ctor t*m**3 + 2*m**4 - 2*m**2 - 3*m**2 + 6*m**2.
m**2*(m + 1)*(2*m + 1)
Let n(u) be the second derivative of u**5/20 + 2*u**4/15 - 2*u**3/15 - 39*u. Factor n(j).
j*(j + 2)*(5*j - 2)/5
Let x = 124/177 + -2/59. Factor -5/3*u - 7/3*u**3 + x*u**4 + 1/3 + 3*u**2.
(u - 1)**3*(2*u - 1)/3
Let b(j) be the second derivative of j**5/10 - j**4/6 - j**3/3 + j**2 + 21*j. Solve b(a) = 0 for a.
-1, 1
Let q = -96 + 96. Factor 2/3*l**3 - 2/3*l**4 + 0*l + 4/3*l**2 + q.
-2*l**2*(l - 2)*(l + 1)/3
Suppose 0 = o - 10 + 6. Find d such that -8*d**3 + 2*d**4 - d + 4*d**2 + d + o*d**2 = 0.
0, 2
Factor -42 + 36*h - 9/2*h**2 - 3/2*h**3.
-3*(h - 2)**2*(h + 7)/2
Let c be (4/6)/(6/225). Suppose t - c = -t + 5*m, 5*t = m + 5. Determine i so that 1/4*i**5 - 1/4*i**3 - 1/4*i**4 + 1/4*i**2 + 0 + t*i = 0.
-1, 0, 1
Let t = 423/1012 - 5/92. Factor 2/11*u**4 - 2/11 - t*u + 0*u**2 + 4/11*u**3.
2*(u - 1)*(u + 1)**3/11
Suppose -2*b = -0*b - 4. Suppose -1 + 3*s + s**3 + s**2 - 2*s**b - 2*s**2 = 0. What is s?
1
Factor 9/4*v**2 - 15/8*v - 3/8.
3*(v - 1)*(6*v + 1)/8
Let h = 4 + 0. Find q such that 36*q**4 + q**5 - q**3 - 36*q**h = 0.
-1, 0, 1
Let c = 161/306 + -4/153. Factor c*f + 1/4*f**2 - 3/4.
(f - 1)*(f + 3)/4
Let u(r) = r**3 + 5*r**2 - 6*r + 2. Let k be u(-6). Suppose 2*h = -0*h. Factor 0 - 2/3*w**3 + 1/3*w**4 + h*w + 1/3*w**k.
w**2*(w - 1)**2/3
Suppose -5*k - 9 = 4*t, 6*t - 2*k - 30 = t. Suppose 4*j - 16 = -t*j. Let 1/2*c**5 - j*c**4 + 0 + 3*c**3 + 1/2*c - 2*c**2 = 0. Calculate c.
0, 1
Determine o, given that 0 - 3/2*o**2 - 3/2*o**4 + 0*o + 3*o**3 = 0.
0, 1
Let s be 1/4 - ((-52)/(-240))/1. Let y(f) be the third derivative of 1/15*f**3 - 3*f**2 + 1/150*f**5 + 0 - s*f**4 + 0*f. Suppose y(k) = 0. Calculate k.
1
What is q in 4*q**2 + 162*q - 4*q**3 + 2*q**3 - 12 - 152*q = 0?
-2, 1, 3
Let m(z) be the first derivative of z**5/420 - z**4/168 - z**3/21 - 2*z**2 - 5. Let c(r) be the second derivative of m(r). Suppose c(j) = 0. What is j?
-1, 2
Let l(w) be the second derivative of -w**7/210 + w**6/120 + 3*w**2/2 - 2*w. Let v(p) be the first derivative of l(p). Factor v(a).
-a**3*(a - 1)
Factor -8*k**4 + 3*k**4 + 5*k + 12*k**3 + 4*k**3 - 15*k**2 - k**3.
-5*k*(k - 1)**3
Factor 12 + 0*k**3 - k**3 - 9*k**2 - 2*k**3.
-3*(k - 1)*(k + 2)**2
Let v = 10 + -7. Let q be v + (-34)/9 + 1. Let 2/9*z**3 - q*z**2 + 0*z + 0 = 0. What is z?
0, 1
Let k(u) be the third derivative of -u**8/112 + u**7/70 + u**6/20 - u**5/10 - u**4/8 + u**3/2 + 8*u**2. Factor k(z).
-3*(z - 1)**3*(z + 1)**2
Let h(s) be the first derivative of 0*s**2 - 3 + 1/4*s**3 + 0*s. What is o in h(o) = 0?
0
Let d(u) = u**3 + 11*u**2 - u + 6. Let z be d(-11). Suppose -18*l = -z*l. Solve 0*n - 1/4*n**2 + l - 1/4*n**3 = 0 for n.
