for v.
-1, 0
Let a(o) be the second derivative of -o**5/20 + o**4/3 - 2*o**3/3 + 45*o. Solve a(l) = 0 for l.
0, 2
Suppose d + 14 = 50. Let c = d - 106/3. Factor -c*f - 4*f**3 + 8/3*f**4 + 8/3*f**2 + 0 - 2/3*f**5.
-2*f*(f - 1)**4/3
Let j(m) be the third derivative of 1/330*m**5 - 1/1155*m**7 + 0 - 1/660*m**6 + 3*m**2 + 0*m + 0*m**3 + 1/132*m**4. Factor j(g).
-2*g*(g - 1)*(g + 1)**2/11
Let q be (-2)/10*(31 - 51). Let p(i) be the second derivative of -1/24*i**q + 0 - i**2 - 1/3*i**3 - i. Factor p(t).
-(t + 2)**2/2
Let y(w) be the first derivative of 4*w**3/3 + 6*w**2 - 1. Factor y(v).
4*v*(v + 3)
Let a(f) be the second derivative of 3*f + 0*f**3 + 0 - 1/21*f**7 + 0*f**2 - 1/15*f**5 + 0*f**4 + 1/9*f**6. Find u, given that a(u) = 0.
0, 2/3, 1
Let b(z) be the third derivative of z**5/60 + z**4/2 + 6*z**3 - 24*z**2. Factor b(d).
(d + 6)**2
Let 0 - 4/9*l - 2/9*l**3 + 2/3*l**2 = 0. Calculate l.
0, 1, 2
Let m(a) be the second derivative of a**4/24 - a**3 + 9*a**2 + 16*a. Factor m(t).
(t - 6)**2/2
What is w in 3/4*w**4 + 0 - w**2 - w**3 + 0*w = 0?
-2/3, 0, 2
Suppose -4*i - 4*x - 20 = 0, -5*i - x - 3*x = 26. Let k = i + 10. Factor -4*n**3 + 3*n**k + 2*n**2 + 3*n**3 + n - 5*n**4.
-n*(n - 1)*(n + 1)*(2*n + 1)
Let o be ((-14)/4 - -3)*2. Let p be (7/28)/(o/(-8)). Determine z so that 6*z**p + 18 - 4*z**2 - 5*z - 7*z = 0.
3
Let k(t) be the third derivative of -t**5/12 + 5*t**4/24 - 3*t**2. Factor k(h).
-5*h*(h - 1)
Suppose -4*a + 4*g + g = -11, -5*a = -3*g - 17. Suppose n + 4*d = a, -5*n + 2*n + 3*d + 12 = 0. Factor -2*k**n + 4*k**4 + 2*k**3 - 4*k**3.
2*k**3*(k - 1)
Suppose 32 = 7*b - 6*b. Let i be 23*2/(b/12). Suppose -9/4*n - 27/2*n**3 - 3/2 + i*n**2 = 0. Calculate n.
-2/9, 1/2, 1
Let w = -9 + 32. Factor 36*c**2 + 2*c**3 - w*c + 8 - 17*c - 16*c**3 + 10*c**2.
-2*(c - 2)*(c - 1)*(7*c - 2)
Solve 2/11*a**5 + 4/11*a + 14/11*a**2 + 18/11*a**3 + 10/11*a**4 + 0 = 0 for a.
-2, -1, 0
Let m(z) be the second derivative of 0*z**3 + 0*z**2 + 1/70*z**5 - 2/105*z**6 + 0 + 2*z + 1/42*z**4. Factor m(t).
-2*t**2*(t - 1)*(2*t + 1)/7
Let q(i) be the third derivative of -i**6/720 + i**4/144 - 8*i**2. Determine x, given that q(x) = 0.
-1, 0, 1
Find q such that 25 + 0*q**2 + 2*q**2 + 4*q - 25 = 0.
-2, 0
Let u(p) be the third derivative of 0 + 0*p**3 + 2*p**2 + 0*p + 0*p**4 - 1/15*p**5 - 1/15*p**6 - 2/105*p**7. Factor u(k).
-4*k**2*(k + 1)**2
Factor -4/3*w**2 + 2/9*w**3 + 0 - 14/9*w.
2*w*(w - 7)*(w + 1)/9
Let m(y) be the first derivative of -y**4/8 + y**3/3 + y**2/4 - y + 37. Factor m(i).
-(i - 2)*(i - 1)*(i + 1)/2
Factor 2*w**2 + 8/3 + 4*w + 1/3*w**3.
(w + 2)**3/3
Factor -1/3 - 4/3*s**4 + 5/6*s**5 - 2/3*s**3 - 1/6*s + 5/3*s**2.
