j*p - 8*p.
-2*p*(p + 1)**2
Factor -5/2*x**4 - 10*x**3 + 0*x + 0 - 15/2*x**2.
-5*x**2*(x + 1)*(x + 3)/2
Let l(a) = a**2 + 7*a - 4. Let k be l(-8). Suppose 4*s - 12 = -k. Suppose 1/3*i + 0 + 1/3*i**s = 0. What is i?
-1, 0
Determine j, given that -2/5*j**5 + 6/5*j**4 + 6/5*j - 4/5*j**3 - 2/5 - 4/5*j**2 = 0.
-1, 1
Suppose -6*s - 4 = -4. Factor 1/4*t**2 - 1/4 + s*t.
(t - 1)*(t + 1)/4
Suppose 1 = 2*n - 7. Factor -4*d - n*d**2 - 6 + 0*d + 2*d**2 + 4.
-2*(d + 1)**2
Let n = -36 - -110/3. Factor 0*d**2 - n*d + 2/3*d**3 + 0.
2*d*(d - 1)*(d + 1)/3
Let w(g) be the first derivative of 9/2*g**2 + 27/2*g - 1 + 1/2*g**3. Let w(u) = 0. Calculate u.
-3
Let i = 14 + -13. Let c(d) be the first derivative of i + 0*d**4 + 1/2*d**2 - 1/6*d**6 - 2/3*d**3 + 0*d + 2/5*d**5. Determine g, given that c(g) = 0.
-1, 0, 1
Let c be 2/(-9) - 220/(-99). Find z such that -2*z**3 + 1 + c*z + 0 + 0*z**4 - z**4 = 0.
-1, 1
Determine t, given that -3*t**2 + 3*t**5 + 2*t + t**5 - 8*t**4 - 6*t + 11*t**2 = 0.
-1, 0, 1
Let u(o) be the second derivative of o**4/36 + 11*o**3/9 + 121*o**2/6 + o. Factor u(t).
(t + 11)**2/3
Let o(p) be the second derivative of p**7/21 - p**6/20 - 7*p**5/30 + p**4/4 + 2*p**3/3 - 3*p**2/2 + 2*p. Let u(z) be the first derivative of o(z). Factor u(j).
2*(j - 1)**2*(j + 1)*(5*j + 2)
Suppose -5*d + 7 + 3 = 0. Determine a so that -2/3 - 2/3*a**d + 4/3*a = 0.
1
Let w(s) be the first derivative of -s**6/15 - 2*s**5/25 - 1. Factor w(v).
-2*v**4*(v + 1)/5
Suppose 12 = 56*p - 50*p. Let 0 + 1/5*k + 2/5*k**p + 1/5*k**3 = 0. Calculate k.
-1, 0
Let m = -138 - -141. Let 2/5*h + 4/15 - 4/15*h**2 - 2/5*h**m = 0. What is h?
-1, -2/3, 1
Let w(h) be the third derivative of 0*h**3 + 1/150*h**5 + 2*h**2 + 1/60*h**6 + 4/525*h**7 + 0*h**4 + 0*h + 0. Factor w(m).
2*m**2*(m + 1)*(4*m + 1)/5
Let v = -13 + 16. Factor 1/2*z**v - 1/2*z + 0*z**2 + 0.
z*(z - 1)*(z + 1)/2
Let 0*y + 2/5*y**3 + 0*y**2 - 4/5*y**4 - 6/5*y**5 + 0 = 0. Calculate y.
-1, 0, 1/3
Let m(a) be the second derivative of -a**4/36 + a**3/6 - 6*a. What is p in m(p) = 0?
0, 3
Determine o so that -2/7*o**4 + 8/7*o + 6/7*o**2 - 8/7 - 4/7*o**3 = 0.
-2, 1
Let z(v) = -3*v**3 - v**2 + v. Suppose -3*k = -4*k + 4. Let b(i) = i**3 + i + k*i**4 - 2*i**3 - 3*i**4. Let l(r) = b(r) - z(r). What is f in l(f) = 0?
-1, 0
Let g(w) be the first derivative of -2 + 0*w**3 + 1/4*w**4 + 0*w - 1/2*w**2. Solve g(f) = 0.
-1, 0, 1
Suppose -6 = -4*h - 2. Let t(a) = a**3 - a**2. Let z be t(h). Determine s so that s**4 - s - 4*s**2 + z*s**3 + 3*s**2 + s**3 = 0.
-1, 0, 1
Let a(l) = -l**2 - 9*l + 7. Let i(b) = 8*b - 6. Let k(g) = -4*a(g) - 6*i(g). What is d in k(d) = 0?
1, 2
Let h be (-2)/(-72) + 18/81. Let z(u) be the first derivative of -1/2*u**2 + h*u**4 - 1 + u - 1/3*u**3. Factor z(b).
(b - 1)**2*(b + 1)
Let x = 66 + -329/5. Let u = 0 + x. Factor -u*k**2 + 4/5*k - 4/5.
