 Factor o(k).
-3*k*(k + 10)/7
Factor 1/2 + 0*r - 1/2*r**2.
-(r - 1)*(r + 1)/2
Let p(l) be the first derivative of l**6/30 + l**5/20 - l**4/12 - l**3/6 + l + 1. Let u(d) be the first derivative of p(d). Let u(n) = 0. Calculate n.
-1, 0, 1
Let p(w) = -12*w**4 - 5*w**3 - 9*w**2 + 8*w. Let g(c) = c**4 + c**2 - c. Suppose -2*l - 2*l = 96. Let t(f) = l*g(f) - 3*p(f). Factor t(i).
3*i**2*(i + 1)*(4*i + 1)
Let h(i) be the second derivative of 0*i**2 + 9*i + 0 + 1/42*i**7 - 1/20*i**5 - 1/30*i**6 + 0*i**3 + 1/12*i**4. Factor h(u).
u**2*(u - 1)**2*(u + 1)
Let l(z) be the first derivative of 2*z**3/27 + 7*z**2/9 - 15. Factor l(j).
2*j*(j + 7)/9
Let o(x) be the first derivative of 0*x**5 + 1/420*x**7 + x**2 - 3 + 0*x**4 + 0*x**3 + 0*x + 1/240*x**6. Let t(u) be the second derivative of o(u). Factor t(q).
q**3*(q + 1)/2
Suppose 2*k = 6*k - 8. Determine v so that 1/2 + 1/6*v**k - 2/3*v = 0.
1, 3
Let g(n) = 2*n**4 - n**3 + 5*n**2 - 4*n - 7. Let r(y) = 3*y**4 + y**2 - 3 + y**2 - 2*y + y**4 - 3*y**4. Let w(l) = -2*g(l) + 5*r(l). Let w(j) = 0. What is j?
-1, 1
Let b(l) be the first derivative of -l + 1/10*l**5 - 1/30*l**6 - 1 + 1/12*l**4 - 1/3*l**3 + 0*l**2. Let h(s) be the first derivative of b(s). Factor h(m).
-m*(m - 2)*(m - 1)*(m + 1)
Let v(g) = -75*g**4 - 141*g**3 - 78*g**2 - 18*g + 6. Let h(c) = -c**3 - c**2 - c + 1. Let f(o) = -6*h(o) + v(o). Factor f(q).
-3*q*(q + 1)*(5*q + 2)**2
Let w(l) = -4*l**4 + 8*l**3 + 4*l**2 - 4*l - 2. Let d(q) = -q**5. Let s(n) = 2*d(n) + w(n). Let z(a) = -a + 1. Let t(v) = -s(v) - 2*z(v). What is m in t(m) = 0?
-3, -1, 0, 1
Let x = 169/2 + -83. Let n(g) be the first derivative of -1 + 1/2*g + 1/5*g**5 + x*g**3 + 7/8*g**4 + 5/4*g**2. Factor n(p).
(p + 1)**3*(2*p + 1)/2
Let g(t) be the third derivative of 1/150*t**5 + 0*t**3 + 0*t**4 + 0 + 1/1050*t**7 + 0*t - 4*t**2 - 1/200*t**6. Solve g(w) = 0.
0, 1, 2
Let t(d) = d + 7. Let j(h) = -h + 2. Let y be j(5). Let w be t(y). Let 38*z**2 - 126*z**4 + 26*z**w + 115*z**3 - 125*z**5 - 16*z + 8 - 28*z = 0. What is z?
-1, 2/5
Let d = 0 - 3. Let v be 0/((2 - 0) + d). Factor -2/5*t**5 + v*t + 0*t**2 - 4/5*t**4 + 0 - 2/5*t**3.
-2*t**3*(t + 1)**2/5
Let j(f) be the third derivative of -f**11/332640 - f**5/20 - 3*f**2. Let v(q) be the third derivative of j(q). Determine w, given that v(w) = 0.
0
Let a = 26 + -86/3. Let d = a - -3. Find u, given that 2/3*u - 1/3 - d*u**2 = 0.
1
Suppose 3*c = -3*d, 5*c - 5 = -4*d - 3. Suppose -j**c + 2*j**3 - 2*j + j**4 - 5 + 5 = 0. What is j?
-2, -1, 0, 1
Let d = -1/1108 + 8877/14404. Factor 0 - d*g - 2/13*g**3 - 8/13*g**2.
-2*g*(g + 2)**2/13
Factor -9*p - 81/2 - 1/2*p**2.
-(p + 9)**2/2
Let s(o) be the second derivative of o**6/1080 - o**5/90 + o**4/18 + o**3/2 + o. Let u(b) be the second derivative of s(b). Factor u(d).
