4/3*l**2 - 1/3*l**4 = 0 for l.
-1, 1, 3
Let b(s) be the first derivative of 4*s**5/15 - 5*s**4/6 - 8*s**3/9 + s**2 - 9. What is k in b(k) = 0?
-1, 0, 1/2, 3
Let s be ((-4)/54)/(10/(-15)). Let l(n) be the second derivative of n + 0 - 1/6*n**2 + 0*n**4 - 1/30*n**5 + 1/90*n**6 + s*n**3. Factor l(c).
(c - 1)**3*(c + 1)/3
Let q(f) be the first derivative of -f**5 - 5*f**4/4 + 5*f**3 + 25*f**2/2 + 10*f + 1. Factor q(a).
-5*(a - 2)*(a + 1)**3
Let t(y) be the third derivative of -y**6/40 + y**5/10 + y**2. Solve t(x) = 0.
0, 2
Factor 2*q**3 - 11/2*q**5 + 0*q**2 + 0*q + 0 - 10*q**4.
-q**3*(q + 2)*(11*q - 2)/2
Let w(v) be the second derivative of -v**5/100 + v**3/10 + 3*v**2/2 - 5*v. Let i(u) be the first derivative of w(u). Suppose i(l) = 0. What is l?
-1, 1
Let o(k) be the first derivative of -1/8*k**2 + 0*k**3 - 1 + 0*k + 1/16*k**4. Find r, given that o(r) = 0.
-1, 0, 1
Let j(i) be the first derivative of -i**5/30 - i**4/8 + i**3/2 - 5*i**2/12 + 23. Let j(u) = 0. What is u?
-5, 0, 1
Let r(f) = f - 8. Let n be r(10). Factor -g**2 - 3*g - 6*g + 30 - 2*g**n - 3*g**4 - 24 + 9*g**3.
-3*(g - 2)*(g - 1)**2*(g + 1)
Let n(g) be the third derivative of 1/3*g**4 + 9*g**2 + 0*g + 0 + 7/90*g**5 - 4/9*g**3. Determine u, given that n(u) = 0.
-2, 2/7
Let j(h) be the third derivative of -h**8/224 + 3*h**7/140 - h**6/40 + 7*h**2. Factor j(k).
-3*k**3*(k - 2)*(k - 1)/2
Factor -24*z**2 + 15*z + 3*z**3 + z + 32*z.
3*z*(z - 4)**2
Let -2*o**3 - 2*o**3 + 6*o**3 + 2*o**3 = 0. What is o?
0
Let r(t) be the second derivative of -3*t**5/10 + 11*t**4/6 - 2*t**3 + 7*t. Let r(k) = 0. What is k?
0, 2/3, 3
Let b(i) be the second derivative of -i**5/20 + 7*i**4/12 - 11*i**3/6 + 5*i**2/2 - 48*i. Let b(t) = 0. Calculate t.
1, 5
Let d(c) = c**3 - 5*c**2 - 3*c + 1. Let x be d(5). Let g be x/8 - (5 + -7). Factor 0*r + 1/4*r**2 - g*r**3 + 0.
-r**2*(r - 1)/4
Let c(o) be the second derivative of -o**6/360 - o**5/60 + o**4/8 + o**3/6 + o. Let p(l) be the second derivative of c(l). Factor p(y).
-(y - 1)*(y + 3)
Let 6/5*r**2 + 2/5*r + 0 = 0. Calculate r.
-1/3, 0
Let r(h) = -7*h**2 - 9*h - 4. Let z be (7 - 7) + (1 - -1). Let u(o) = 10 + 19*o + 11*o**2 + 3 + 4*o**z - 4. Let g(k) = -15*r(k) - 6*u(k). Solve g(i) = 0 for i.
-1, -2/5
Suppose 0 = 4*h - 0*h - 28. Suppose -5*r - 2*m + 18 = 0, -2*r = -0*r + m - h. Let -4/3*a**2 + 0 + 2/3*a**3 - 2/3*a + 4/3*a**r = 0. Calculate a.
-1, -1/2, 0, 1
Let y = -7 - -5. Let r = 4 + y. Find d such that 4*d**2 - 2*d**4 - 4*d + r*d**5 + 2*d - 2*d**4 = 0.
-1, 0, 1
Let n = -6 - -6. Let o(f) be the third derivative of -1/336*f**8 + 0*f + n*f**3 - 1/20*f**6 - 1/24*f**4 - f**2 + 1/15*f**5 + 2/105*f**7 + 0. Factor o(u).
-u*(u - 1)**4
Let j(c) = -16*c**3 - 8*c**2 - 10*c. Let q(v) = 15*v**3 + 9*v**2 + 9*v. Let z(t) = 5*j(t) + 6*q(t). Factor z(i).
