o.
2*(y - 2)*(y + 1)/7
Let p(n) be the first derivative of 3*n**5/20 + 9*n**4/16 + n**3/4 - 9*n**2/8 - 3*n/2 + 8. Factor p(m).
3*(m - 1)*(m + 1)**2*(m + 2)/4
Let z(u) = 2 + 2*u**4 - u**2 + 2*u**2 + 2*u**2 + u**4. Let a(w) = -13*w**4 - w**3 - 13*w**2 - 9. Let n(h) = -2*a(h) - 9*z(h). What is k in n(k) = 0?
0, 1
Let v be (-2)/3 - (-88)/33. Let b(p) be the second derivative of -1/30*p**3 + 0*p**4 + 1/100*p**5 + 0 - 3*p + 0*p**v. Factor b(k).
k*(k - 1)*(k + 1)/5
Factor -4 - 2*f - 1/4*f**2.
-(f + 4)**2/4
Let m(x) be the first derivative of -3 + 0*x - 1/2*x**4 - 4/3*x**5 + 1/3*x**2 + 8/9*x**6 + 8/9*x**3. Solve m(a) = 0.
-1/2, -1/4, 0, 1
Let i(t) = -3*t**3 + 3*t**2 - 19*t - 3. Let o(f) = 2*f**3 - 2*f**2 + 10*f + 2. Let c(n) = 6*i(n) + 11*o(n). Find u, given that c(u) = 0.
-1, 1
Let r(m) = m**2 - 7*m + 5. Let f be r(7). Suppose f*g - 11 + 1 = 0. Factor -1/4*j**g + 0 - 1/4*j.
-j*(j + 1)/4
Let p(m) be the first derivative of 3*m**5/5 + 25*m**4/12 - 2*m**3/3 - 6*m**2 + 8*m/3 - 17. Factor p(a).
(a - 1)*(a + 2)**2*(9*a - 2)/3
Let l(h) be the first derivative of -h**7/525 + h**6/100 - h**5/50 + h**4/60 - h**2 + 5. Let z(k) be the second derivative of l(k). Factor z(o).
-2*o*(o - 1)**3/5
Let g be (4/(-8))/(1/(-4)). Factor -g*f**2 - 2 - 2*f**2 - 4*f + 0*f**2 + 2*f**2.
-2*(f + 1)**2
Let a = -9/28 + 101/140. Suppose 6/5*s**2 + a*s**4 + 2/5*s + 0 + 6/5*s**3 = 0. What is s?
-1, 0
Suppose 9*x + 7 = 25. Suppose -1/5*h + 0 + 1/5*h**x = 0. Calculate h.
0, 1
Let r(q) be the third derivative of -q**7/6300 - q**6/900 - q**5/300 + q**4/12 - 5*q**2. Let z(a) be the second derivative of r(a). Factor z(i).
-2*(i + 1)**2/5
Let s be 27/(-3)*16/6. Let j = s + 122/5. Determine c so that 2/5*c**2 + 2/5*c**3 - 2/5*c - j = 0.
-1, 1
Let z(a) = -2*a**4 - 4*a**3 - 3*a**2 + a + 2. Let m(r) be the first derivative of -r**3/3 - r**2/2 + 4. Let u(b) = 3*m(b) - z(b). Factor u(j).
2*(j - 1)*(j + 1)**3
Let d(k) be the second derivative of -5*k**4/24 - 5*k**3/12 - 4*k. Suppose d(g) = 0. What is g?
-1, 0
Factor 6*j**3 + 9*j**2 + 0*j**2 - 3*j**3 + 6*j.
3*j*(j + 1)*(j + 2)
Let x(l) be the second derivative of -7*l**5/5 + 5*l**4/3 + 4*l**3/3 + 12*l. Find i such that x(i) = 0.
-2/7, 0, 1
Let j = -19/5 + 53/10. Let d(f) be the first derivative of -1 + j*f**2 + 2*f + 1/3*f**3. Suppose d(b) = 0. Calculate b.
-2, -1
Find n, given that -n**4 + 2*n - 4*n**3 + 1 + 0*n + 2*n**3 = 0.
-1, 1
Let b(w) = -2*w**3 + 18*w**2 - 22*w + 8. Suppose 5*x - 5 - 5 = 0. Let d(f) = -2*f + 3*f + x*f**3 - f**3. Let n(a) = -b(a) + 2*d(a). Let n(h) = 0. Calculate h.
1/2, 2
Let r(k) be the second derivative of k**7/1680 - k**6/960 - 4*k**2 + 10*k. Let s(l) be the first derivative of r(l). Factor s(q).
q**3*(q - 1)/8
Let w(r) be the second derivative of 5*r**4/4 + 10*r**3/3 - 10*r**2 + r - 24. Let w(v) = 0. What is v?
