r + 32/3*r**2.
-(r - 3)**2*(5*r - 2)/3
Let u(o) be the second derivative of -o**5/40 - o**4/12 - 20*o. Factor u(d).
-d**2*(d + 2)/2
Let x be 120/(-63) - (-5)/((-15)/(-6)). Let n(i) be the first derivative of -4/7*i + 1 - 1/7*i**2 + x*i**3. Factor n(z).
2*(z - 2)*(z + 1)/7
Let s(d) = -2*d**2 + 3*d**2 + 0*d - 2*d**2 - d + d**4. Let t(u) = -2*u**5 + 10*u**4 - 4*u**3 - 8*u**2 + 2*u - 2. Let h(x) = 4*s(x) - t(x). Factor h(f).
2*(f - 1)**4*(f + 1)
Let a(i) be the third derivative of 0*i + 27/14*i**4 + 1/490*i**7 + 27/70*i**5 + 0 + 3/70*i**6 + 4*i**2 + 81/14*i**3. Factor a(h).
3*(h + 3)**4/7
Let n(y) = -23*y**2 + 66*y + 24. Let w(t) = 34*t**2 - 98*t - 36. Let k(g) = -8*n(g) - 5*w(g). Factor k(q).
2*(q - 3)*(7*q + 2)
Determine y, given that 3/4*y**3 + 3*y**2 + 9/4*y + 0 = 0.
-3, -1, 0
Factor 0 + 3/5*a**3 + 0*a - 3/5*a**2.
3*a**2*(a - 1)/5
Let p be (-9 - -12)*(-4)/(-6). Determine z so that 8*z**4 - 9*z**4 + 6*z**3 + 2*z**2 + 7*z**4 + p*z**5 = 0.
-1, 0
Suppose 0 = -5*o + o + 12. Let -h**4 + h**4 + h**4 - 2*h**o + 0*h**3 + h**2 = 0. Calculate h.
0, 1
Factor 0*f - 20/7*f**4 + 0 + 32/7*f**2 - 72/7*f**3.
-4*f**2*(f + 4)*(5*f - 2)/7
Let j(g) be the first derivative of -g**7/105 + g**6/60 - g**2/2 - 3. Let u(r) be the second derivative of j(r). Determine z, given that u(z) = 0.
0, 1
Let p be 4*1 + -8*6/12. Factor -4/5*l**4 + 0 - 2/5*l**5 + 4/5*l**2 + p*l**3 + 2/5*l.
-2*l*(l - 1)*(l + 1)**3/5
Let l(o) be the first derivative of -o**5/15 + o**4/3 - 4*o**3/9 + 31. Solve l(s) = 0 for s.
0, 2
Factor -18 - 30*n - 25/2*n**2.
-(5*n + 6)**2/2
Let i(b) = 2*b**2 - 5*b + 9. Let o(j) = -6*j**2 + 14*j - 28. Let q(c) = -20*i(c) - 6*o(c). Suppose q(x) = 0. What is x?
1, 3
Determine x so that -100*x - 27*x**2 + 46 - 3*x**2 + 85*x**3 - 6 - 2*x**4 - 23*x**4 = 0.
-1, 2/5, 2
Let q(d) = d**5 - 4*d**4 + 6*d**3 + 4*d**2 - 7*d - 4. Let n(k) = -k**5 + k**4 - k**2 + k + 1. Let l(z) = 4*n(z) + q(z). Factor l(h).
-3*h*(h - 1)**2*(h + 1)**2
Let z be 51/7 - (-18)/(-63). Suppose -6*p + z*p = 0. Let p*m + 0 + 2/5*m**4 - 2/5*m**3 - 2/5*m**2 + 2/5*m**5 = 0. What is m?
-1, 0, 1
Let h(q) = -9*q**3 + 60*q**2 - 30*q. Let w(n) = n**3 - 6*n**2 + 3*n. Let m(u) = -2*h(u) - 21*w(u). Find f such that m(f) = 0.
0, 1
Let y be 4/(-18) - 5/(-27)*3. Factor 1/3*x**4 + 0 - 1/3*x + 1/3*x**3 - y*x**2.
x*(x - 1)*(x + 1)**2/3
Suppose 0 - 1/5*y**4 + 2/5*y + 1/5*y**5 - 3/5*y**3 + 1/5*y**2 = 0. What is y?
-1, 0, 1, 2
Let i(v) be the second derivative of v**8/3360 + v**7/630 + v**6/360 + v**4/2 + 6*v. Let y(j) be the third derivative of i(j). Determine l, given that y(l) = 0.
-1, 0
Suppose 12 = -5*g + 2. Let s be (g/(-16))/((-6)/(-12)). Solve s*y**3 + 1/4*y**2 + 0*y + 0 = 0.
