 + 1)
Let r be 2/5 + (-72)/(-45). Factor 2*m**2 - 3*m - 8*m**2 + r*m**2 + m**2.
-3*m*(m + 1)
Let t(l) be the first derivative of -l**4/14 - 2*l**3/21 + 5*l**2/7 - 6*l/7 - 18. What is m in t(m) = 0?
-3, 1
Suppose 5*t - 3 = -g, -3 = -t + 2*t - g. Let m(v) be the second derivative of v**2 - 1/3*v**4 + 0*v**5 - v + t*v**3 + 0 + 1/15*v**6. Factor m(a).
2*(a - 1)**2*(a + 1)**2
Suppose m = g - 2*g, 24 = 4*m - 4*g. Suppose -4*p + m*p = 0. Factor -2*s**3 + s - 2 + p*s**2 + s + 2*s**2.
-2*(s - 1)**2*(s + 1)
Let r(c) be the first derivative of 2*c**5/15 + 4*c**4/3 + 16*c**3/3 + 32*c**2/3 + 32*c/3 + 14. Find t, given that r(t) = 0.
-2
Let w = 181 - 2171/12. Let l(a) be the third derivative of -3*a**2 + 0*a + 1/3*a**3 + 1/60*a**6 - 1/30*a**5 + 0 - w*a**4. Determine g, given that l(g) = 0.
-1, 1
Suppose -2*d + 4*d = 3*d. Factor 1/2*p - 1/2*p**2 + d.
-p*(p - 1)/2
Let y = 122 - 121. Let n(m) be the first derivative of y + 1/18*m**3 - 1/12*m**4 + 1/12*m**2 + 0*m. Find w, given that n(w) = 0.
-1/2, 0, 1
Suppose 50 = 5*v + 5*c, -34 = 2*v - 5*v - 5*c. What is w in 4*w**3 + 0*w**3 - 2*w**3 + 8*w + v*w**2 + 0*w**3 = 0?
-2, 0
Let w(d) be the third derivative of d**6/180 - d**5/45 - 7*d**4/36 - 4*d**3/9 + 7*d**2. Factor w(a).
2*(a - 4)*(a + 1)**2/3
Let t(z) be the third derivative of -z**8/840 + z**7/210 - z**6/180 + z**3/3 - 6*z**2. Let f(c) be the first derivative of t(c). What is w in f(w) = 0?
0, 1
Factor 8 - 2*i**2 + 0*i**2 - 5*i**2 + 6*i**2 - 2*i.
-(i - 2)*(i + 4)
Let j(i) be the second derivative of 0*i**5 + 0 - 1/14*i**4 + 0*i**2 - 2/21*i**3 + 1/105*i**6 + 2*i. Determine c, given that j(c) = 0.
-1, 0, 2
Let y(d) be the second derivative of 1/12*d**3 + 0 + 5*d + 1/48*d**4 + 0*d**2. Suppose y(t) = 0. What is t?
-2, 0
Suppose -d - 3*f = -8, 7*d - 2*d - 4 = 3*f. Suppose b - d + 3 = v, 0 = -4*v - 3*b + 25. Factor -n**v + n**5 - n**4 + 1 - 3*n + 2*n**2 + 2*n**3 - n**4.
(n - 1)**4*(n + 1)
Let p(s) be the second derivative of s**5/80 - s**3/24 - 7*s. Factor p(q).
q*(q - 1)*(q + 1)/4
Let m = 38/9 + -277/72. Let w = m + -1/24. Factor -w*n**2 - n**4 + 0*n + 1/3*n**5 + n**3 + 0.
n**2*(n - 1)**3/3
Let i(g) be the first derivative of -g**3/6 + g**2/2 - 1. Solve i(f) = 0 for f.
0, 2
Let t(w) = w**2. Suppose 14 = 4*k - 26. Let x(r) = 2*r**3 + 10*r**2 - 2*r. Let o(y) = k*t(y) - x(y). Factor o(b).
-2*b*(b - 1)*(b + 1)
Let c(j) = -j**3 + 11*j**2 + 12*j + 3. Let u be c(12). Let f(o) be the first derivative of 0*o - 2/21*o**u + 2 - 1/7*o**2. Factor f(z).
-2*z*(z + 1)/7
Let j(c) be the second derivative of -3*c + 0 + 0*c**2 - 2/63*c**7 + 1/9*c**6 - 2/15*c**5 + 0*c**3 + 1/18*c**4. Factor j(i).
-2*i**2*(i - 1)**2*(2*i - 1)/3
Let v(c) be the third derivative of -1/90*c**6 + 0 + 0*c + 0*c**4 + 0*c**3 - 1/315*c**7 + 4*c**2 - 1/90*c**5. Suppose v(h) = 0. Calculate h.
