4*k**2.
-(k - 1)*(k + 1)/4
Suppose 5*b - 25*b**2 + 4*b**3 + 11*b**3 + 97 - 92 = 0. What is b?
-1/3, 1
Suppose 5*y + 9 = 4*u + 4*y, -u - 5*y - 24 = 0. Factor -u + 1 + 3*w - 6*w + w**2.
w*(w - 3)
Let t(p) be the second derivative of -p**7/84 + p**5/20 - p**3/12 - 14*p. Find l, given that t(l) = 0.
-1, 0, 1
Suppose 9*u + 39 = 22*u. Let i(q) be the third derivative of 1/150*q**5 + 0*q + 0 + u*q**2 - 1/20*q**4 - 2/15*q**3 + 1/100*q**6 + 1/525*q**7. Solve i(j) = 0.
-2, -1, 1
Determine w so that -4*w - 2*w**2 + w**4 - 3*w**2 + 2 - w**3 + 5*w + 2*w**4 = 0.
-1, -2/3, 1
Let o(t) be the second derivative of t**4/6 - 2*t**3/3 - 3*t. Let o(v) = 0. What is v?
0, 2
Factor 27*b - 10*b**2 + 5*b + 208 - 4*b - 232 + b**3.
(b - 6)*(b - 2)**2
Suppose 5*h + 3*i - 143 = 0, -5*h = -5*i - 0*i - 135. Let m = -14 + h. Let 8*l**3 + 3*l**3 - l**3 + m*l**2 + 4*l = 0. What is l?
-1, -2/5, 0
Factor 0*z + 5 + 4*z + 2*z**2 - 3*z**2 + 0*z.
-(z - 5)*(z + 1)
Let w(y) = -3*y**3 + 2*y**2 - 1. Let c be w(-1). Factor -3*z**2 - 7*z**3 - z**2 + 2*z**2 + c*z**4.
z**2*(z - 2)*(4*z + 1)
Suppose 5*j = 2*l + 18, 0 = -j + 2*l + l + 14. Let g(v) be the first derivative of v**2 + j + 1/3*v**3 + v. Factor g(f).
(f + 1)**2
Suppose -12*z**2 - 14*z**2 + 2*z + 17*z**2 = 0. What is z?
0, 2/9
Let -2*m + 2*m**3 - 2/7 + 2/7*m**2 = 0. What is m?
-1, -1/7, 1
Let m = -3/610 + 19547/5490. Determine a, given that 34/9*a**2 - 2*a**5 - 14/3*a**4 + 8/9 + m*a - 14/9*a**3 = 0.
-1, -2/3, 1
Suppose -9*m**2 + 10*m**2 + 5 + 5 - 8*m + 6 = 0. What is m?
4
Let r be 28/(-24)*(-2)/7. Factor r + 1/3*g**2 + 2/3*g.
(g + 1)**2/3
Suppose -5*r - 50 = -5*s, 2*r - 3*r = s. Suppose 0*n = 3*n - 3*v + 3, -s*n - 2 = -2*v. Factor n*q**2 + 0 + 1/2*q**3 + 1/2*q**4 + 0*q.
q**3*(q + 1)/2
Let r(b) be the first derivative of -b**4/12 + b**3/9 + b**2/6 - b/3 + 3. Solve r(w) = 0 for w.
-1, 1
Let v(y) be the second derivative of -2/7*y**2 + 0 + 4*y + 1/21*y**4 - 1/21*y**3 + 1/70*y**5. Suppose v(c) = 0. Calculate c.
-2, -1, 1
Suppose 0 = -2*v - v. Let p(k) be the second derivative of k + 0 + v*k**3 + 0*k**2 + 1/42*k**4. Let p(b) = 0. What is b?
0
Let l(p) be the first derivative of -2*p**3/9 - 22*p**2/3 - 242*p/3 + 42. Suppose l(j) = 0. What is j?
-11
Let n be ((-4)/(-6))/((-2)/(-15)). Suppose o = 4*u - 54, n*u = 2*o + 24 + 45. Suppose g - 5*g + 3*g**3 + 14*g**2 - u*g**3 = 0. Calculate g.
0, 2/5, 1
Suppose -l + 2 = 1. Let i be (45/12)/3 - l. Determine n, given that -1/4*n**4 - i*n**3 + 0*n + 0*n**2 + 0 = 0.
-1, 0
Let s(o) be the first derivative of -2 - 1/18*o**4 - 2*o + 2/9*o**3 - 1/3*o**2. Let g(b) be the first derivative of s(b). Factor g(y).
-2*(y - 1)**2/3
Suppose y - 2*y = -3. Factor -3*t**y - 3 + 3 - 3*t**5 + 6*t**4.
