ate j.
0, 2/7
Let c(f) be the third derivative of -f**7/13860 - f**6/1980 + f**4/6 + f**2. Let u(o) be the second derivative of c(o). Find l such that u(l) = 0.
-2, 0
Let p = 60/37 - 189/185. Factor 1/5*r**4 + 0 - 3/5*r + p*r**3 - 1/5*r**2.
r*(r - 1)*(r + 1)*(r + 3)/5
Let y(m) be the first derivative of 5*m**7/63 + 4*m**6/15 + 3*m**5/10 + m**4/9 - m - 3. Let q(c) be the first derivative of y(c). Suppose q(o) = 0. What is o?
-1, -2/5, 0
Let u(f) be the first derivative of f**6/27 - 2*f**5/45 - f**4/9 + 4*f**3/27 + f**2/9 - 2*f/9 - 10. Factor u(i).
2*(i - 1)**3*(i + 1)**2/9
Let m be 126/(-24)*(-8)/(-3). Let d be (m/(-10) + -1)*5. Factor -2*b**2 - b**3 - b**3 + 2*b**2 + d*b.
-2*b*(b - 1)*(b + 1)
Suppose -4*d = 5*i - 1500, 2*i - 4*d + 1196 = 6*i. Let n be i/72 + (-4)/18. Factor -15*f**n + 29*f**3 + 17*f - 2*f + 3 - 6 - 30*f**2 + f**3 + 3*f**5.
3*(f - 1)**5
Let d(s) be the first derivative of 9/50*s**5 - 2 + 13/15*s**3 + 2/3*s**4 + 3*s + 2/5*s**2. Let n(l) be the first derivative of d(l). Factor n(c).
2*(c + 1)**2*(9*c + 2)/5
Let a = 10 - 6. Suppose -k = -2*g - g + 3, -2*k = 4*g - a. Factor 0*i**3 - g + 4*i**3 - 2*i + i**4 - 2*i**3.
(i - 1)*(i + 1)**3
Suppose -3*j + 0 + 12 = 0. Let w(z) be the first derivative of -3/25*z**5 - 1 + 1/5*z**3 + 0*z + 1/20*z**j - 1/10*z**2. Find i such that w(i) = 0.
-1, 0, 1/3, 1
Let q(z) be the second derivative of -z**7/2520 - z**6/960 + z**5/480 - z**4/6 - 4*z. Let h(v) be the third derivative of q(v). Factor h(p).
-(p + 1)*(4*p - 1)/4
Let u = -820 + 822. Suppose 3/2*z - 3*z**u + 3/2 = 0. What is z?
-1/2, 1
Find n such that -6 + 42*n**3 + 25*n - 37*n**3 - 4 - 20*n**2 = 0.
1, 2
Let r be ((-3)/(-6))/((-1)/(-42)). Let f be ((-35)/10)/((-3)/r). Factor -f*b**3 + 0 - 14*b**2 - 2*b.
-b*(7*b + 2)**2/2
Let v(j) be the first derivative of 4/25*j**5 + 6/5*j**4 + 16/5*j**3 + 0*j - 3 + 16/5*j**2. Factor v(t).
4*t*(t + 2)**3/5
Suppose -2*o + 4 = -0. Let q(m) be the third derivative of -m**o - 1/30*m**5 + 0*m**4 + 1/3*m**3 + 0 + 0*m. Suppose q(y) = 0. Calculate y.
-1, 1
Let m(c) = -7*c**4 - 8*c**3 - 17*c**2 - 13*c - 2. Let t(o) = -4*o**4 - 4*o**3 - 9*o**2 - 7*o - 1. Let x(w) = -6*m(w) + 10*t(w). Suppose x(r) = 0. What is r?
-1
Let q(o) = o**3 + 7*o**2 + 5*o - 3. Let a be q(-6). Suppose 0 = -u + 5 - 2. Factor 0 - 4 + u - 7*k**2 + 3*k**a + 5*k.
(k - 1)**2*(3*k - 1)
Let y = 4451/417 + -1/139. Factor -14/3*s**2 - 8/3 - y*s.
-2*(s + 2)*(7*s + 2)/3
Determine d, given that -5*d**3 - 5*d - 18*d**4 - 20*d**5 + 3*d**4 + 12*d**3 + 18*d**3 + 15*d**2 = 0.
-1, 0, 1/4, 1
Suppose 261 = -4*d + 269. Factor 2/5*l**d + 0*l + 0.
2*l**2/5
Let i(y) be the third derivative of -y**9/3780 + y**8/1120 - y**6/360 + y**4/8 - 2*y**2. Let c(h) be the second derivative of i(h). Factor c(m).
-2*m*(m - 1)**2*(2*m + 1)
Let w(d) be the first derivative of 0*d + 0*d**2 - 1 - 2/15*d**3 + 1/10*d**4. Factor w(f).