-1, 0
Suppose 0 = -4*n - w + 46, -2*w = 4*n - 0*w - 44. Suppose -n = -3*s - s. What is j in 5*j**3 - 5*j**s - j**3 = 0?
0
Factor 4 - 4*s**2 - 9*s**2 - 8*s + 17*s**2.
4*(s - 1)**2
Let x(r) be the third derivative of -r**5/100 + r**4/10 - 3*r**3/10 + r**2 - 2*r. Suppose x(c) = 0. Calculate c.
1, 3
Let t(a) be the first derivative of -81/4*a**4 + 1 - 27*a**3 - 3*a - 27/2*a**2. Suppose t(q) = 0. Calculate q.
-1/3
Suppose 1/3*p**5 + 1/3 - 5/6*p**3 + 1/2*p - 5/6*p**2 + 1/2*p**4 = 0. Calculate p.
-2, -1, -1/2, 1
Let t be 5 + (-61)/4*(-20)/(-65). Find q, given that 2/13*q - 4/13*q**4 + t*q**2 - 2/13*q**5 + 0 + 0*q**3 = 0.
-1, 0, 1
Solve -25/4 + 5/2*s - 1/4*s**2 = 0.
5
Suppose -4*c + 3*l + 21 = 0, -5*c - 3*l + 21 = -5*l. Determine f, given that f - 1/3 + 1/3*f**c - f**2 = 0.
1
Let u(v) = -13*v**4 + 16*v**3 + 5*v**2 + 5. Let b(x) = 20*x**4 - 24*x**3 - 8*x**2 - 8. Let k(r) = -5*b(r) - 8*u(r). Factor k(g).
4*g**3*(g - 2)
Let w(n) = n**2 - 4. Let c be w(3). Suppose -c*r + 0*r - 17 = 4*t, -3*t - 2*r = 4. Let 0 - 1/4*l**3 + 0*l**t + 1/4*l = 0. Calculate l.
-1, 0, 1
Let v = 0 + 2. Factor -2 - 2*o**v + o**2 - 2 + 4*o.
-(o - 2)**2
Let n(w) = -w**2 - 7*w - 10. Let d be n(-3). Let l = -19/2 + 10. Factor 1/2*c**d + c + l.
(c + 1)**2/2
Let x(p) = -5*p**4 - 5*p**3 + 5*p**2 + 5*p. Let i(z) = z**4 + z**3 - z**2 - z. Let m(h) = -12*i(h) - 3*x(h). Factor m(n).
3*n*(n - 1)*(n + 1)**2
Let l(o) be the first derivative of -2*o**2 - 16/3*o**3 + 5*o**5 - 5/4*o**4 + 0*o + 4. Factor l(m).
m*(m - 1)*(5*m + 2)**2
Suppose 16*l - 3*h = 17*l - 18, 2*l = -5*h + 31. Factor -1/4*u**4 + 1/4*u - 3/4*u**2 + 3/4*u**l + 0.
-u*(u - 1)**3/4
Suppose -5*g = 3*y - 14 - 41, -g = 3*y - 23. Let t = 8 - g. Factor 0*q + 2/7*q**2 + t - 2/7*q**3.
-2*q**2*(q - 1)/7
Let h(p) = -5*p - 3. Let k be h(-2). Factor 21*r**3 + r - 11*r**3 - 10*r - 6 - k*r**3.
3*(r - 2)*(r + 1)**2
Let c(b) = -4*b**2 - 11*b + 3. Let q(l) = -4*l**2 - 10*l + 2. Let f(x) = 2*c(x) - 3*q(x). Factor f(m).
4*m*(m + 2)
Let b(f) = f**5 - f**3 + f**2 + f. Let h(m) = 11*m**5 - 15*m**4 + 4*m**3 + 6*m**2 + 6*m. Let o(q) = -6*b(q) + h(q). Determine p so that o(p) = 0.
0, 1, 2
Let m(r) be the first derivative of 0*r**2 + 1/20*r**5 + 0*r**4 + 2*r - 1/6*r**3 + 1. Let c(f) be the first derivative of m(f). Factor c(q).
q*(q - 1)*(q + 1)
Suppose -4 + 16 = -3*y, 5*j + 2*y = 12. Let h(c) be the second derivative of 0*c**3 + c - 1/12*c**j + 1/2*c**2 + 0. Suppose h(q) = 0. Calculate q.
-1, 1
Determine f, given that -9/4*f**3 + 0*f + 0 + 0*f**2 + 3/4*f**5 + 3/2*f**4 = 0.
-3, 0, 1
Suppose 4*d - 1 = 15, -3*d = 3*v - 12. Let g(p) be the third derivative of 1/27*p**3 + v - 1/54*p**4 + 1/270*p**5 + 0*p + p**2. Find s such that g(s) = 0.
1
Let r be 2 + -3 + (-3)/(-6)*6. Factor -2/5*n + 4/5*n**4 + 0 - 4/5*n**r + 2/5*n**5 + 0*n**3.