(d - 2)**2/3
Let p(t) be the second derivative of t**5/210 - t**3/21 - t**2 - 2*t. Let q(j) be the first derivative of p(j). Suppose q(w) = 0. What is w?
-1, 1
Let o(y) = -78*y**2 + 12*y + 27. Let q(c) = 6*c**2 - c - 2. Suppose j = 2 - 4. Let m(r) = j*o(r) - 27*q(r). Factor m(g).
-3*g*(2*g - 1)
Let z = -696 + 698. Factor -i + 0 + 1/3*i**z.
i*(i - 3)/3
Let h(q) be the first derivative of 8*q**5/45 + q**4/2 + 4*q**3/27 + 15. Factor h(t).
2*t**2*(t + 2)*(4*t + 1)/9
What is x in -686/11*x**4 + 588/11*x**3 + 16/11*x - 168/11*x**2 + 0 = 0?
0, 2/7
Let k(n) be the second derivative of -n**4/4 - n**3 - 7*n. Factor k(f).
-3*f*(f + 2)
Let f(u) be the first derivative of u**4/6 + u**3/3 - 2*u**2 + 6*u + 2. Let y(v) be the first derivative of f(v). Factor y(c).
2*(c - 1)*(c + 2)
Let b(x) = -x + 12. Let k be b(9). What is d in -12*d**3 + 8*d**2 - 5*d + 5*d + 4*d**2 + k*d**4 = 0?
0, 2
Let j be (-1)/1 + -2 + 3. Let y(b) be the first derivative of 1/10*b**4 + 4/15*b**3 + j*b + 1/5*b**2 - 3. Let y(t) = 0. Calculate t.
-1, 0
Suppose -v - 2*x = 11, 5*v + 8 = -3*x - 19. Let s be (v - (-2)/(-6)) + 4. Factor s + 1/3*z - 1/3*z**2.
-(z - 2)*(z + 1)/3
Suppose -51 = -7*j - 23. Factor 7/5*h**j + 4*h**2 + 4/5*h + 23/5*h**3 + 0.
h*(h + 1)*(h + 2)*(7*h + 2)/5
Let k(g) be the first derivative of 4 + 1/18*g**4 + 2/27*g**3 - 2/9*g - 1/9*g**2. Determine w so that k(w) = 0.
-1, 1
Suppose 6 = 4*u - u. Factor 2*d**2 + d - 2*d**u - 3*d**2 - 4*d**3.
-d*(d + 1)*(4*d - 1)
Let f = 9 - 13. Let a = f + 4. Factor a*u**2 + 0*u**2 - 12*u**4 + 6*u**3 + 9*u**5 - 3*u**4.
3*u**3*(u - 1)*(3*u - 2)
Determine x, given that -x**2 - 2*x + 0*x**3 + 2*x**3 + 0*x - x**3 = 0.
-1, 0, 2
Let 15/2 - 25/4*z - 5/4*z**2 = 0. What is z?
-6, 1
Suppose -17*a = -v - 16*a + 6, 2*v = -4*a - 12. Factor 4/5*m - 2*m**v + 8/5*m**3 - 2/5*m**4 + 0.
-2*m*(m - 2)*(m - 1)**2/5
Let j = 61/2 - 365/12. Let t(z) be the first derivative of -1/4*z - 4 - j*z**3 - 1/4*z**2. Solve t(k) = 0 for k.
-1
Let i(f) = 3*f**2 - 2*f**2 + 0*f**3 - 2*f + 3*f**2 - 4 + f**3. Let z be i(-4). Suppose 80/7*w**3 - 32/7*w**z - 34/7*w**2 + 4/7*w + 0 = 0. What is w?
0, 1/4, 2
Suppose -4*m = -2*m - 10. Suppose 0 = t - 0*t - m. Factor 0*w**2 + w**4 + 0*w + 0 - 1/2*w**3 - 1/2*w**t.
-w**3*(w - 1)**2/2
Suppose -2*g + 3*g + 4*g = 0. Factor r**3 - 2/3*r**2 - 1/3*r**4 + 0 + g*r.
-r**2*(r - 2)*(r - 1)/3
Let b = -4 + 8. Suppose b*d - 6*d - 6 = 3*y, y = -5*d + 11. Let o**2 + 0*o**3 + o**3 + 0*o**d = 0. Calculate o.
-1, 0
Let o(d) be the second derivative of -d**6/105 - 2*d**5/35 - d**4/14 + 4*d**3/21 + 4*d**2/7 + d. Solve o(v) = 0 for v.
-2, -1, 1
Factor -3 - 43*u + 3*u**2 - 3 + 46*u.
3*(u - 1)*(u + 2)
Let m(l) = 3*l**2 + 3*l - 6. Let h(r) = 15*r**2 + 15*r - 30. Suppose x + 3 = 5*j, -5*x + 0*j - 5*j + 15 = 0. Let c(i) = x*h(i) - 11*m(i). Factor c(w).
