*7 - q**2 + 0*q**5 + 0*q + 0*q**6 + r*q**4. Find g such that h(g) = 0.
0
Suppose 0*b**2 - 3/4*b**4 + 0 - 1/4*b**5 + 0*b - 1/2*b**3 = 0. Calculate b.
-2, -1, 0
Let n(u) be the first derivative of -u**5/60 + u**3/6 - u**2/2 + 2. Let m(j) be the second derivative of n(j). Factor m(k).
-(k - 1)*(k + 1)
Let s(j) be the third derivative of -j**8/1176 + j**7/147 - j**6/42 + j**5/21 - 5*j**4/84 + j**3/21 + 4*j**2. Factor s(h).
-2*(h - 1)**5/7
Suppose -4*v = 0, 4*w - 1 = 5*v + 7. Factor -7*y**5 + 11*y**5 - 9*y**4 - 4*y**2 + y**w - y**5 + 9*y**3.
3*y**2*(y - 1)**3
Suppose 0 = f + a - 5, -5*f + 2*f - 2*a + 12 = 0. Let l be (-2)/((-10)/8*2). Solve l*y - 2/5*y**f - 2/5 = 0 for y.
1
Let j = -704 - -4940/7. Factor 0 - 2/7*s**5 - j*s**3 - 8/7*s**2 - 8/7*s**4 - 2/7*s.
-2*s*(s + 1)**4/7
Suppose 2*b + 0*z - z = 8, -4*b + 3*z = -20. Factor -x**3 - 4*x**2 - 7*x + 2*x - 2 - b + 2.
-(x + 1)**2*(x + 2)
Suppose 26/5*g + 54/5*g**2 + 4/5 + 14/5*g**4 + 46/5*g**3 = 0. What is g?
-1, -2/7
Determine i so that 4*i + 4*i**2 + 2 + 0*i**2 - 2 = 0.
-1, 0
Find m, given that 0*m + 0 - 2*m**3 + 4/3*m**2 + 2/3*m**4 = 0.
0, 1, 2
Let k be 1/(3*(-5)/(-15)) + 1. Solve -2*u - 4/3 - 2/3*u**k = 0.
-2, -1
Let d be 2/(-6) - (-20)/6. Let w(h) = -3*h**2 - h + 2. Let o be w(0). Factor -o*g - g**d + g + 2*g.
-g*(g - 1)*(g + 1)
Let p(h) be the first derivative of 3*h**5/5 + 15*h**4/4 + 3*h**3 - 27*h**2/2 + 7. Solve p(t) = 0 for t.
-3, 0, 1
Find s such that -s**3 - 2*s**2 + 22 - 36 + 14 = 0.
-2, 0
Let j(a) be the third derivative of -a**5/75 + 4*a**4/15 - 32*a**3/15 + 9*a**2. Factor j(g).
-4*(g - 4)**2/5
Let a(j) = -j**3 + 4*j**2 + 7*j - 4. Let l(i) = -i**2 - i. Let b(p) = 4*a(p) + 12*l(p). Find z such that b(z) = 0.
-2, 1, 2
Let a be ((-3)/63*-3)/(-5 - -10). Let o(w) be the second derivative of -a*w**5 + 0 - w + 2/21*w**3 + 1/105*w**6 + 0*w**4 - 1/7*w**2. Factor o(r).
2*(r - 1)**3*(r + 1)/7
Suppose -t - 19 = -6. Let r be 2/14 - t/7. Factor -1/4*s + 0*s**3 + 3/4*s**r + 0 - s**4.
-s*(s + 1)*(2*s - 1)**2/4
Find g such that 15/2*g**4 - 21/2*g**2 + 3 + 9/2*g**3 - 9/2*g = 0.
-1, 2/5, 1
Let k(r) be the first derivative of r**6/9 - 8*r**5/15 + 2*r**4/3 + 4*r**3/9 - 5*r**2/3 + 4*r/3 + 5. Factor k(o).
2*(o - 2)*(o - 1)**3*(o + 1)/3
Let f = 47 + -43. Let 0*a**3 - a**2 - 1/2*a**5 + 0 + a**f + 1/2*a = 0. Calculate a.
-1, 0, 1
Let b(k) be the second derivative of 1/24*k**4 - 1/12*k**3 - 3*k - 1/120*k**5 + k**2 + 0. Let p(y) be the first derivative of b(y). Factor p(s).
-(s - 1)**2/2
Determine l, given that -9/4 - 1/4*l**2 + 3/2*l = 0.
3
Let x(j) = -j**2 - j - 1. Let i(d) = 2*d**2 + 2*d + 1. Suppose -2*l + 6 + 0 = 0. Let s(o) = l*i(o) + 5*x(o). Let s(y) = 0. Calculate y.
-2, 1
Suppose -1 = m - 8. Factor 7 + 0 - m - 8*z + 6*z**2 + 2.