2*n*(n - 1)*(n + 1)**3/5
Let h(x) be the second derivative of 1/35*x**5 + 0*x**2 + 2/21*x**3 + 0 + 2/21*x**4 - 2*x. Factor h(c).
4*c*(c + 1)**2/7
Let n be 76/40 + (-3)/2. Let x(o) be the first derivative of -n*o**3 - 2/5*o + 3/5*o**2 + 1/10*o**4 - 2. Suppose x(u) = 0. Calculate u.
1
Let y = 6 + -9. Let l be (4 + -3)/(y/(-6)). Factor 1/2*x - 1 + 1/2*x**l.
(x - 1)*(x + 2)/2
Let v(d) = -17*d**4 - d**3 + 12*d**2 + 4*d - 1. Let i(f) = f**4 + f**3 + 1. Let l(b) = -i(b) - v(b). Factor l(y).
4*y*(y - 1)*(2*y + 1)**2
Suppose -2*v - 8 = 2*j, -3*v - 20 = j + 2*v. Suppose 0 = -3*z - 3*q + 24, 3*z - 5*z + 31 = 5*q. Factor 2/3*y**4 + 0*y**2 + 0 + j*y**z + 0*y + 2/3*y**5.
2*y**4*(y + 1)/3
Let k(h) be the first derivative of 1/6*h**4 + 0*h**2 + 0*h + 3 + 1/6*h**6 - 7/15*h**5 + 0*h**3. What is i in k(i) = 0?
0, 1/3, 2
Factor 1/2*z + 1/2*z**3 - z**2 + 0.
z*(z - 1)**2/2
Let i(k) be the first derivative of -k**8/84 - 2*k**7/35 - k**6/10 - k**5/15 - 7*k**2/2 + 5. Let n(a) be the second derivative of i(a). Factor n(g).
-4*g**2*(g + 1)**3
Let b be (2/4)/(2/178). Let z = -43 + b. Determine g, given that z*g**3 + 7/2*g + 1 + 4*g**2 = 0.
-1, -2/3
Let u(a) = 18*a**5 - 4*a**4 - 18*a**3 + 6*a**2 - 2*a. Let f(d) = d**2 - d. Let x(g) = 2*f(g) - u(g). Suppose x(s) = 0. What is s?
-1, 0, 2/9, 1
Solve 0 + 2/5*z**2 + 6/5*z = 0 for z.
-3, 0
Solve -16*g**3 + 15*g**3 - 2*g**2 + 2 - 2*g + 3*g**3 = 0.
-1, 1
Factor -w**4 - 631 + 631 - w**2 - 2*w**3.
-w**2*(w + 1)**2
Let b(p) be the third derivative of -p**6/80 - 3*p**5/40 + p**4/16 + 3*p**3/4 - 5*p**2. Factor b(o).
-3*(o - 1)*(o + 1)*(o + 3)/2
Let p(i) = -i**2 - 4*i + 5. Let r = 11 + -16. Let q be p(r). Factor 58*z**3 + q + 40*z**3 - 48*z + 8 + 42*z**2.
2*(z + 1)*(7*z - 2)**2
Let g(y) = y**3 + 5*y**2 - 8*y - 9. Let o be g(-6). Suppose 0 = 2*z - 12 + 4. Let -2*i**o + 3*i + 2*i**z - 3*i = 0. Calculate i.
0, 1
Suppose 0 = 3*h - 0*h + 4*h. Factor 2/5*y**4 + 0*y + 1/5*y**5 + h + 1/5*y**3 + 0*y**2.
y**3*(y + 1)**2/5
Let h(n) be the second derivative of n**6/30 + n**5/10 - n**3/3 - n**2/2 + 3*n. Factor h(y).
(y - 1)*(y + 1)**3
Let h(z) be the first derivative of 7*z**5/5 + 3*z**4/8 - 37*z**3/6 + 6*z**2 - 2*z - 8. Suppose h(m) = 0. What is m?
-2, 2/7, 1/2, 1
Let o = -208 + 212. Let 0*m - 2/3*m**2 + 7/3*m**5 - 16/3*m**o + 0 + 11/3*m**3 = 0. What is m?
0, 2/7, 1
Let b(y) be the third derivative of -y**6/900 + y**5/225 + y**4/180 - 2*y**3/45 + 3*y**2. Factor b(a).
-2*(a - 2)*(a - 1)*(a + 1)/15
Let n = -2 + 2. Let l(t) be the second derivative of 0*t**4 + 0 + n*t**3 + 0*t**2 - 4/45*t**6 - t - 1/30*t**5. Factor l(c).
-2*c**3*(4*c + 1)/3
Let q be (-3)/(-4) + 77/(-252). Determine t so that 2/9*t**3 + 0*t + 0 + q*t**