2*f**2*(f - 1)/5
Let m(c) be the first derivative of c**3 + 1/2*c**6 + 2 + 9/5*c**5 + 0*c**2 + 0*c + 9/4*c**4. Factor m(a).
3*a**2*(a + 1)**3
What is m in 12*m - 2/3*m**2 + 0 = 0?
0, 18
Let w be -3 - (17 + -3 + 5). Let i be w/(-24) + (-5)/20. Factor i*m**3 + 1/3 + 0*m**2 - 2/3*m - 1/3*m**4.
-(m - 1)**3*(m + 1)/3
Let o(m) = 3*m**5 - 2*m**4 - m**3 - 2. Let h(k) = 60 + k**5 - 33 - k**4 - 28. Let q be 0/(1 + -3) - 1. Let u(a) = q*o(a) + 2*h(a). Solve u(x) = 0 for x.
-1, 0, 1
What is u in 2*u - 12*u**2 - 25/2*u**4 + 45/2*u**3 + 0 = 0?
0, 2/5, 1
Let p(m) be the first derivative of m**4/2 - 4*m**3/3 - m**2 + 4*m + 3. Suppose p(l) = 0. Calculate l.
-1, 1, 2
Suppose 5*t - 11 + 1 = 0. Let s(f) be the first derivative of -21/2*f**2 + t*f**3 + 6*f - 4 + 9/4*f**4. Factor s(v).
3*(v - 1)*(v + 2)*(3*v - 1)
Suppose 0 = 46*n - 50*n. Find v, given that 2/9*v**4 + 0*v + 2/9*v**3 + 0 + n*v**2 = 0.
-1, 0
Let a = -489 + 3425/7. Find z, given that 0*z - 2/7*z**2 - a*z**3 + 2/7*z**5 + 2/7*z**4 + 0 = 0.
-1, 0, 1
Let y = 202 - 387. Let d = y - -1297/7. Factor 0*m + 0 - 2/7*m**3 - d*m**2.
-2*m**2*(m + 1)/7
Let b(q) be the second derivative of 0*q**2 - 3/20*q**5 - 3*q + 0 + 1/2*q**4 - 1/2*q**3. Solve b(u) = 0 for u.
0, 1
Let z(x) = -x**3 - x**2 + 3*x - 2. Let i be z(-3). Let k = i - 4. Find r, given that -2*r**2 + 2*r**2 - r**4 + r + 3*r**k + r**2 - 4*r**2 = 0.
0, 1
Let f(k) be the second derivative of -7*k**7/18 - 91*k**6/30 - 134*k**5/15 - 110*k**4/9 - 8*k**3 - 8*k**2/3 - 6*k. Let f(j) = 0. Calculate j.
-2, -1, -2/7
Let m = 487/11310 - 2/435. Let t = 55/78 - m. Factor 2/3*c**2 + 2/3*c - t*c**3 - 2/3.
-2*(c - 1)**2*(c + 1)/3
Let z(x) be the third derivative of -1/90*x**5 + 0*x + 1/18*x**4 + 2*x**2 + 0 - 1/9*x**3. Suppose z(g) = 0. Calculate g.
1
Let c = 6/31 - -19/62. Let 0 - 1/2*z**4 + 1/2*z**3 + 1/2*z**2 - c*z = 0. Calculate z.
-1, 0, 1
Factor -2*o - 2*o**5 - 15*o**3 - 16*o**3 + 35*o**3.
-2*o*(o - 1)**2*(o + 1)**2
Let k(c) be the first derivative of -2/5*c**5 + 4/3*c**3 - 18*c - 1 + 2*c**4 - 12*c**2. Factor k(v).
-2*(v - 3)**2*(v + 1)**2
Let f(r) = -4*r**4 - 10*r**3 - 15*r**2 - 4*r - 1. Let w(c) = -c**3 + c**2 - c. Let x(b) = 5*f(b) + 10*w(b). Factor x(i).
-5*(i + 1)**2*(2*i + 1)**2
Let l = -2219/3 + 740. Let -2/3*v**2 - l*v**3 + 0 - 1/3*v = 0. Calculate v.
-1, 0
Let k = -3025/4 + 759. Factor -k*c**4 + 0 + 5*c**3 - 1/2*c - 7/4*c**2.
-c*(c - 1)**2*(11*c + 2)/4
Factor -1/4 - 1/2*c - 1/4*c**2.
-(c + 1)**2/4
Let j = 29 + -27. Let f(q) = -3*q - 1. Let t be f(-1). Factor 2*h**3 - 2*h + 2*h**t - j*h**2.
2*h*(h - 1)*(h + 1)
Let h = 827/7 + -118. Solve 4/7*r + 4/7 + h*r**2 = 0 for r.
-2
Let d(j) be the third derivative of -1/120*j**6 + 0*j + 1/24*j**4 - j**2 + 1/18*j**3 - 1/315*j**7 + 0 + 1/180*j**5. Suppose d(x) = 0. Calculate x.