(s - 1)**3*(s + 1)*(5*s + 2)/6
Let w(j) = 4*j**3 + j**2. Let l(t) = -9*t**3 - 2*t**2. Let u be (-1 - -2)/((-1)/(-3)). Let f(p) = u*l(p) + 7*w(p). Solve f(h) = 0 for h.
-1, 0
Factor 24/11*c**3 + 0*c + 10/11*c**4 + 8/11*c**2 + 0.
2*c**2*(c + 2)*(5*c + 2)/11
Suppose 0 + 0 + 1407*n - 3*n**2 - 1410*n = 0. What is n?
-1, 0
Let h(w) be the first derivative of -2*w**5/5 - w**4/2 + 2*w**3 + 5*w**2 + 4*w - 26. Solve h(t) = 0.
-1, 2
Let v(w) be the third derivative of 0*w**4 + 5*w**2 + 1/672*w**8 + 0*w**3 + 0*w - 1/240*w**6 + 0*w**5 + 0 + 0*w**7. What is n in v(n) = 0?
-1, 0, 1
Let f(n) be the first derivative of -n**5/30 + n**4/6 - n**3/3 + 3*n**2/2 - 3. Let p(y) be the second derivative of f(y). Factor p(h).
-2*(h - 1)**2
Let c be (-2)/6*(-6 - 210/25). Solve 8/5*s + 18/5*s**3 + 4/5*s**4 + 0 + c*s**2 = 0 for s.
-2, -1/2, 0
Let l(j) be the third derivative of j**8/1848 + 2*j**7/385 + 7*j**6/330 + 8*j**5/165 + 3*j**4/44 + 2*j**3/33 + 3*j**2. What is n in l(n) = 0?
-2, -1
Suppose -n - 3*h = -1 - 7, -n + h = 0. Factor 2/3*b**3 - 4/3 + 4/3*b**n - 2/3*b.
2*(b - 1)*(b + 1)*(b + 2)/3
Let m(k) be the second derivative of k**5/120 - k**4/24 + k**3/12 - k**2/12 - 18*k. Determine t, given that m(t) = 0.
1
Suppose 18 = 3*c + q - 4*q, c = 3*q + 4. Factor -4*n**3 - 5*n**3 + c*n**2 + 15*n**4 - 6*n**3 - n - 6*n**4.
n*(n - 1)*(3*n - 1)**2
Determine n so that -1/3*n**3 + 0*n**2 + n + 2/3 = 0.
-1, 2
Let y = 214/15 + -68/5. Determine q so that 0*q - 1/3*q**2 - y*q**4 + q**3 + 0 = 0.
0, 1/2, 1
Factor 6/5*m**2 + 0*m + 3/5*m**3 + 0.
3*m**2*(m + 2)/5
Let y(o) be the second derivative of 0 + 1/20*o**6 - 1/4*o**3 - 2*o + 3/40*o**5 - 1/8*o**4 + 0*o**2. Let y(h) = 0. What is h?
-1, 0, 1
Let m = 16 - 28. Let l be (-1)/2 - 14/m. Factor -11/3*p**2 + 16/3*p**3 + l*p - 7/3*p**4 + 0.
-p*(p - 1)**2*(7*p - 2)/3
Let u be ((-3)/(-9) - 0) + (-14)/(-6). Factor 8/3*y**2 + 2/3*y + 0 + u*y**4 + 4*y**3 + 2/3*y**5.
2*y*(y + 1)**4/3
Suppose 3 = 4*u - 3*u. Factor -52/5*p**u - 22/5*p - 4/5 - 48/5*p**2 - 28/5*p**4 - 6/5*p**5.
-2*(p + 1)**4*(3*p + 2)/5
Suppose 10*q = 54 + 6. Suppose -4/3 - 10/3*p**3 - 8*p**2 - q*p = 0. Calculate p.
-1, -2/5
Let m = 19 + -16. Factor 10*a**4 + m*a**2 - 3*a**4 - 6*a**4 - a - 3*a**3.
a*(a - 1)**3
Suppose o + 10 = 4*s, 3*s - o = -4*o. Determine a, given that 4 + 2*a**s - 12*a + 14 + 0*a = 0.
3
Let f(j) be the first derivative of -9*j**6 + 78*j**5/5 - 20*j**4/3 + 8*j**3/9 - 10. Factor f(l).
-2*l**2*(l - 1)*(9*l - 2)**2/3
Let m(s) = -3*s**5 - 7*s**4 - s**3 + 7*s**2 - 4*s. Let z(f) = 3*f**5 + 6*f**4 - 6*f**2 + 3*f. Let k(i) = -3*m(i) - 4*z(i). Determine y so that k(y) = 0.
-1, 0, 1
Let v(r) be the first derivative of -r**3/9 + 8. Solve v(w) = 0 for w.
0
Let d(b) be the first derivative of -b**8/56 + b**7/70 + b**6/20 - b**5/20 - 4*b**2 + 3. Let v(l) be the second derivative of d(l). What is j in v(j) = 0?