-1, 0
Let t(r) be the second derivative of r**5/160 - r**3/48 + 9*r. Suppose t(n) = 0. Calculate n.
-1, 0, 1
Let w(a) be the first derivative of 0*a**2 - 1 - 1/48*a**4 + 1/360*a**6 + 1/3*a**3 + 0*a + 1/240*a**5. Let j(c) be the third derivative of w(c). Factor j(b).
(b + 1)*(2*b - 1)/2
Factor 29*p**3 + 2*p**2 + 4*p - 66*p**3 + 35*p**3 - 4*p**2.
-2*p*(p - 1)*(p + 2)
Suppose 9/4*v**2 + 3/2*v - 9/2*v**3 + 0 - 39/4*v**4 - 9/2*v**5 = 0. What is v?
-1, -2/3, 0, 1/2
Let p be 594/2673 - (95/(-99) + 1). Factor 4/11*m + 2/11*m**2 + p.
2*(m + 1)**2/11
Factor 2*s**2 + 10/3*s - 4/3.
2*(s + 2)*(3*s - 1)/3
Let k(i) = 10 + 0*i + 4*i + i - 6*i. Let u be k(7). Let -n**2 - 2*n**4 + 3*n**2 + 5*n - 4*n - 4*n**u + 3*n = 0. Calculate n.
-2, -1, 0, 1
Let w = 13 - 9. Let z(f) = -f**2 + 2*f - 1. Let y(m) = -3*m**2 + 3 - 4*m - 6*m + 6*m**2 + 4*m. Let k(a) = w*y(a) + 11*z(a). Find i, given that k(i) = 0.
1
Let f(n) be the first derivative of 2/21*n**3 + 2/7*n + 2/7*n**2 + 1. Factor f(v).
2*(v + 1)**2/7
Let u(v) = v + 10. Let p be u(-6). Factor 4*y**2 - 2*y**3 - p*y**3 - y**2 + 3*y**4.
3*y**2*(y - 1)**2
Let s(u) = -7*u**5 - 22*u**4 - 27*u**3 - 8*u**2 - 2*u. Let j(g) = -15*g**5 - 45*g**4 - 55*g**3 - 15*g**2 - 5*g. Let x(t) = -2*j(t) + 5*s(t). Factor x(a).
-5*a**2*(a + 1)**2*(a + 2)
Suppose 4*f - 16 = -y, -3*y + 11 + 2 = 5*f. Suppose -2*k - 5*v + 33 = 2*k, -f*k - 2*v + 20 = 0. Let -1/2*n**4 + 0*n + 1/2*n**3 + n**k + 0 = 0. What is n?
-1, 0, 2
Factor -3*q**2 + 6*q**2 - 2*q - 4*q + 0*q**2.
3*q*(q - 2)
Suppose -2*l + 2 + 0 = 0, -2*b = 5*l - 13. Suppose -b*c = -0*c + 8, -14 = -4*r + c. Factor 2/11*z**r + 0*z**2 + 2/11*z**4 + 0 + 0*z.
2*z**3*(z + 1)/11
Let y be -3 - (-24)/(5 - 2). Find g, given that 3*g**2 - y*g - 4*g - 6*g**2 = 0.
-3, 0
Let z(g) be the second derivative of -g**7/1260 - g**6/180 - g**5/60 + g**4/3 - 2*g. Let o(l) be the third derivative of z(l). Let o(p) = 0. Calculate p.
-1
Suppose 12 = 12*v - 9*v. Determine p so that 2*p**2 - v*p + 4*p = 0.
0
Suppose -i = 2*i. Let x be (4 - i)*1/2. Find v such that -4 - v**x + 4*v + 6 + 3*v**2 = 0.
-1
Let l(y) be the first derivative of y**6/16 + 7*y**5/40 + y**4/8 + y**2 + 4. Let j(i) be the second derivative of l(i). Find k, given that j(k) = 0.
-1, -2/5, 0
Let w(n) = -n**3 - 2*n**2 - 3*n - 3. Let s = -12 + 15. Let v(t) = -t**3 - 4*t**2 - 5*t - 5. Let m(a) = s*v(a) - 5*w(a). Determine h, given that m(h) = 0.
0, 1
Let m = 74 + -1331/18. Let z(g) be the second derivative of -2/63*g**7 + 1/30*g**6 - 2*g + 1/12*g**5 + 0 + 0*g**2 - 1/12*g**4 - m*g**3. Let z(s) = 0. What is s?
-1, -1/4, 0, 1
Let t(d) be the third derivative of d**6/120 + d**5/60 - d**4/24 - d**3/6 - 4*d**2 - 2. Factor t(o).
(o - 1)*(o + 1)**2
Let w(q) be the first derivative of 9/14*q**4 + 0*q + 12/7*q**2 + 4 + 3/35*q**5 + 12/7*q**3. Factor w(y).
