 970/11 + y. Find o such that 4/11*o - 2/11 - p*o**2 = 0.
1
Factor -4/9*h - 1/9*h**2 - 4/9.
-(h + 2)**2/9
Let h(m) = -5*m**5 + 4*m**4 - 10*m**3 + 2*m**2 - 6. Let t(a) = a**5 - a**4 + a**3 + a**2 + 1. Let p(i) = -h(i) - 6*t(i). Let p(s) = 0. What is s?
-2, 0, 2
Let s = -13 + 47. Let p be (-8)/(-36) + s/9. Let -6 + 6 + 3*k**3 + 3*k**4 - 4*k - 2*k**p = 0. Calculate k.
-2, 0, 1
Let t(k) be the first derivative of 0*k + 4 - 3/5*k**2 - 3/5*k**4 + 3/25*k**5 + k**3. Factor t(d).
3*d*(d - 2)*(d - 1)**2/5
Let d = -437/3 + 147. Let 0*p**3 + 2/3*p**4 + 0*p - d*p**2 + 2/3 = 0. What is p?
-1, 1
Let z(b) be the first derivative of -1/12*b**4 - 6 + 1/3*b**3 - 1/15*b**5 + 5/6*b**2 + 2/3*b. Factor z(j).
-(j - 2)*(j + 1)**3/3
Let f = -7 - -9. Factor -m + 2 + 2*m**3 - 3*m**3 + f*m - 2*m**2.
-(m - 1)*(m + 1)*(m + 2)
Let f = -6/101 - -389/4848. Let r(k) be the third derivative of 0 - f*k**4 - 1/60*k**5 - 4*k**2 + 0*k**3 + 0*k. Find h such that r(h) = 0.
-1/2, 0
Let o(x) be the second derivative of -1/21*x**4 + 0*x**2 + 1/21*x**3 + 4*x + 0 + 1/70*x**5. Solve o(c) = 0 for c.
0, 1
Let o = 90 + -89. Suppose 5*a - 4*i = 29, -a + 5*i = -3*a + 5. Let m(u) = -1. Let z(g) = -g**2 + g + 5. Let x(r) = a*m(r) + o*z(r). Let x(p) = 0. Calculate p.
0, 1
Let s = -4 - -8. Determine v, given that 2*v**2 - v**s - 6 + 5 - 2*v**3 + v + 0*v**3 + v**5 = 0.
-1, 1
Let k = -4 + 6. Suppose -k*s**5 + 3*s**4 + 0*s**4 - 5*s**4 = 0. What is s?
-1, 0
Let f(l) = 5*l**2 - 9*l + 20. Let m(h) = -h**2 + 2*h - 4. Suppose -2*t = 4*d - 8, -2*t + 10 = 2*d - 0. Let g(b) = t*f(b) + 33*m(b). Factor g(v).
-3*(v - 2)**2
Solve -44/5*n**3 - 14*n**4 - 8/5*n**2 + 0 + 0*n - 5*n**5 = 0 for n.
-2, -2/5, 0
Suppose 4*k = 2*k + 8. Suppose 0 = -u + 2, 3*a = -2*a + k*u + 7. Factor -2/3*p + 1/3 + 0*p**2 - 1/3*p**4 + 2/3*p**a.
-(p - 1)**3*(p + 1)/3
Let h(x) = -9*x**5 + 5*x**3 - 4*x**2 + 4. Let l(s) = 125*s**5 - 70*s**3 + 55*s**2 - 55. Let k(i) = 55*h(i) + 4*l(i). Solve k(r) = 0.
-1, 0, 1
Let c(q) be the first derivative of -5*q**4 - 25*q**3 - 20*q**2 + 15*q - 7. Determine p so that c(p) = 0.
-3, -1, 1/4
Let f(d) = 2*d**2 - 4*d - 4. Let u be f(-1). Factor 2/7*c**u + 4/7*c + 2/7.
2*(c + 1)**2/7
Factor -7/5*g**2 - 2/5 - 9/5*g.
-(g + 1)*(7*g + 2)/5
Let a(c) be the third derivative of c**5/330 - c**4/44 + 2*c**3/33 - 4*c**2. Determine t so that a(t) = 0.
1, 2
Let l(f) be the first derivative of -2/5*f**3 + 0*f - 3/10*f**2 + 2. Suppose l(p) = 0. What is p?
-1/2, 0
Let q be (-3)/(-2) - (-5)/(-10). Suppose -5*s = 5*p, 4 + 0 = -2*p. Factor -i**2 + 2*i**2 - 3*i**s + 3*i**2 - q.
(i - 1)*(i + 1)
Let w = 73/78 - 10/13. Factor -1/3*r - 1/6 - w*r**2.
-(r + 1)**2/6
Suppose -799 + 787 = -6*c. Suppose 3 - 2*u + 1/3*u**c = 0. Calculate u.