-(k - 2)**2/5
Let w(b) be the first derivative of -b**6/15 - 8*b**5/25 - b**4/2 - 4*b**3/15 + 18. Let w(o) = 0. Calculate o.
-2, -1, 0
Let r(b) be the second derivative of -1/3*b**2 + 3*b + 0 + 7/18*b**4 - 2/9*b**3 - 2/15*b**5. What is p in r(p) = 0?
-1/4, 1
Let k = 255/4 + -60. Suppose 21/4*x**3 + k*x**4 + 3/4*x**5 - 3 - 3/4*x**2 - 6*x = 0. Calculate x.
-2, -1, 1
Let g be (0 + 3)/(3/2). Suppose 3*i**g + 3*i - 5*i - i**2 - 2*i = 0. Calculate i.
0, 2
Let k be (-270)/12*4/(-5). Suppose 0 = -4*m + k - 2. Factor 2*w**2 + 0 + 8/3*w**3 + 10/9*w**m + 4/9*w.
2*w*(w + 1)**2*(5*w + 2)/9
Factor -2/9*q + 0 + 0*q**2 + 2/9*q**3.
2*q*(q - 1)*(q + 1)/9
Suppose -25 = 2*c - 7*c. Let b be c + (-2 - -2)/(-1). Factor 3*m**2 + 0*m**3 - b*m**2 + 2*m**3.
2*m**2*(m - 1)
Let q(t) = t**2 - t - 1. Let s(p) = p**2 + 9*p + 9. Let i(x) = q(x) + s(x). Factor i(k).
2*(k + 2)**2
Let p = -9 - -5. Let r be (p/12)/(1/(-6)). Factor 2*v - 3*v + 2*v**2 - 3*v**r.
-v*(v + 1)
Let k be (((-10)/6 - -1) + 1)*2. Factor 4/3*m - 2/3*m**2 - k.
-2*(m - 1)**2/3
Let d be (0 - (-12)/(-14))*(-56)/60. Let -2/5*l + d - 4/5*l**2 + 2/5*l**3 = 0. What is l?
-1, 1, 2
Determine j so that 0 - 2/3*j**4 + 0*j + 2*j**3 - 4/3*j**2 = 0.
0, 1, 2
Let p = 64 + -1919/30. Let a(k) be the second derivative of 0 - k + 1/3*k**2 - p*k**5 - 1/18*k**4 + 1/9*k**3. Suppose a(v) = 0. What is v?
-1, 1
Let c be 2/(-8) + 261/(-12). Let q = -41/2 - c. Suppose -q*m**2 + 1/2 + m = 0. Calculate m.
-1/3, 1
Let z(y) be the first derivative of -2*y**5/3 - 2*y**4/3 + 2*y**3/9 - 14. Factor z(f).
-2*f**2*(f + 1)*(5*f - 1)/3
Let a = -12 + 12. Let r(x) be the first derivative of -9/5*x**5 + 7/6*x**6 - x**2 + 3*x**3 - 1 - 5/4*x**4 + a*x. Factor r(y).
y*(y - 1)**2*(y + 1)*(7*y - 2)
Let g(i) = i - 3. Let m(f) = f - 4. Let y(s) = -4*g(s) + 3*m(s). Let h(w) = 3*w**2. Let q(l) = h(l) - 6*y(l). Let q(v) = 0. Calculate v.
-2, 0
Factor -13/3*w**4 + 0 + 5*w**3 + 1/3*w + 4/3*w**5 - 7/3*w**2.
w*(w - 1)**3*(4*w - 1)/3
Suppose 2*g - 2*s + 2 = -g, 2 = 3*g - s. Let d = -10/19 - -97/76. Factor 13/4*x**g + 4*x + 1 + d*x**3.
(x + 2)**2*(3*x + 1)/4
Let c(u) be the third derivative of -5*u**8/336 + u**6/12 - 5*u**4/24 - 6*u**2. Factor c(d).
-5*d*(d - 1)**2*(d + 1)**2
Let z(j) = -2*j**5 + 2*j**4 - j**3 - 5*j**2. Let b(l) = l**5 - 2*l**4 + l**3 + 4*l**2. Let t(w) = 3*b(w) + 2*z(w). Find k such that t(k) = 0.
-2, -1, 0, 1
Let y(g) = -g**3 - 6*g**2 - 6*g. Let a be y(-5). Let u be 58/70 - (100/(-28) - -4). Factor u*z**a + 2/5*z - 2/5*z**4 + 4/5*z**2 - 2/5 - 4/5*z**3.
2*(z - 1)**3*(z + 1)**2/5
Suppose -19 = -2*p + 3*s, 5*s + 27 = p - 0*p. Solve 37*r**p + 0 - 31*r + r + 71*r**2 + 81*r**4 - 162*r**3 + 3 = 0 for r.