3*y*(y + 2)**3/7
Let h(y) be the third derivative of -y**7/525 + y**6/150 + y**5/150 - y**4/30 + 41*y**2. Factor h(s).
-2*s*(s - 2)*(s - 1)*(s + 1)/5
Suppose -y + 2 = -2. Suppose -4*a**2 + 2*a**2 - a**2 + 3*a**y = 0. Calculate a.
-1, 0, 1
Suppose 4*r + 3*b - 20 = b, -5*r - 4*b = -31. Suppose -u = -0*u + 2*z - 5, 8 = 2*u + r*z. Factor -3/2*a - u - 1/2*a**2.
-(a + 1)*(a + 2)/2
Let i(s) be the first derivative of s**6/2 - 39*s**5/35 + 15*s**4/28 + s**3/7 + 8. Let i(r) = 0. Calculate r.
-1/7, 0, 1
Solve 2/3*g**2 + 2/3 - 4/3*g = 0.
1
Suppose 4*h = 2*r, 4*h + 3 = 5*r - 9. What is u in 2/5*u - 1/5 - 1/5*u**h = 0?
1
Let v(l) be the first derivative of -l**5/10 + l**4/2 - 2*l**3/3 + 2*l - 2. Let c(t) be the first derivative of v(t). Factor c(p).
-2*p*(p - 2)*(p - 1)
Let w(v) be the third derivative of v**7/1260 - v**6/120 + v**5/30 - 5*v**4/72 + v**3/12 - 15*v**2. Determine l so that w(l) = 0.
1, 3
Let h = -12 + -2. Let o be (-3 + h/(-6))/(-1). Find k, given that 0*k**2 - 2/3*k + 1/3 - 1/3*k**4 + o*k**3 = 0.
-1, 1
Let p be (7/(42/(-18)))/(9/(-12)). Factor 0*r - 4/7*r**3 + 0 - 2/7*r**p - 2/7*r**2.
-2*r**2*(r + 1)**2/7
Determine m, given that 4/3*m - 20/3*m**4 + 8/3 - 52/3*m**3 - 12*m**2 = 0.
-1, 2/5
Suppose 0 = 37*v - 39*v. Let -2/9*h**2 + 4/9*h + v = 0. What is h?
0, 2
Factor 2/5*u**2 + 0 + 0*u - 1/5*u**3.
-u**2*(u - 2)/5
Let t(z) be the second derivative of -z**7/84 + z**6/60 + 3*z**5/40 - 5*z**4/24 + z**3/6 + 14*z. Factor t(i).
-i*(i - 1)**3*(i + 2)/2
Let j = -20 - -62/3. Factor j*u - 4/3 - 2/3*u**3 + 4/3*u**2.
-2*(u - 2)*(u - 1)*(u + 1)/3
Let z = 1 - -3. Let a = 55 - 51. Factor -4*l**3 - 29*l**a + l**3 + 32*l**z.
3*l**3*(l - 1)
Let i(k) be the second derivative of k**8/504 - 2*k**7/315 + k**6/180 - 3*k**2/2 + k. Let b(s) be the first derivative of i(s). Factor b(x).
2*x**3*(x - 1)**2/3
Let k(z) = -z**3 - 5*z**2 - 4*z. Let l(n) = -n**2 - n. Let m(p) = p**3 - 6*p**2 + 5*p - 5. Let x be m(5). Let o(y) = x*l(y) + k(y). Factor o(r).
-r*(r - 1)*(r + 1)
Let a be 0 - (-2)/(-1)*-2. Factor 0 - s**4 - 2*s**5 - 2*s - 2 + 4*s**3 - s**a + 0 + 4*s**2.
-2*(s - 1)**2*(s + 1)**3
Let b be 1/(-5) + 52/10. Solve -b*o**3 + o**4 + 2*o**3 + 2*o**3 = 0 for o.
0, 1
Let i(z) = -3*z + 42. Let s be i(14). Let w(p) be the third derivative of -1/6*p**4 + 0*p - 1/30*p**5 + 0 + s*p**3 - 4*p**2. Factor w(g).
-2*g*(g + 2)
Let k = -32/3 + 11. Let j = 83/39 + -6/13. Factor k*h**4 + 2/3 + 7/3*h + j*h**3 + 3*h**2.
(h + 1)**3*(h + 2)/3
Let m(t) be the second derivative of -11*t - 2*t**4 + 0 - 1/14*t**7 + 3/10*t**5 - 3*t**2 + 7/2*t**3 + 1/5*t**6. Factor m(c).
-3*(c - 1)**4*(c + 2)
Factor -96*v - 8*v**4 - 32*v**3 + 4*v**4 - 36 - 38*v**2 - 50*v**2.
-4*(v + 1)**2*(v + 3)**2
Let k(c) be the second derivative of c**5/20 - c**4/4 + c**3/3 + 3*c. Sol