3
Let h(p) be the first derivative of p**7/420 - p**5/40 + p**4/24 - 3*p**2/2 - 5. Let u(m) be the second derivative of h(m). Factor u(s).
s*(s - 1)**2*(s + 2)/2
Suppose 0*y + 0*y**3 - 4/3*y**2 + 2/3*y**4 + 2/3 = 0. What is y?
-1, 1
Let w(x) be the first derivative of x**6/360 - x**5/180 + 3*x**2/2 - 4. Let h(z) be the second derivative of w(z). Factor h(u).
u**2*(u - 1)/3
Let v(q) be the second derivative of q**5/80 + q**4/48 - q**3/6 - q**2/2 - 2*q. Factor v(a).
(a - 2)*(a + 1)*(a + 2)/4
Solve 1/4*a**3 + 1 - 1/4*a**2 - a = 0 for a.
-2, 1, 2
Let d(o) be the first derivative of o**6/6 + o**5/5 - 3*o**4/4 - o**3/3 + o**2 - 3. Solve d(a) = 0.
-2, -1, 0, 1
Let o(p) be the second derivative of -1/10*p**5 + 0 + 0*p**2 + 0*p**4 + 7*p + 1/3*p**3. Factor o(l).
-2*l*(l - 1)*(l + 1)
Let q(r) be the second derivative of -5*r**7/252 + 17*r**6/180 - 11*r**5/120 - 13*r**4/72 + 4*r**3/9 - r**2/3 + 10*r. Solve q(t) = 0.
-1, 2/5, 1, 2
Factor -4/5*u**2 - 2/5 + 1/5*u**3 + u.
(u - 2)*(u - 1)**2/5
Let j = 16 + -22. Let k = 8 + j. Factor 2/3*v**k + 0 + 0*v.
2*v**2/3
Let n be (-3)/6 - (-10)/4. Suppose n*p + 17 = 4*s + 5, 4*p + 15 = 5*s. Suppose -6*a**s - 2*a**2 + 0*a**2 + 6*a**2 = 0. Calculate a.
0, 2/3
Let o(z) = 4*z**4 + 12*z**3 - 8*z**2 - 8*z. Let k(d) = -4*d**4 - 13*d**3 + 9*d**2 + 8*d. Let u(i) = 4*k(i) + 5*o(i). Factor u(r).
4*r*(r - 1)*(r + 1)*(r + 2)
Suppose -20*a**2 + 6*a + 2*a + 20*a**4 - 3*a - 5*a**3 = 0. Calculate a.
-1, 0, 1/4, 1
Suppose 0 = -5*t - 33 + 8. Let m(x) = -2*x**3 - 6*x**2 + 6*x - 1. Let q(p) = 3*p**3 + 11*p**2 - 11*p + 2. Let f(r) = t*m(r) - 3*q(r). Factor f(j).
(j - 1)**3
Let h(r) be the first derivative of 2*r**3/9 - r**2 + 4*r/3 - 7. Find a, given that h(a) = 0.
1, 2
Let j(n) be the third derivative of n**6/320 - 7*n**5/160 + 38*n**2. Determine s so that j(s) = 0.
0, 7
Factor 2/13*k**2 - 20/13*k + 0.
2*k*(k - 10)/13
Let y(t) be the first derivative of -t**5/5 + t**4/2 + 20. Suppose y(g) = 0. Calculate g.
0, 2
Let o(j) be the first derivative of -2*j**3/33 + 7*j**2/11 - 20*j/11 - 30. Factor o(d).
-2*(d - 5)*(d - 2)/11
Let f(j) be the second derivative of 2*j**7/21 - 2*j**6/5 + j**5/5 + j**4 - 4*j**3/3 - j - 7. What is p in f(p) = 0?
-1, 0, 1, 2
Suppose -18*k = -11*k - 21. Suppose -3/5*w - 3/5*w**2 - 1/5*w**k - 1/5 = 0. What is w?
-1
Factor -10*v**3 + 3*v**2 - 2*v - 4*v + 9*v**3 + 3*v + 1.
-(v - 1)**3
Let u(i) be the first derivative of -2*i**5/35 + i**4/14 + 4*i**3/21 + 2. Factor u(b).
-2*b**2*(b - 2)*(b + 1)/7
Suppose 2*j - 12 + 0 = 0. Let n be (0 - (-1)/j)*3. Let f - n*f**4 + 3/2*f**3 + 5/2*f**2 + 0 - 1/2*f**5 = 0. Calculate f.
-1, 0, 2
Let p(t) = -t**3 + t**2 + 1. Let y(o) = -7*o**3 + 5*o**2 + 12. Let c(j) = -24*p(j) + 3*y(j). Factor c(d).
3*(d - 2)**2*(d + 1)
Let g(c) be the third derivative of -c**8/336 - c**7/105 - c**6/120 - 2*c**2. Factor g(l).