-1, 0, 1/2, 1
Let r be 0/((-2 - -3) + -3). Let y(i) be the second derivative of 0*i**2 + r*i**4 + 0 - 2*i + 0*i**3 + 1/20*i**5. Find g such that y(g) = 0.
0
Let l(r) be the first derivative of -r**8/1512 + r**7/315 - r**6/180 + r**5/270 - r**2/2 + 3. Let a(p) be the second derivative of l(p). Factor a(z).
-2*z**2*(z - 1)**3/9
Factor -2*y**2 - 1761*y + 3*y**3 - y**5 + 1761*y.
-y**2*(y - 1)**2*(y + 2)
Let b be -2 + -3*15/(-9). Let g(p) be the second derivative of 4/15*p**6 - p + 13/10*p**5 + 0 + 7/3*p**b + p**2 + 5/2*p**4. Factor g(m).
2*(m + 1)**3*(4*m + 1)
Let x(r) be the third derivative of -r**6/160 + 3*r**5/20 - 3*r**4/2 + 8*r**3 - 3*r**2. What is s in x(s) = 0?
4
Let r be 4 + 78/(-28)*(-32)/(-24). Let -r*x**2 + 0 + 4/7*x = 0. Calculate x.
0, 2
Let i(v) be the second derivative of -7*v**5/80 + 19*v**4/48 - v**3/3 - v**2/2 + 4*v. Factor i(u).
-(u - 2)*(u - 1)*(7*u + 2)/4
Let n(l) = -5*l**4 + 28*l**3 - 47*l**2 - 2. Let w(t) = 10*t**4 - 55*t**3 + 95*t**2 + 5. Let x(v) = -5*n(v) - 2*w(v). Factor x(r).
5*r**2*(r - 3)**2
Let p be (-12)/78 + 6/39. Factor p - 2/9*w**2 + 2/9*w.
-2*w*(w - 1)/9
Determine f, given that -12*f**3 - 3*f + 17*f**3 - 2*f = 0.
-1, 0, 1
Suppose 2*w = 4*w - 4. Solve -5 - w + 6 - 6*u**2 - 6*u - 2*u**3 - 1 = 0 for u.
-1
Factor 12 + 243*o**2 + 108*o + 3 - 3.
3*(9*o + 2)**2
Let u(z) = -z**3 - 7*z**2 - 4*z + 6. Let d be u(-6). Let b be (4/d)/((-32)/24). Let 3/4*g**4 + 0*g - b*g**2 - 1/4*g**3 + 0 = 0. What is g?
-2/3, 0, 1
Let z(x) = 5*x**3 + 2*x**2 - 2*x + 1. Let d be z(1). Let o be d/(-4) + 2 - 0. Factor -1/2 + p**3 + o*p**4 - p + 0*p**2.
(p - 1)*(p + 1)**3/2
Let p(f) = 2*f**2 - f + 3. Let r(m) = 3*m**2 - 2*m + 5. Let q(n) = 10*p(n) - 6*r(n). Factor q(a).
2*a*(a + 1)
Suppose 4*j = 5*q + 98, 0 = -5*q - 3*j + j - 86. Let t = q - -73/4. What is d in -1/2*d**2 + t*d**4 + 1/4*d + 1/4*d**5 - 1/2*d**3 + 1/4 = 0?
-1, 1
Let h(f) be the second derivative of f**4/2 + 20*f**3/9 + 4*f**2/3 + 66*f. Find o, given that h(o) = 0.
-2, -2/9
Let m(w) be the first derivative of 1/10*w**6 - 1/5*w**4 + 2/5*w + 1/10*w**2 - 3 - 2/5*w**3 + 4/25*w**5. Factor m(a).
(a - 1)*(a + 1)**3*(3*a - 2)/5
Let v(f) be the first derivative of -f**4/4 - 4*f**3/3 + 5*f**2/2 + 4*f - 3. Let b be v(-5). Factor z**2 - z**4 + 2*z + 2*z**4 + b*z**3 + 4*z**2.
z*(z + 1)**2*(z + 2)
Let w = 11 - 5. Suppose -15 = k - w*k. Let 2*c**2 + 1/2*c**5 + 2*c**4 + 1/2*c + 3*c**k + 0 = 0. Calculate c.
-1, 0
Suppose -4*c + 17 = 5. Let g(s) be the third derivative of 0*s**4 + 2*s**2 + 0 - 1/600*s**6 + 0*s + 0*s**5 + 0*s**c. Find o such that g(o) = 0.
0
Let a(y) be the second derivative of -y**6/24 + y**5/8 - 5*y**4/48 + 14*y. Determine u so that a(u) = 0.
0, 1
Let p(l) be the second derivative of 0*l**4 + 1/40*l**5 + 0*l**2 + 1/60*l**6 + 2