2*(z - 1)*(3*z - 1)
Let n(i) = -11*i - 3*i**2 - 13 + 9 - 4*i**2. Let c(t) = -3*t**2 - 5*t - 2. Let a(s) = -9*c(s) + 4*n(s). Suppose a(h) = 0. Calculate h.
-1, 2
Suppose h - 5 = b, -5*b - 20 = h - b. Let r(t) be the second derivative of 0 - 3/20*t**5 + 2*t + 0*t**3 + h*t**4 + 0*t**2 + 1/10*t**6. What is l in r(l) = 0?
0, 1
Factor 8 + 8*a + 28*a**3 - 20*a - 16*a - 8*a**2.
4*(a - 1)*(a + 1)*(7*a - 2)
Let w(h) = -3*h**3 - 72*h**2 - 576*h - 1531. Let q(z) = 15*z**3 + 360*z**2 + 2880*z + 7656. Let b(l) = -5*q(l) - 24*w(l). Factor b(y).
-3*(y + 8)**3
Let q(m) be the first derivative of m**4/4 + 4*m**3/3 + m**2/2 + 3. Let x be q(-3). Factor -6*r**3 + 4 + x*r - 7 + 6*r**4 - 2*r**4 - r**4.
3*(r - 1)**3*(r + 1)
Let q(i) be the second derivative of 0 + 1/42*i**7 + 0*i**3 + i + 0*i**4 + 0*i**2 + 0*i**5 - 1/15*i**6. Let q(f) = 0. Calculate f.
0, 2
Let r(u) = 5*u**2 - 8*u - 1. Let x(s) = -3*s**2 + 4*s. Let d(l) = -4*r(l) - 7*x(l). Suppose d(m) = 0. Calculate m.
-2
Let a(q) be the third derivative of -q**8/21 - 2*q**7/35 + 23*q**6/60 + q**5/15 - 3*q**4/4 - 2*q**3/3 + 33*q**2. Determine l, given that a(l) = 0.
-2, -1/2, -1/4, 1
Let h(z) = 4*z**4 + 2*z**3 - 4*z**2 - 2*z + 2. Let v(w) = 5*w**4 + 3*w**3 - 4*w**2 - 3*w + 2. Let i(k) = -6*h(k) + 4*v(k). Factor i(d).
-4*(d - 1)**2*(d + 1)**2
Determine m, given that 8/5*m**2 - 8/5*m + 2/5 = 0.
1/2
Find h such that -1/2 + 9/4*h - 7/4*h**2 = 0.
2/7, 1
Factor -3*l**4 + 3*l**3 - 3*l**2 + l + 0*l**3 + 0*l**4 + 2*l**4.
-l*(l - 1)**3
Let g = -45 - -45. Let 2/5*w**2 + g + 4/5*w = 0. What is w?
-2, 0
Let l = 298/237 - -6/79. Let f be (4/15)/((-8)/(-20)). Suppose l + 10/3*v + f*v**3 + 8/3*v**2 = 0. What is v?
-2, -1
Let p(j) be the third derivative of -3*j**7/280 - 17*j**6/160 - 11*j**5/40 - j**4/4 - 5*j**2. Let p(r) = 0. What is r?
-4, -1, -2/3, 0
Let j(q) be the second derivative of q**4/72 + q**3/36 - q**2/6 - q. Suppose j(y) = 0. What is y?
-2, 1
Find u such that -30*u**2 - 97*u**2 - 80*u - 8 - 162*u**3 - 107*u**2 = 0.
-1, -2/9
Let j = -87 - -42. Let z = -81/2 - j. Factor -9/2*s**2 + 3/2*s**3 + z*s - 3/2.
3*(s - 1)**3/2
Let v(k) = 56*k**2 + k - 2*k - 4*k**2 - 1. Let f be v(1). What is o in 181/2*o**2 + f*o**5 + 173*o**3 + 22*o + 305/2*o**4 + 2 = 0?
-1, -2/5, -1/4
Suppose 5*q**5 + 0*q**4 + 2*q**3 - 4*q**4 - 13*q**5 + 2*q**3 = 0. Calculate q.
-1, 0, 1/2
Let i be 37/4 - 9/36. Let q be 21/i + -3 + 2. Let 0*h**3 + 2/3*h**5 + 4/3*h**4 + 0 - 2/3*h - q*h**2 = 0. Calculate h.
-1, 0, 1
Let d(v) = 2*v**2 - 2*v + 4. Let u(w) = -10*w**2 + 9*w - 21. Let h(t) = 11*d(t) + 2*u(t). Determine i, given that h(i) = 0.
1
Let h = -38 + 59. Factor 23*m**3 - h*m**3 - 3*m + 4*m**2 + 5*m.