-2, 2/3
Find y, given that -1/4*y**3 + 0*y**2 - 1/4*y**4 + 0 + 0*y = 0.
-1, 0
Let g(x) be the third derivative of -x**6/720 + x**5/240 + x**4/24 - x**3/2 + 3*x**2. Let v(d) be the first derivative of g(d). Find z such that v(z) = 0.
-1, 2
Find c, given that 2/9*c**3 - 1/9 + 0*c**2 - 2/9*c + 1/9*c**4 = 0.
-1, 1
Let g = 6 + -7. Let c be g - ((-8)/3 - -1). Factor -c*l**3 + 1/3*l**4 + 0*l + 0 + 1/3*l**2.
l**2*(l - 1)**2/3
Let h(m) be the second derivative of m**7/4200 - m**5/200 - m**4/12 - 3*m. Let b(t) be the third derivative of h(t). Suppose b(z) = 0. What is z?
-1, 1
Let i be 6*((-44)/(-12) + -3). Let n be ((-18)/(-84))/(1/i). Factor 0 - 6/7*c**3 - 2/7*c**4 - 2/7*c - n*c**2.
-2*c*(c + 1)**3/7
Let n(w) be the second derivative of 5*w**7/56 + 11*w**6/24 + 7*w**5/8 + 5*w**4/8 - 5*w**3/24 - 5*w**2/8 + 30*w. Factor n(a).
5*(a + 1)**4*(3*a - 1)/4
Let f(y) be the second derivative of 2*y + 1/3*y**2 + 0 - 1/6*y**3 + 1/36*y**4. Let f(t) = 0. What is t?
1, 2
Let v(b) be the third derivative of b**7/420 + b**6/60 + b**5/24 + b**4/24 - 5*b**2. Factor v(q).
q*(q + 1)**2*(q + 2)/2
Suppose -3*m + 8 - 2 = 0. Suppose 0*v - 9 = -3*v. Suppose s - v*s**2 + s**m + 0*s**2 + s**3 = 0. Calculate s.
0, 1
Suppose -24 = -i + 4*i. Let w(z) = z**3 + 9*z**2 + 8*z + 2. Let q be w(i). Factor q - j - 12*j**3 + 11*j + 32*j**3 + 10*j**4 + 20*j**2 + 0 + 2*j**5.
2*(j + 1)**5
Let k(v) = 8*v**3 + 8*v**2 - 3*v - 8. Let c(l) = 12*l**3 + 12*l**2 - 4*l - 12. Let h(o) = 5*c(o) - 8*k(o). Factor h(p).
-4*(p - 1)*(p + 1)**2
Let s(p) = 4*p**2 - 6*p + 4. Let b(d) = 17*d**2 - 24*d + 16. Let r(i) = 2*b(i) - 9*s(i). Let r(w) = 0. Calculate w.
1, 2
Let b(l) be the first derivative of l**3/3 - 5. Factor b(c).
c**2
Factor 0*r**3 + 1/2*r**5 + 0*r**4 + 0*r**2 + 0*r + 0.
r**5/2
Let m(x) = x**3 - 3*x**2 - 3*x - 2. Let q(l) = 4*l. Let z be q(1). Let u be m(z). Factor -8/3 - 2/3*h**u + 8/3*h.
-2*(h - 2)**2/3
Suppose -3*a = -2*q - 0*q, -5*a = 5*q - 25. Factor -3*h**5 + h**3 + 6*h**q - h**3 - 3*h.
-3*h*(h - 1)**2*(h + 1)**2
Determine m so that 10/21*m**3 - 26/21*m - 2/7*m**2 + 20/21 + 2/21*m**4 = 0.
-5, -2, 1
Factor 1/2*x**2 + 2 + 2*x.
(x + 2)**2/2
Let w(f) = 5*f - 7. Let h be w(3). Suppose n + 3*l = 4 + h, 3*l = n + 12. Suppose n*k**3 + 0 - 2/3*k**4 + 2/3*k**2 + 0*k = 0. Calculate k.
-1, 0, 1
Factor 0*k + 4/9*k**2 - 2/9*k**3 - 2/9*k**4 + 0.
-2*k**2*(k - 1)*(k + 2)/9
Suppose 26 = 3*t - 4*i, -8 - 6 = -3*t - 2*i. Factor -t*d**2 - 11*d**4 + 12*d**4 + 1 + 4*d**2.
(d - 1)**2*(d + 1)**2
Let i(c) be the first derivative of -4*c + 1/50*c**5 + 0*c**4 + 0*c**2 - 1/15*c**3 + 4. Let y(t) be the first derivative of i(t). Factor y(a).
2*a*(a - 1)*(a + 1)/5
Let o(v) be the second derivative of -v**4/36 + v**3/3 - 3*v**2/2 - 7*v. Suppose o(l) = 0. Calculate l.