2*i*(i + 1)*(5*i + 2)
Suppose 2*g - 15 = -3*g. Factor g - 3 + s**4 + 0*s**4 + s**3.
s**3*(s + 1)
Let c = -5 - -9. Suppose 0 = -c*i + 3*i. Factor i + 1 - 2*m**2 + 1.
-2*(m - 1)*(m + 1)
Suppose -4*o + 6 = 2. Let m be (o - 1) + 3 + -1. Let -19*p**2 + 2*p**3 + p**4 + 18*p**m - p**5 - p**5 = 0. What is p?
-1, 0, 1/2, 1
Let p be (-8)/50*(-5)/2. Let u be (24/16)/(3/10). Factor a + 4/5*a**4 - p*a**2 - 4/5*a**3 - 2/5 - 1/5*a**u.
-(a - 2)*(a - 1)**3*(a + 1)/5
Suppose 2*i + 3*z - 24 = -0*i, 5*z + 4 = 4*i. Let k be (i + -1)*(-10)/(-75). Determine t so that -2/3 + k*t**2 + 0*t = 0.
-1, 1
Let c(h) be the first derivative of -2*h**2 - 2*h + 2 - 2/3*h**3. Factor c(r).
-2*(r + 1)**2
Let n(h) = 12*h**3 - 16. Let k(c) = 4*c**3 - 5. Let s(b) = -16*k(b) + 5*n(b). Factor s(r).
-4*r**3
Let c(y) be the first derivative of -3 + 2/27*y**3 + 0*y - 1/9*y**2. Factor c(t).
2*t*(t - 1)/9
Let f(n) = -54*n**4 - 29*n**3 + 41*n**2 + 5*n + 11. Let l(q) = -27*q**4 - 15*q**3 + 21*q**2 + 3*q + 6. Let w(b) = 6*f(b) - 11*l(b). Factor w(z).
-3*z*(z + 1)*(3*z - 1)**2
Let f(j) be the second derivative of 0*j**2 - 2*j + 0*j**3 - 1/42*j**4 + 0. Factor f(b).
-2*b**2/7
Suppose 3 = -4*s - 1. Let w be 3*((-8)/6)/s. Factor -2*o**2 + o**3 + o**2 - 2*o**4 + o**w - 3*o**3.
-o**2*(o + 1)**2
Let h be ((-60)/(-18))/(2/6). Factor k**3 - 7*k**2 + k**4 - 4 + 4*k - 5*k**3 + h*k**2.
(k - 2)**2*(k - 1)*(k + 1)
What is z in 1/7*z**2 + 0*z - 1/7 = 0?
-1, 1
Let p(b) be the third derivative of -b**6/300 - b**5/200 + b**4/40 + b**3/2 + b**2. Let l(u) be the first derivative of p(u). Let l(z) = 0. Calculate z.
-1, 1/2
Let u(l) be the third derivative of l**5/40 - l**4/4 + l**3 + 4*l**2. Factor u(z).
3*(z - 2)**2/2
Let q(w) be the second derivative of 1/6*w**3 - 1/84*w**7 - 4*w + 0 + 0*w**2 - 1/8*w**4 - 1/40*w**5 + 1/20*w**6. Let q(g) = 0. Calculate g.
-1, 0, 1, 2
Factor -1/5*v**3 - 9/5*v**2 - 16/5 - 24/5*v.
-(v + 1)*(v + 4)**2/5
Suppose 3/2*p**2 - 1/2*p**3 - p + 0 = 0. Calculate p.
0, 1, 2
Let a(g) be the first derivative of 2 + 1/26*g**4 - 3/13*g**2 + 4/13*g + 0*g**3. Factor a(f).
2*(f - 1)**2*(f + 2)/13
Let d(a) be the second derivative of a**4/4 + a**3 - 6*a. Find u such that d(u) = 0.
-2, 0
Let t(u) = 4*u - 7. Let n(j) = -5*j + 8. Let q(g) = -5*n(g) - 6*t(g). Let s be q(2). Factor 4*k + 8*k**3 + 4*k**s + 10*k**2 + 3*k**4 - 5*k**4.
2*k*(k + 1)**2*(k + 2)
Let j be (-198)/(-84) - (-3)/(-2). Factor j*s - 2/7*s**3 - 4/7 + 0*s**2.
-2*(s - 1)**2*(s + 2)/7
Let h(a) be the first derivative of 1/6*a**4 + 0*a - 1/6*a**2 - 1 + 0*a**5 + 0*a**3 - 1/18*a**6. Factor h(x).
-x*(x - 1)**2*(x + 1)**2/3
Suppose 4/11*o**3 - 4/11*o + 2/11*o**4 - 2/11*o**2 + 0 = 0. Calculate o.
-2, -1, 0, 1
Let l(m) = 4*m + 1. Let u be l(2). Let f = -17/2 + u. Determine a so that -a - 1/2 - f*a**2 = 0.