2*m*(m + 1)**2
Let z(m) be the first derivative of -2*m**3/9 + m**2 + 5. Factor z(o).
-2*o*(o - 3)/3
Let u be 4/8 + 0 - 9/42. Let 0 + u*m + 4/7*m**2 = 0. What is m?
-1/2, 0
Let j = 1/556 - -8887/5004. Let r(f) be the first derivative of j*f**3 + 4/3*f**2 + 0*f - 1 + 2/15*f**5 + 5/6*f**4. Factor r(x).
2*x*(x + 1)*(x + 2)**2/3
Suppose -78*y + 80*y + 6 = -3*n, -5*y - 4*n = 8. Factor -2/5*c**3 + y*c**2 + 0 + 2/5*c.
-2*c*(c - 1)*(c + 1)/5
Factor 0 + 2/3*t**2 + 2/9*t**4 - 2/3*t**3 - 2/9*t.
2*t*(t - 1)**3/9
Let i(c) be the first derivative of c**8/840 + 4*c**3/3 - 3. Let s(y) be the third derivative of i(y). Factor s(u).
2*u**4
Let f(c) = -4*c**4 - 24*c**3 + 28*c**2 + 5. Let m(v) = 6*v**4 + 36*v**3 - 42*v**2 - 7. Let a(u) = 7*f(u) + 5*m(u). Determine h, given that a(h) = 0.
-7, 0, 1
Let x(g) be the first derivative of 4*g**5/5 - 4*g**4 + 16. Factor x(f).
4*f**3*(f - 4)
Let p(y) be the third derivative of -y**7/840 - y**6/48 - 3*y**5/20 - 9*y**4/16 - 9*y**3/8 + 16*y**2. Determine l so that p(l) = 0.
-3, -1
Let s be 45/(-20)*8/3. Let x be (s/14)/(6/(-8)). What is l in 2/7*l**2 + 2/7 - x*l = 0?
1
Suppose 2*z = -3*r - r + 10, 0 = -4*r + 5*z + 3. Factor 0 - 1/6*q + 1/6*q**r.
q*(q - 1)/6
Let w(d) be the second derivative of -d**7/14 + 3*d**6/20 + 3*d**5/40 - 3*d**4/8 + d**3/4 + 6*d. Solve w(f) = 0 for f.
-1, 0, 1/2, 1
Let t(k) = -3*k**3 - 2*k**2 - k. Let r be t(-1). Let 8 + p**3 + 17*p - r*p**2 - 36*p + 15*p = 0. Calculate p.
-2, 2
Let y(n) = -n. Let g be y(-1). Suppose 0 = -4*s + 7 + g. What is l in l**2 - s*l - l + l**2 - l + 2*l**3 = 0?
-2, 0, 1
Let f(k) be the second derivative of -k**6/10 + 3*k**5/5 - k**4 - 6*k. Factor f(m).
-3*m**2*(m - 2)**2
Let m(w) = -3*w - 3. Let y be m(-2). Suppose 3*c = 3*c - 2*c. Determine h so that 1/5*h**4 + c + 0*h + 0*h**y + 0*h**2 = 0.
0
Let b(n) = n**2 - n + 3. Let v(q) = -q**2 + q - 2. Let h be 2*(-2)/4*3. Let g(p) = h*v(p) - 2*b(p). Factor g(z).
z*(z - 1)
Let g(k) be the first derivative of k**7/210 + k**6/45 - k**5/30 - k**4/3 - 10*k**3/3 - 7. Let j(f) be the third derivative of g(f). Factor j(l).
4*(l - 1)*(l + 1)*(l + 2)
Let k(h) be the second derivative of h**7/21 + h**6/5 - h**5/5 - 2*h**4 - 8*h**3/3 + 23*h. Let k(o) = 0. What is o?
-2, -1, 0, 2
Let p(k) be the third derivative of -k**5/30 + k**4/24 - 4*k**2. Factor p(b).
-b*(2*b - 1)
Suppose -h = 2 + 7. Let k be 1 - 2 - -2 - h. Let -4*v**4 - 2*v - 8*v**2 + 5*v - 5*v - k*v**3 + 0*v = 0. Calculate v.
-1, -1/2, 0
Let l = -4/77 + 19/154. Let w(q) be the first derivative of -l*q**4 - 1/7*q**2 + 4/21*q**3 + 3 + 0*q. Factor w(b).
-2*b*(b - 1)**2/7
Let d(s) be the third derivative of -s**2 + 1/120*s**5 + 0*s + 0 + 0*s**4 - 1/12*s**3. Find f such that d(f) = 0.
-1, 1
Suppose 0*d**3 + 5*d**3 + 0*d**3 + 8*d**2 - 4*d = 0. Calculate d.
-2, 0, 2/5
Let z(v) = -v**2 - v + 5. Let f be z(-2). Let s(p) be the third derivative of -f*p**2