3
Suppose 0 = -3*t + 4*d - 16, -2*t + t - 3*d + 12 = 0. Let y(m) be the second derivative of -1/3*m**3 + 1/12*m**4 + t + 1/2*m**2 + 3*m. Solve y(u) = 0 for u.
1
Let t(a) be the second derivative of -1/16*a**5 + 3*a + 0 + 5/24*a**3 - 1/4*a**2 + 1/24*a**4. Solve t(j) = 0.
-1, 2/5, 1
Find w such that 0*w**2 + 0*w + 0*w**3 + 0 + 2/3*w**4 + 2/3*w**5 = 0.
-1, 0
Let k(j) be the first derivative of j**4/4 - 3*j**3 + 27*j**2/2 - 27*j - 11. Factor k(v).
(v - 3)**3
Let c(f) be the first derivative of -f**7/35 + f**6/30 + f**5/10 - f**4/6 - 2*f**2 + 5. Let b(r) be the second derivative of c(r). Factor b(k).
-2*k*(k - 1)*(k + 1)*(3*k - 2)
Let x = -144/7 - -21. Find m, given that 3/7 + x*m**3 - 3/7*m**2 - 3/7*m = 0.
-1, 1
Suppose k = 23 - 8. Suppose -2*x = 4*u - 10, -2*u + 6*u = 3*x + k. Factor -b**2 + 2*b**3 - 4*b**u + b**3.
-b**2*(b + 1)
Let x(n) be the second derivative of -1/30*n**4 + 1/15*n**3 + 0*n**2 + 0 + 4*n. Factor x(a).
-2*a*(a - 1)/5
Let z(l) be the third derivative of l**6/60 - l**5/30 - 5*l**4/12 - l**3 - 16*l**2. Factor z(d).
2*(d - 3)*(d + 1)**2
Let q(b) be the second derivative of 2*b + 1/21*b**4 + 0*b**3 - 1/7*b**2 + 0 - 1/105*b**6 + 0*b**5. Factor q(l).
-2*(l - 1)**2*(l + 1)**2/7
Let p be (5/600*1)/((-3)/(-4)). Let y(s) be the second derivative of p*s**6 + 1/15*s**5 + 2/9*s**3 - s + 0 + 1/6*s**4 + 1/6*s**2. Factor y(n).
(n + 1)**4/3
Let i(m) be the first derivative of 243*m**6/13 - 486*m**5/65 - 189*m**4/13 - 200*m**3/39 - 8*m**2/13 + 2. Solve i(q) = 0.
-2/9, 0, 1
Let h(u) be the first derivative of u**4/4 + u**3/3 - 2*u**2 - 4*u + 3. Factor h(b).
(b - 2)*(b + 1)*(b + 2)
Let r be (-4)/(-10) - 10/25. Factor r - 2/7*o**2 + 4/7*o.
-2*o*(o - 2)/7
Suppose -18 = -4*l - 2. Determine f so that -188*f**2 + 188*f**2 + 2*f**l + 2*f**5 = 0.
-1, 0
Let m be (-11)/(-4) + (-2)/(-8). Solve -10/9*w**m + 0 + 2/3*w + 4/9*w**2 = 0.
-3/5, 0, 1
Let c be -1 - 203*6/(-10). Let t = -120 + c. Factor -2/5*l**5 - 2/5*l + 2/5*l**4 - t*l**2 + 2/5 + 4/5*l**3.
-2*(l - 1)**3*(l + 1)**2/5
Suppose 1 = -a + 3*p - 0*p, 4*a = 4*p - 4. Let g be 3/12 - a/(-4). Factor 0*w - 1/3*w**3 + g + 1/3*w**4 + 1/3*w**5 - 1/3*w**2.
w**2*(w - 1)*(w + 1)**2/3
Let o(k) = -2*k + 16. Let p be o(8). Factor p*c**4 + 26*c + 0 + 9 - 2*c + 18*c**2 - 3*c**4.
-3*(c - 3)*(c + 1)**3
Let b(n) = n**2 - 5*n - 1. Let g be b(6). Let s be 2 - g - (-46)/14. Factor 2/7 + 0*r - s*r**2.
-2*(r - 1)*(r + 1)/7
Suppose 4*v = 8*v - 56. Solve -5*n**2 - 10*n - 6*n + v*n**2 - 4 = 0.
-2/9, 2
Suppose -2*d = 2*a + 2*d - 4, -d = a - 2. Suppose a*z + 2*u = 9 - 1, u - 8 = -3*z. Factor -w**z - 4*w**2 - w + 4*w**2.
-w*(w + 1)
Let l(u) be the second derivative of -u**7/357 - u**6/255 + u**5/85 + 8*u. Let l(f) = 0. What