-1, -1/2, 1
Factor -30 + 0*u - 7*u**2 - 7*u + 2*u + 42*u**2.
5*(u - 1)*(7*u + 6)
Let j = -1 - 0. Let n be j/6*-13 - 2. What is q in n*q**4 + 0*q**3 - 1/3*q**2 + 1/6 + 0*q = 0?
-1, 1
Find g such that 2/3*g**3 + 2/3*g**4 + 4/3 - 2/3*g - 2*g**2 = 0.
-2, -1, 1
What is f in -14/5*f**5 + 0*f + 0 - 4*f**2 + 54/5*f**3 + 12*f**4 = 0?
-1, 0, 2/7, 5
Let f(y) be the third derivative of 8*y**7/525 + 3*y**6/25 + 97*y**5/300 + 3*y**4/10 + 2*y**3/15 + 5*y**2. Factor f(x).
(x + 2)**2*(4*x + 1)**2/5
Let u(d) = -d**3 + 6*d**2 - 2*d + 12. Let o(z) = 2*z**3 - 13*z**2 + 5*z - 26. Let m(c) = -6*o(c) - 13*u(c). Factor m(w).
w*(w - 2)*(w + 2)
Let r(a) be the first derivative of 2*a**5/5 + a**4 - 2*a**3/3 - 2*a**2 + 2. Suppose r(o) = 0. What is o?
-2, -1, 0, 1
Factor 1/4*s**3 + 35/4*s + 11/4*s**2 + 25/4.
(s + 1)*(s + 5)**2/4
Suppose 4*d - 9 = 2*l + 3, -4 = -2*l. Let -2/9*s - 2/9 + 4/9*s**3 - 2/9*s**d - 2/9*s**5 + 4/9*s**2 = 0. Calculate s.
-1, 1
Let s be 30/(-45)*(-11 - -3). Factor -3*u**4 + 4/3*u - s*u**2 + 7*u**3 + 0.
-u*(u - 1)*(3*u - 2)**2/3
Factor 2/3*f**2 - 4 + 2/3*f.
2*(f - 2)*(f + 3)/3
Let r be (-4)/(-14) + 38/14. Let b(c) = -3*c**2 - c - 4. Let n(l) = 7*l**2 + 5 + 4*l**2 - 7*l**2. Let k(v) = r*b(v) + 2*n(v). Find f, given that k(f) = 0.
-2, -1
Let f(y) = -4*y**4 - 18*y**3 + 32*y**2 - 30*y + 8. Let n(j) = -j**4 - j**3 + j**2 - j. Let t(a) = f(a) - 6*n(a). Suppose t(x) = 0. Calculate x.
1, 2
Solve -4/7*u**3 + 4/7*u**2 + 0*u + 0 = 0 for u.
0, 1
Let w(h) be the second derivative of 0 - 16/3*h**3 - 16*h**2 - 4*h + 0*h**4 + 2/5*h**5 + 1/15*h**6. Determine q so that w(q) = 0.
-2, 2
Let m(a) = -5 + 2 - 8*a**2 + 12*a - 1. Let n(b) = b - 1. Let z(t) = 7*t**2 - 17*t + 10. Let q(w) = -6*n(w) - z(w). Let o(g) = -5*m(g) + 6*q(g). Factor o(d).
-2*(d - 2)*(d - 1)
Let m be ((-42)/4)/7*-2. Factor -5/3*d**2 - 7/3*d - 1 - 1/3*d**m.
-(d + 1)**2*(d + 3)/3
Let r = 13 + -11. Find h such that 0*h**2 + h - 9 - h**r - 2*h + 7*h = 0.
3
Factor 1/5*g**3 - 1/5*g**2 + 0*g + 0.
g**2*(g - 1)/5
Let g(b) = -4*b**2 + 5*b + 0 - 4 + 5*b**2. Let q(w) = w - 1. Let y(i) = -g(i) + 4*q(i). Find z, given that y(z) = 0.
-1, 0
Let j(g) = 2*g - 20. Let l be j(11). Let p = 82/3 - 27. Determine d so that 0 + 0*d - p*d**l = 0.
0
Let v = -25 + 29. Let l(r) be the second derivative of -1/30*r**6 + 0*r**2 - 1/20*r**5 + 1/6*r**3 - 2*r + 1/12*r**v + 0. Factor l(c).
-c*(c - 1)*(c + 1)**2
Let h(i) be the third derivative of i**6/30 - 7*i**4/6 - 4*i**3 - 38*i**2. Factor h(o).
4*(o - 3)*(o + 1)*(o + 2)
Let p = 1/65 - -193/130. Let -p*x + 1/2*x**2 + 1 = 0. What is x?
1, 2
Let w(z) = z**2 - z - 3. Let r be w(-2). What is g in -2*g**4 + 6*g*