1/3, 1
Let q(o) = 2*o**2 - 7*o. Let m(r) = 3*r**2 - 8*r + 1. Let f(z) = -3*m(z) + 4*q(z). Factor f(j).
-(j + 1)*(j + 3)
Let h be (3 + -6)*(0 + -1). Let f be 1 + 19/h + 0. Factor 6*t**2 - f*t + 4/3.
2*(t - 1)*(9*t - 2)/3
What is q in 3/7*q**5 - 2/7 + 4/7*q**3 - 6/7*q**2 - q + 8/7*q**4 = 0?
-1, -2/3, 1
Let g be 124/(-7) - (-4)/(-14). Let d be (-10 + 13)*(-2)/g. Factor -1/3 - d*t**2 + 2/3*t.
-(t - 1)**2/3
Let f be 14/(-35) - (-4)/10. Let b(g) be the third derivative of -1/105*g**5 + 2*g**2 + 0*g - 1/84*g**4 + f*g**3 + 0 - 1/420*g**6. Factor b(u).
-2*u*(u + 1)**2/7
Let y be (-2)/9 - 58/(-18). Suppose -2*p - 4 = 4, 0 = v + y*p + 10. Factor 0 - 1/4*a**3 - 1/4*a**v + 1/4*a**4 + 1/4*a.
a*(a - 1)**2*(a + 1)/4
Let f(d) = d**5 + d**4 - d**2 - d. Let z(l) = 2*l**5 + 5*l**4 + l**3 - 5*l**2 - 3*l. Let w(u) = 3*f(u) - z(u). Find n such that w(n) = 0.
-1, 0, 1, 2
Let t(d) be the third derivative of d**7/12600 + d**6/900 + d**5/150 - d**4/24 + 2*d**2. Let v(a) be the second derivative of t(a). Factor v(u).
(u + 2)**2/5
Let 0*z**2 + 1/4*z**3 + 0 - 1/4*z = 0. What is z?
-1, 0, 1
Suppose -9 = -2*g - g. Let t = 9 - 5. Solve -2*s**g + 2*s + 2*s**2 + 4 - 2*s**t - 4 = 0.
-1, 0, 1
Solve 9*z + 8*z + 40*z**3 - z + 64*z**2 + 36*z**4 + 44*z**3 = 0 for z.
-1, -2/3, 0
Factor -4/5*v**3 + 0 - 12/5*v + 16/5*v**2.
-4*v*(v - 3)*(v - 1)/5
Suppose 2*q = 2*w - 1 - 5, 5*w = 2*q + 21. Determine m so that 0 + 0*m + 2/3*m**q = 0.
0
Let m = 22 + -6. Let n = 22 - m. Find v, given that 7 + 6*v**2 - 7 + 2*v**4 - 2*v - n*v**3 = 0.
0, 1
Let a(p) = 14*p**4 - 20*p**2 - 2. Suppose -5*l = -5*q + 15, 0*q = 5*l - 2*q + 21. Let r(v) = 9*v**4 - 13*v**2 - 1. Let n(d) = l*a(d) + 8*r(d). Factor n(b).
2*(b - 1)**2*(b + 1)**2
Let m = -65/2 - -33. Let h = 0 + 2. Factor 1/2*s**3 - 1/2*s - 1/2 + m*s**h.
(s - 1)*(s + 1)**2/2
Let i(y) = y**2 + 8*y + 13. Let g be i(-6). Let j be (g + -1)*4/4. Determine a, given that -2/3*a**2 + 2/3*a**4 + 2/3*a**3 + 0*a - 2/3*a**5 + j = 0.
-1, 0, 1
Let c(d) be the third derivative of d**8/784 - d**6/140 + d**4/56 - 15*d**2. Factor c(p).
3*p*(p - 1)**2*(p + 1)**2/7
Suppose 4*n + 112 = 4*b, -4*n = 4*b - 5*b + 100. Let o = 27 + n. Let 3/2*m**2 + 1/4 - m + 1/4*m**4 - m**o = 0. What is m?
1
Let o(u) be the third derivative of -u**11/110880 + u**9/20160 + u**5/60 - 3*u**2. Let h(v) be the third derivative of o(v). Factor h(z).
-3*z**3*(z - 1)*(z + 1)
Find o such that 3/4*o**2 + 3/2 - 9/4*o = 0.
1, 2
Let f be ((-55)/(-50))/(-11) - (-6)/20. Factor f*m**2 + 2/5*m + 1/5.
(m + 1)**2/5
Let p(u) = 6*u**5 - 15*u**4 - 10*u**3 + 21*u**2 + 26*u - 6. Let r(n) = n**5 - 3*n**4 - 2*n**3 + 4*n**2 + 5*n - 1. Let t(v) = 2*p(v) - 11*r(v). Factor t(b).
(b - 1)*(b + 1)**4
Let -2/3*i**2 - 10/9*i**4 + 0 - 2/9*i**5 - 14/9*i**3 + 0*i = 0. What is i?
-3, -1, 0
Let