-3*(w - 1)*(w + 2)
Let x(z) be the first derivative of -2*z**3/39 - z**2/13 + 15. Factor x(n).
-2*n*(n + 1)/13
Let v(w) be the second derivative of 1/9*w**3 + 0 + 1/12*w**4 + 1/60*w**5 + 0*w**2 + w. Factor v(p).
p*(p + 1)*(p + 2)/3
Let a be (1/(1/10))/2. Let y(h) = h**2 + 6*h + 3. Let n be y(-6). Suppose -f**4 + 2*f**2 + f**a - n*f**2 + 2*f**2 - f**3 = 0. Calculate f.
-1, 0, 1
Let t(z) be the third derivative of 7*z**6/40 - z**5/10 - 7*z**4/2 + 4*z**3 - 8*z**2. Factor t(r).
3*(r - 2)*(r + 2)*(7*r - 2)
Let c(w) be the second derivative of -w**5/100 - w**4/20 - w**3/10 - w**2/10 + 6*w. Suppose c(o) = 0. Calculate o.
-1
Let v(y) be the third derivative of 1/350*y**7 + 0*y + 0*y**4 + 0*y**5 + 0 - 5*y**2 - 1/200*y**6 + 0*y**3. Factor v(g).
3*g**3*(g - 1)/5
What is o in 5/3*o + 2 + 1/3*o**2 = 0?
-3, -2
Let q(o) = -3*o**4 - o**3 + o**2 + o. Let b(j) = -13*j**4 - 3*j**3 + 5*j**2 + 3*j - 1. Let x(p) = 2*b(p) - 9*q(p). Factor x(z).
(z - 1)*(z + 1)**2*(z + 2)
Let j be (-2)/((-2)/(-5)*-1). Factor 0 + 1/4*p + 3/2*p**3 + 1/4*p**j + p**2 + p**4.
p*(p + 1)**4/4
Let m(y) be the third derivative of -y**7/105 - y**6/60 + y**5/10 + y**4/12 - 2*y**3/3 - 7*y**2. Factor m(o).
-2*(o - 1)**2*(o + 1)*(o + 2)
Factor 2*z**4 + 2/3*z**5 - 2*z - 2/3 - 4/3*z**2 + 4/3*z**3.
2*(z - 1)*(z + 1)**4/3
Determine d, given that 54/7*d**2 - 3/7*d**3 - 600/7 - 180/7*d = 0.
-2, 10
Let v(t) = -t**3 + t + 1. Let h(j) = 7*j**3 - j**2 - 4*j - 3. Let s(o) = h(o) + 4*v(o). Let n be s(1). Factor 0*k**2 + 1 - n*k + k**2 + 5*k.
(k + 1)**2
Let q(s) be the third derivative of s**8/40320 - s**5/30 + 3*s**2. Let z(a) be the third derivative of q(a). Factor z(f).
f**2/2
Let i(m) = -m**5 - 41*m**4 + 120*m**3 - 89*m**2 - 7*m. Let s(q) = -q**5 - 27*q**4 + 80*q**3 - 59*q**2 - 5*q. Let k(a) = 5*i(a) - 7*s(a). Factor k(g).
2*g**2*(g - 4)*(g - 2)**2
Let g(h) be the first derivative of h**6/30 - h**4/12 + 4*h + 3. Let l(i) be the first derivative of g(i). Determine q so that l(q) = 0.
-1, 0, 1
Let h(q) be the second derivative of -q**4/24 + q**3/2 - 9*q**2/4 + 8*q. Factor h(o).
-(o - 3)**2/2
Let q be (-45)/(-35) - (-2)/(-7). Let r = 2 + q. Determine h so that 0*h**4 - 5*h**5 + 2*h**4 - 2*h**2 + 8*h**3 - r*h**3 = 0.
-1, 0, 2/5, 1
Let t(y) be the second derivative of -y**6/180 + y**5/60 + y**3/2 + 2*y. Let n(u) be the second derivative of t(u). Solve n(s) = 0.
0, 1
Let r(t) = -3*t**5 + 17*t**3 - 10*t**2 - 2*t + 2. Let n(f) = -8*f**5 + 52*f**3 - 30*f**2 - 7*f + 7. Let u(x) = -2*n(x) + 7*r(x). Solve u(h) = 0.
-2, 0, 1
Let b(m) be the second derivative of -m**2 + 0 - 3*m - 1/5*m**5 - 5/6*m**4 - 4/3*m**3. Factor b(z).
-2*(z + 1)**2*(2*z + 1)
Let p(n) = -6*n**2 + 4*n. Let t(w) = 6*w**2 - 4*w