-3*t**3*(t - 1)**2
Let z(c) be the third derivative of -c**7/49 + 17*c**6/210 - 2*c**5/105 - 2*c**4/21 - 10*c**2. Solve z(w) = 0.
-2/5, 0, 2/3, 2
Factor 69*x + 110*x**2 + 51*x + 45 + 40*x**3 + 4*x**4 + x**4.
5*(x + 1)**2*(x + 3)**2
Let u(d) = -4*d + 20. Let m be u(5). Suppose m - 2/7*c**5 + 0*c - 6/7*c**4 - 2/7*c**2 - 6/7*c**3 = 0. Calculate c.
-1, 0
Let q(a) = -12*a**5 + 45*a**3 + 21*a**2 + 9*a - 21. Let h(p) = 3*p**5 - 11*p**3 - 5*p**2 - 2*p + 5. Let n(s) = -21*h(s) - 5*q(s). Factor n(r).
-3*r*(r - 1)**2*(r + 1)**2
Suppose -76*d + 4 = -75*d. Factor 3/2*n**2 + n + 1/4*n**d + 1/4 + n**3.
(n + 1)**4/4
Let v(m) be the third derivative of 0*m**5 + 0*m**4 - 1/540*m**6 + 5*m**2 + 0*m - 1/945*m**7 + 0*m**3 + 0. Find k such that v(k) = 0.
-1, 0
Let h = 40 - 42. Let o be 0/(-3) - h/9. Solve 0*x**4 - o*x**5 - 2/9*x + 4/9*x**3 + 0 + 0*x**2 = 0 for x.
-1, 0, 1
Let v(p) be the first derivative of -4*p**3/21 - 8*p**2/7 - 9. Factor v(q).
-4*q*(q + 4)/7
Let w be (50/375)/(((-1)/(-42))/1). Solve -w*x**3 + 4/5*x + 11*x**2 - 4/5 = 0.
-2/7, 1/4, 2
Let k(u) = -2*u - 7. Let v be k(-5). Suppose -3*j - 8 = 2*h - 0*h, 8 = v*j - 2*h. Factor 1/3*q + j*q**3 - 1/3*q**5 + 0 - 2/3*q**4 + 2/3*q**2.
-q*(q - 1)*(q + 1)**3/3
Let t(o) be the first derivative of -2*o**3/21 - 2*o**2/7 + 6*o/7 - 9. Solve t(h) = 0.
-3, 1
Let o(m) be the first derivative of -2*m**3/9 - 2*m**2/3 - 2. Determine k so that o(k) = 0.
-2, 0
Let y(b) = -b**2 + 21*b + 16. Let o(l) = 5*l**2 - 85*l - 65. Let f(u) = -6*o(u) - 25*y(u). Factor f(m).
-5*(m + 1)*(m + 2)
Let x(q) = q**2. Let u(i) = 32*i**2 - 36*i + 12. Let c(d) = u(d) - 5*x(d). Factor c(k).
3*(3*k - 2)**2
Let i(p) be the first derivative of -2/33*p**3 + 0*p + 0*p**2 - 8 - 8/55*p**5 + 5/22*p**4. Factor i(u).
-2*u**2*(u - 1)*(4*u - 1)/11
Let c be (-345)/(-80) - 4 - (-2)/(-8). Let m(n) be the first derivative of -1/4*n + 1 + c*n**4 + 3/8*n**2 - 1/4*n**3. Suppose m(d) = 0. Calculate d.
1
Let r(k) be the first derivative of -k**4/5 - 7*k**3/15 - k**2/5 + k/5 - 6. Determine z so that r(z) = 0.
-1, 1/4
Let y(l) be the second derivative of -l**5/15 + 2*l**3/3 + 4*l**2/3 - 8*l. What is x in y(x) = 0?
-1, 2
Let v(s) be the second derivative of 3*s**5/140 - 3*s**4/28 + s**3/7 - 27*s. Find i such that v(i) = 0.
0, 1, 2
Let s(p) be the first derivative of -p**4/16 + p**3/3 - 5*p**2/8 + p/2 - 8. Factor s(b).
-(b - 2)*(b - 1)**2/4
Let t(a) be the first derivative of a**5/40 + a**4/24 - a**3/12 - a**2/4 + 5*a + 2. Let u(o) be the first derivative of t(o). Solve u(l) = 0.
-1, 1
Let o = 11/19 - 212/399. Let n(t) be the second derivative of 0 + 0*t**2 + 0*t**3 - o*t**4 - t + 1/70*t**5. What is v in n(v) = 0?
0, 2
Let q(f) be the third derivative of f**5/690 + f**4/69 - f**2. Let q(w) = 0. What is w?
-4, 0
Let o(x) be the first derivative of -2*x**6/3 + 4*x**5/5 + 8*x**4 - 32*x**3/3 - 32*x**2 + 64*x - 4. Suppose o(m) = 0. Calculate m.