-1, 0
Let b(g) be the third derivative of -5*g**7/42 - 3*g**6/2 - 8*g**5 - 70*g**4/3 - 40*g**3 + 2*g**2 - 2. Find i, given that b(i) = 0.
-2, -6/5
Let d be (-7)/(-2)*(-4)/(-7). Suppose d*k - 5*k + 2 = 2*b, 4 = 2*b + 2*k. Suppose 2*x + 3*x**3 + x**4 - x**2 + b*x**2 - x = 0. Calculate x.
-1, 0
Let r(z) be the second derivative of 0 - 1/42*z**4 + 2*z - 2/21*z**3 - 1/7*z**2. Find h such that r(h) = 0.
-1
Suppose 0 = 58*l - 6*l - 156. What is f in -2/3*f - 1/3*f**l + f**2 + 0 = 0?
0, 1, 2
Let b(t) = -t**5 + t**4 - t**3 + t**2 + t. Let k(l) = 7*l**5 - 7*l**4 + 4*l**3 - 4*l**2 - 5*l - 1. Let d(q) = 6*b(q) + k(q). Let d(p) = 0. Calculate p.
-1, 1
Let z(g) = 25*g**3 - 15*g**2 - 45*g - 8. Let k(n) = 76*n**3 - 44*n**2 - 134*n - 24. Let d(j) = -3*k(j) + 10*z(j). Factor d(t).
2*(t - 2)*(t + 1)*(11*t + 2)
Let k(s) be the first derivative of 2*s**5/5 - 4*s**4 + 10*s**3 + 8*s**2 - 32*s - 22. Factor k(a).
2*(a - 4)**2*(a - 1)*(a + 1)
Let q(y) be the first derivative of 4*y**7/735 - y**6/140 - y**5/210 - 2*y**2 + 2. Let l(k) be the second derivative of q(k). Determine h so that l(h) = 0.
-1/4, 0, 1
Let d(v) be the third derivative of -v**6/120 + v**5/30 - v**4/24 - 54*v**2. Factor d(r).
-r*(r - 1)**2
Solve -49/4 - 63/4*j - 15/4*j**2 - 1/4*j**3 = 0.
-7, -1
Let h(p) be the first derivative of -14*p**3/3 + 12*p**2 + 8*p + 3. Suppose h(f) = 0. What is f?
-2/7, 2
Factor -40/3*j - 250/9*j**3 + 100/3*j**2 + 16/9.
-2*(5*j - 2)**3/9
Factor b**3 + b - 36 + 36 - 2*b**2.
b*(b - 1)**2
Let 207*j**2 + 2*j**5 - 3*j**4 - 206*j**2 + 0*j**4 = 0. Calculate j.
-1/2, 0, 1
Let x(q) be the first derivative of -q**4/12 + q**3/9 - 2. What is j in x(j) = 0?
0, 1
Suppose 0 = 3*x - 0 + 3, -10 = -3*c + 4*x. Let m be 2/(-9) + (-96)/(-189). Find b, given that -4/7 - m*b + 2/7*b**c = 0.
-1, 2
Let r be (-190)/4*(-10)/(-30). Let s = r - -487/30. Factor -6/5*a**3 + s*a**2 + 2/5*a**4 - 4/5 + 6/5*a.
2*(a - 2)*(a - 1)**2*(a + 1)/5
Let f(j) be the second derivative of -5*j**7/42 - j**6/6 + j**5/4 + 5*j**4/12 + 4*j. Factor f(y).
-5*y**2*(y - 1)*(y + 1)**2
Let s(h) be the third derivative of h**5/36 - 5*h**3/2 + 66*h**2. Let s(n) = 0. Calculate n.
-3, 3
Let x(s) = 3*s**2 + 2*s - 2. Let z be x(1). Let j(u) be the second derivative of 0 - u + 0*u**z + 0*u**2 - 1/18*u**4 + 1/30*u**5. Factor j(c).
2*c**2*(c - 1)/3
Factor 0 + 6/7*i + 2/7*i**2.
2*i*(i + 3)/7
Let m(o) be the first derivative of 2*o**5/35 - 2*o**4/7 + 4*o**3/21 + 4*o**2/7 - 6*o/7 - 5. Solve m(x) = 0 for x.
-1, 1, 3
Factor 0*d + 2/11*d**2 - 2/11.
2*(d - 1)*(d + 1)/11
Let z(d) be the third derivative of -d**5/15 - d**4/3 - 10*d**2. Let z(n) = 0. Calculate n.
-2, 0
Let t = -6903/5 - -1381. Factor 2/5*r**4 - 2/5*r**3 + 2/5*r**5 - t*r**2 + 0 + 0*r.
2*r**2*(r - 1)*(r + 1)**2/5
Let h = 49 + -49. Let d(y) be the first derivative of -y + h*y**2 + 1/3*y**3 + 1. Find m such that d(m) = 0.