-l**3*(l + 1)**2
Let i(c) be the second derivative of -c**5/10 + c**4 - 5*c**3/3 - 17*c. Let i(b) = 0. Calculate b.
0, 1, 5
Let x(p) be the first derivative of -p**3/12 - 5*p**2/8 + 9. Find q such that x(q) = 0.
-5, 0
Let v(r) be the first derivative of -r**4/10 - 2*r**3/5 + 2. Solve v(p) = 0.
-3, 0
Let j be -7 - (-153)/18 - (-23)/(-18). Factor 2/9*k**2 + 4/9*k + j.
2*(k + 1)**2/9
Let f(b) be the first derivative of -1/180*b**5 + 2/3*b**3 + 1/72*b**4 + 1/1080*b**6 + 0*b**2 + 0*b - 1. Let o(y) be the third derivative of f(y). Factor o(r).
(r - 1)**2/3
Let z be ((-15)/(-6) + -3)*-2. Suppose 3*c + 1 = 2*t, -c - 1 - z = -t. Suppose -1/3*q**2 + 1/3 + 1/3*q - 1/3*q**c = 0. Calculate q.
-1, 1
Factor 7 - 5*o + 5 + 5*o**3 - 10*o**2 - 2.
5*(o - 2)*(o - 1)*(o + 1)
Let h = 1 - 6. Let z be -3 + (0 - h - 0). Factor -2/5*i**3 + 2/5*i - 4/5*i**z + 4/5.
-2*(i - 1)*(i + 1)*(i + 2)/5
Let g(f) be the second derivative of f**6/900 + f**5/300 + f**3/6 - 2*f. Let q(h) be the second derivative of g(h). Factor q(v).
2*v*(v + 1)/5
Let z(o) be the third derivative of -o**7/175 - o**6/60 + 2*o**5/75 + o**4/15 - 7*o**2. Find n, given that z(n) = 0.
-2, -2/3, 0, 1
Let m(i) = 7 + 10 - 4 + i - 2. Let r be m(-9). Let 2 + 0 - s**2 + s - r = 0. What is s?
0, 1
Let f(i) be the third derivative of -i**7/560 + i**6/80 - 3*i**5/160 - i**4/16 + i**3/4 - 4*i**2. Suppose f(j) = 0. Calculate j.
-1, 1, 2
Let r(h) be the third derivative of 3*h**2 + 1/4*h**4 + 0*h - 1/420*h**7 - 13/120*h**5 + 0 - 1/3*h**3 + 1/40*h**6. Factor r(l).
-(l - 2)**2*(l - 1)**2/2
Factor -2/3*i**4 + 0 + 8/9*i**2 + 0*i - 2/9*i**5 + 0*i**3.
-2*i**2*(i - 1)*(i + 2)**2/9
Suppose -146 = -5*m - 26. Let b be m/11 - 32/176. Let 0*r**b + 0 - 2/3*r**3 + 2/3*r = 0. Calculate r.
-1, 0, 1
Let s(y) = y**3 + 3*y**2 - 4*y. Let f be s(-4). Determine g so that -1/2*g + f + 1/2*g**4 - 3/2*g**3 + 3/2*g**2 = 0.
0, 1
Let d = -31 - -34. Factor 0 - 1/5*a - 2/5*a**2 - 1/5*a**d.
-a*(a + 1)**2/5
Factor 6/11 - 10/11*x + 4/11*x**2.
2*(x - 1)*(2*x - 3)/11
Suppose 5*i + 3*x = -114, 2*i + 2*x + 111 = -3*i. Let t be 1/4 + i/(-12). Determine l so that -3*l**t - 15*l**5 + 0*l**2 + 15*l**3 - l**4 + 9*l**2 - 5*l**4 = 0.
-1, -2/5, 0, 1
Suppose -a + 2 = -4. Let o be -8*(9/a + -2). What is s in o*s**5 + 0*s**2 - 2*s**2 - 3*s**3 - s**3 + 2*s**4 = 0?
-1, -1/2, 0, 1
Let n(r) = -r**2 - 7*r + 3. Let y(j) = -8*j + 4. Let f(k) = 4*n(k) - 3*y(k). What is s in f(s) = 0?
-1, 0
Let v(w) = -3*w**3 + 7*w**2 - 9*w. Let k(m) = -m**3 + 3*m**2 - 4*m. Suppose 4*d = 5*d - 4. Let b(o) = d*v(o) - 10*k(o). Factor b(u).
-2*u*(u - 1)*(u + 2)
Factor 0*c**2 - 1/3*c**3 + 0*c + 0 - 1/3*c**4.
-c**3*(c + 1)/3
Let n(o) be the first derivative of -2/27*o**3 + 0*o**4 + 0*o**2 - 3 + 2/45*o**5 