/231 - 4*b**6/165 + 2*b**5/55 - 23*b. Factor q(t).
2*t**3*(t - 2)**2/11
Let a be 0/(((-8)/4)/4*-2). Factor 1/5*t**2 + 1/5*t + a.
t*(t + 1)/5
Let z(p) be the second derivative of -p**9/1512 - p**8/560 + p**6/360 - 2*p**3/3 - 4*p. Let h(j) be the second derivative of z(j). Solve h(b) = 0 for b.
-1, 0, 1/2
Let n = 4 - 2. Let a(l) = -l**3 - 2*l**2 + l - 2. Let t be a(-3). Factor -4 + o + 6*o**4 - 4*o**2 + n + 0*o**5 + 2*o**5 - 7*o + t*o**3.
2*(o - 1)*(o + 1)**4
Suppose -4*f = 4 - 12. Let 2*i + 4*i**4 - i**4 - f*i**4 - 3*i**2 = 0. Calculate i.
-2, 0, 1
Let k(p) = -15*p**3 + 6*p**2 + 3*p. Suppose -4*a + 4 = -0. Let j(l) = l. Let h(f) = a*k(f) - 3*j(f). Solve h(x) = 0 for x.
0, 2/5
Let l = 17 + -15. Let r(t) be the third derivative of -l*t**2 - 1/3*t**3 - 1/6*t**4 + 0*t + 0 - 1/30*t**5. Factor r(k).
-2*(k + 1)**2
Let y = 4 + -2. Solve -6*r**3 + r + 4*r - 4*r**4 - 3*r - 4*r**y - 3*r - r**5 = 0 for r.
-1, 0
Suppose -3*m - 6 = -18. Suppose 4 - m - 6*w + 2*w**3 - 4 = 0. Calculate w.
-1, 2
Suppose 0*u - 5*u = 0. Let r(j) be the second derivative of -1/60*j**6 + 1/40*j**5 - 1/84*