-1, 1
Suppose 1 = 2*m - 3. Let y(z) be the first derivative of -2 + 2/5*z**5 + 0*z**3 - 2*z + m*z**2 - z**4. Find l such that y(l) = 0.
-1, 1
Let v(p) be the second derivative of -2*p**6/15 - p**5/5 + 3*p. Factor v(c).
-4*c**3*(c + 1)
Let t(v) = -v**3 + 12*v**2 - 12*v + 2. Let m = 14 - 16. Let i(x) = 12*x**2 - 12*x + 3. Let q(r) = m*i(r) + 3*t(r). Find o such that q(o) = 0.
0, 2
Let v(a) = -116*a**3 - 120*a**2 - 4*a + 8. Let t(f) = -77*f**3 - 80*f**2 - 3*f + 5. Let b(n) = 8*t(n) - 5*v(n). Solve b(g) = 0 for g.
-1, -1/9, 0
Suppose -2*x - 3 = -3*x. Let m(b) be the second derivative of 3*b + b**2 - 1/12*b**4 + 0 + 1/6*b**x. Factor m(j).
-(j - 2)*(j + 1)
Let f(j) = -5*j**2 + 7*j. Let b(p) = -p**2 - p + 1. Let q(g) = 6*b(g) + 3*f(g). Let q(n) = 0. What is n?
-2/7, 1
Let a(u) = u**3 + u**2 + u. Let y(d) = -25*d**3 - 25*d**2 - 20*d. Let m(o) = -20*a(o) - y(o). Factor m(g).
5*g**2*(g + 1)
Let z(w) be the first derivative of w**4/3 - 4*w**3/9 - 4*w**2/3 + 29. Factor z(a).
4*a*(a - 2)*(a + 1)/3
Factor 43*o**2 + 12 + 0*o**4 - 4*o**4 + 6*o**5 - 47*o**3 - 50*o + 11*o**3 + 29*o**2.
2*(o - 1)**3*(o + 3)*(3*o - 2)
Let v(r) = -r**3 + 5*r**2 - r - 3. Let q(u) = u**3 - 9*u**2 + 3*u + 5. Let a(y) = -3*q(y) - 5*v(y). Find l, given that a(l) = 0.
-2, 0, 1
Suppose 0 = j - 2*j + 7. Suppose -2*h + j - 3 = 0. Determine c, given that 4/3*c + 4/3 + 1/3*c**h = 0.
-2
Let m(a) = a**3 + 6*a**2 - 5*a + 8. Let z be m(-7). Let x(h) = 4*h**2 + 2*h + 4. Let y(b) = -9*b**2 - 4*b - 9. Let n(p) = z*y(p) - 14*x(p). Factor n(c).
-2*(c + 1)**2
Suppose -2*h - 2 = -5*j + 1, h - j = 3. Let x = h + -4. Factor -2/5*g - 2/5*g**x + 0 + 2/5*g**3 + 2/5*g**4.
2*g*(g - 1)*(g + 1)**2/5
Suppose h + 5*p + 16 = -h, 0 = -h - 3*p - 10. Let k(t) be the second derivative of -1/30*t**3 + t + 0*t**h + 0 - 1/60*t**4. Factor k(r).
-r*(r + 1)/5
Let j(h) be the first derivative of -h**5/20 + h**4/4 - h**3/2 + 5*h**2/2 + 4. Let r(c) be the second derivative of j(c). Factor r(k).
-3*(k - 1)**2
Suppose -4*l + 3 = -5. Let w(i) be the second derivative of 1/14*i**7 - 3*i + 0 + 11/6*i**3 + 13/10*i**5 + l*i**4 + 7/15*i**6 + i**2. Factor w(v).
(v + 1)**4*(3*v + 2)
Let h(l) be the second derivative of l**6/10 - l**4/4 + 4*l. Factor h(b).
3*b**2*(b - 1)*(b + 1)
Let y = 37 + -20. Determine b, given that 2*b + 0 + y*b**3 - 19*b**3 + 0 = 0.
-1, 0, 1
Let c(l) be the second derivative of l**6/15 - l**4/2 - 2*l**3/3 - 19*l. Factor c(f).
2*f*(f - 2)*(f + 1)**2
Let w(s) be the third derivative of s**5/90 + s**4/12 + 4*s**2. Factor w(x).
2*x*(x + 3)/3
Let -17*t**2 + 15*t**2 - 5 + 33 - 10*t = 0. Calculate t.
-7, 2
Factor -6 - 4 - 6 + 4*y**2.
4*(y - 2)*(y + 2)
Let i be (52/(-91))/(6/(-7)). Let z be -5 + 8 - (-8)/(-3). Factor i*r**2 + z - r - r**4 + 2/3*r**