-1
Let g(m) = 4*m**2 - 5*m - 2. Let p(j) = -7*j**2 + 9*j + 3. Let a(f) = -5*g(f) - 3*p(f). What is b in a(b) = 0?
1
Let b(w) = 15*w**2 + 24*w. Let x(s) = -s**2. Let m(i) = b(i) + 12*x(i). Determine y so that m(y) = 0.
-8, 0
Suppose -4 + 75*j**5 + 14*j**2 - 2*j**4 - 8*j**4 - 14*j - 83*j**5 + 10*j**3 + 12*j**3 = 0. Calculate j.
-2, -1, -1/4, 1
Let i(w) be the first derivative of -w**6/10 + 3*w**5/25 + 3*w**4/10 - 2*w**3/5 - 3*w**2/10 + 3*w/5 + 4. Solve i(k) = 0.
-1, 1
Let p(k) be the first derivative of 2 - 3/2*k**4 + 5*k**2 + 8/3*k**3 - 4*k. Solve p(u) = 0 for u.
-1, 1/3, 2
Let l(i) be the third derivative of -i**5/45 - 5*i**4/9 - 2*i**3 - 52*i**2. Find w, given that l(w) = 0.
-9, -1
Let k(s) = -s**2 - 6*s + 1. Let o(d) = 3*d**2 + 17*d - 2. Let c(m) = 8*k(m) + 3*o(m). Let c(f) = 0. What is f?
-2, -1
Let -3/2*p**2 + 9/2 - 3*p = 0. Calculate p.
-3, 1
Let z(y) = y**4 + 10*y**3 + 9*y**2 + 9. Let t(u) = u**3 + u**2 + 1. Let o(x) = 36*t(x) - 4*z(x). Determine r so that o(r) = 0.
-1, 0
Suppose -3*i = 5*x - 86, 6*i - 4*i - 20 = -x. Suppose -4*r = -5*n + 7, r - x = -4*n - r. Determine k, given that 0 + 1/3*k**n + 1/3*k + 2/3*k**2 = 0.
-1, 0
Factor 0*a**2 + 1/3*a - 1/3*a**3 + 0.
-a*(a - 1)*(a + 1)/3
Factor -2/7*f**3 + 18/7*f**2 - 54/7*f + 54/7.
-2*(f - 3)**3/7
Suppose 2*b - 7*b + 10 = 0. What is v in 3*v + 3 - 10*v**3 - 7 + 7*v + 4*v**b = 0?
-1, 2/5, 1
Let u(z) be the first derivative of -z**5/210 + z**4/84 - 3*z**2/2 + 1. Let t(o) be the second derivative of u(o). Determine k so that t(k) = 0.
0, 1
Let c(l) be the second derivative of -l**4/36 - l**3/6 - l**2/3 - l. Suppose c(h) = 0. What is h?
-2, -1
Let y be (1 + -3)*3/(-6). Suppose -2*m + y = -m. Let q(b) = -b**3 + b + 1. Let l(p) = -2*p**4 + 2*p + 2. Let w(v) = m*l(v) - 2*q(v). Factor w(g).
-2*g**3*(g - 1)
Let h = -133/3 - -45. Suppose -h*s + 7/3*s**2 + 0 - 5/3*s**3 = 0. Calculate s.
0, 2/5, 1
Let 5*f**5 - 4*f**4 + 20*f - 3*f**4 + 7*f**4 - 25*f**3 = 0. What is f?
-2, -1, 0, 1, 2
Let n(r) = -r**2 + 7*r + 1. Let o be n(6). Let i = -5 + o. Factor -2*u**3 + 5*u**2 + i*u**2 + u**2 - 10*u + 4.
-2*(u - 2)*(u - 1)**2
Let i = -22/9 + 34/9. Factor 2/3*l**2 + 2*l + i.
2*(l + 1)*(l + 2)/3
Let s = 6 - 2. Suppose -2 = -2*b + s. Factor 4/5 + 2/5*p**b - 2/5*p - 6/5*p**2 + 2/5*p**4.
2*(p - 1)**2*(p + 1)*(p + 2)/5
Let z(d) = -6*d**5 + 6*d**4 + 12*d**3 - 12*d**2 - 20*d + 6. Let i(w) = -2*w**5 + 2*w**4 + 4*w**3 - 4*w**2 - 7*w + 2. Let s(h) = 14*i(h) - 5*z(h). Factor s(n).
2*(n - 1)**3*(n + 1)**2
Let r(y) = y + 11. Suppose 12 = -3*o, 3*f + o = -2*f - 44. Let v be r(f). Factor v*c**2 - 1/2*c - c**3 + 3/2*c**5 - 5/2*c**4 - 1/2.
(c - 1)**3*(c + 1)*(3*c + 1)/2
Let a(v) be the third derivative of v**7/1680 + v**6/320