-2, 1, 2
Let k(z) be the first derivative of -z**3 + 22. Factor k(a).
-3*a**2
Let p(n) be the first derivative of n**3/15 - n**2/10 + 19. Find f, given that p(f) = 0.
0, 1
Let d(o) be the first derivative of o**3/6 - o/2 + 20. What is x in d(x) = 0?
-1, 1
Let j(w) be the first derivative of -1 + 4/15*w**5 + 4/3*w - 8/9*w**3 - 2/9*w**6 + 2/3*w**4 - 2/3*w**2. Let j(u) = 0. Calculate u.
-1, 1
Let a(k) be the third derivative of -k**9/7560 - k**4/12 - 3*k**2. Let b(u) be the second derivative of a(u). Let b(o) = 0. Calculate o.
0
Let h = -1/16 + 179/48. Let j = -10/3 + h. Determine a, given that -1/3*a + 1/3*a**3 + 0 - 1/3*a**4 + j*a**2 = 0.
-1, 0, 1
Let b(r) be the third derivative of r**6/45 + r**5/15 + r**4/18 + 14*r**2. Let b(a) = 0. What is a?
-1, -1/2, 0
Let y(u) be the third derivative of -1/180*u**6 + 0*u**3 - 1/9*u**4 + 0 + 2/45*u**5 + 0*u - 2*u**2. Find f such that y(f) = 0.
0, 2
What is g in 0 + 35/6*g**5 - 4*g**4 - 31/6*g**3 + 4*g**2 - 2/3*g = 0?
-1, 0, 2/7, 2/5, 1
Let k(x) be the first derivative of 4*x**5/5 + 3*x**4 + 4*x**3/3 - 6*x**2 - 8*x - 3. Let k(o) = 0. What is o?
-2, -1, 1
Let m = -617/9 + 69. Let p be (8/14)/(360/140). Solve 2/3*s - 2/3*s**4 + 4/9*s**2 - m*s**3 - p*s**5 + 2/9 = 0 for s.
-1, 1
Let d(q) be the first derivative of -q**5/15 + 2*q**4/3 - 22*q**3/9 + 4*q**2 - 3*q - 8. Factor d(x).
-(x - 3)**2*(x - 1)**2/3
Let q = 210 + -210. Factor 0*w + 0 - w**4 + 1/3*w**3 + q*w**2.
-w**3*(3*w - 1)/3
Suppose 3*k + 2*k + 14 = -2*d, 5*k = -20. Suppose -d*x = -4*x + 4. Factor 0 + 6/5*g**x - 6/5*g**3 - 2/5*g**5 + 2/5*g**2 + 0*g.
-2*g**2*(g - 1)**3/5
Let r(u) be the first derivative of -u**5/30 + u**4/12 + 2*u**3/3 - u**2/2 - 3. Let o(i) be the second derivative of r(i). Find t, given that o(t) = 0.
-1, 2
Factor -1/3*a**3 - 8/3*a - 5/3*a**2 - 4/3.
-(a + 1)*(a + 2)**2/3
Let h be ((-1)/12)/((-5)/20). Factor -1/3*d**4 + 2/3*d**2 + 0 - h*d**3 + 0*d.
-d**2*(d - 1)*(d + 2)/3
Factor 0 + 2/7*f**3 + 2/7*f**4 - 2/7*f - 2/7*f**2.
2*f*(f - 1)*(f + 1)**2/7
Let c = -19/10 - -331/90. Factor 10/9*z**3 + 2/9*z + c*z**2 - 4/9.
2*(z + 1)**2*(5*z - 2)/9
Suppose 19 = -3*y - 2*s, 0*s + s + 20 = -5*y. Let v = y - -6. Suppose -1/2*n - 3*n**v - 2*n**4 - 1/2*n**5 - 2*n**2 + 0 = 0. Calculate n.
-1, 0
Suppose -19 = -2*m - 2*m - w, -2*w = m - 3. Suppose -4*a + 6 = 2*k, 4*k - m*k + 12 = 5*a. Find b such that -2/7*b**4 - 4/7*b - 8/7*b**a + 0 - 10/7*b**2 = 0.
-2, -1, 0
Find h, given that 3*h**3 + 3*h**2 - 9/2*h**4 + 3/2*h**5 - 9/2*h + 3/2 = 0.
-1, 1
Let x = 37981/60 - 633. Let n(r) be the second derivative of x*r**5 + 0 - 1/18*r**3 - r - 1/36*r**4 + 1/6*r**2. Factor n(v).
(v - 1)**2*(v + 1)/3
Factor 0 - 12/7*k**3 + 4/7*k**4 - 4/7*k + 1