k*z - 22*z - 2*z**2 = 0?
0
Let n(f) = -2*f**3 - 24*f**2 + 4*f + 48. Let w be n(-12). Let o(p) = -4*p. Let i be o(-1). Factor -1/2*s**3 + w + 1/2*s + 1/2*s**i - 1/2*s**2.
s*(s - 1)**2*(s + 1)/2
Let k(d) be the third derivative of d**8/448 + d**7/105 + d**6/80 - d**4/96 + 7*d**2. Factor k(i).
i*(i + 1)**3*(3*i - 1)/4
Let s = 39 + -39. Solve 0*x - 2/7*x**2 - 2/7*x**4 + s - 4/7*x**3 = 0.
-1, 0
Let h(x) be the third derivative of x**6/20 - 3*x**5/40 - 3*x**4/32 + x**3/8 + 4*x**2. Determine v, given that h(v) = 0.
-1/2, 1/4, 1
Find c such that 4*c**4 - 34*c**4 + 10*c**4 - 12*c**3 + 5*c**5 + 3*c**5 = 0.
-1/2, 0, 3
Let x(f) be the third derivative of f**8/16 + 8*f**7/35 + f**6/10 - 7*f**5/10 - 11*f**4/8 - f**3 + f**2. Solve x(r) = 0.
-1, -2/7, 1
Let g(r) = r**3 - 9*r**2 + 8*r + 3. Let m be g(8). Factor -2*f + 3*f + 4*f**m + 2*f**2 - 3*f**3.
f*(f + 1)**2
Determine w so that -1/3*w**2 - 4/3*w - 4/3 = 0.
-2
Let f(h) = h + 5. Let q be f(-5). Let v(z) be the first derivative of q*z + 1 + 1/2*z**2 - 1/4*z**4 - 1/3*z**3 + 1/5*z**5. Factor v(j).
j*(j - 1)**2*(j + 1)
Let r(n) = -n**2 - 5*n + 3. Let h be r(-6). Let p = -8/3 - h. Factor -p*m**2 + 1/3*m + 2/3.
-(m - 2)*(m + 1)/3
Let d(n) be the third derivative of -2*n**2 + 0*n - 1/60*n**5 + 0 + 0*n**3 - 1/12*n**4. Suppose d(f) = 0. What is f?
-2, 0
Suppose 4*m + 4*r - 16 = 0, 0 = -2*m + m + 3*r. Factor -2*h**2 + 4*h**3 - 6*h - 2*h**m - 2 - 4*h**2 - 4*h**3.
-2*(h + 1)**3
Suppose -r + 24 = 2*r. Let k = 8 - r. Factor 1/2*v**2 + k*v + 3/2*v**4 + 0 - 3/2*v**3 - 1/2*v**5.
-v**2*(v - 1)**3/2
Factor 3/5*b + 3/5*b**5 - 6/5*b**3 + 3/5*b**4 + 3/5 - 6/5*b**2.
3*(b - 1)**2*(b + 1)**3/5
Let r(x) be the first derivative of -2*x**6/3 - 4*x**5/5 + 3*x**4 + 4*x**3/3 - 4*x**2 - 13. Determine p, given that r(p) = 0.
-2, -1, 0, 1
Let j(y) be the second derivative of y**7/1400 - y**6/300 - y**5/200 + y**4/20 - 7*y**3/6 + y. Let m(t) be the second derivative of j(t). Factor m(c).
3*(c - 2)*(c - 1)*(c + 1)/5
Let s(i) be the first derivative of -3/5*i**2 - 2 + 2/15*i**3 + 4/5*i. Determine t, given that s(t) = 0.
1, 2
Let h(v) be the first derivative of -v**5/70 - v**4/42 + v + 2. Let m(s) be the first derivative of h(s). Factor m(q).
-2*q**2*(q + 1)/7
Let w(x) be the first derivative of x**6/15 - x**5/5 + 2*x**3/3 - x**2 - x + 1. Let i(t) be the first derivative of w(t). Factor i(q).
2*(q - 1)**3*(q + 1)
Let j(v) be the second derivative of 3*v**5/40 + 3*v**4/8 + 3*v**3/4 + 3*v**2/4 - 3*v. Solve j(m) = 0 for m.
-1
Let f(w) be the second derivative of 5*w + 0 - 1/135*w**6 - 1/45*w**5 + 2/27*w**3 + 1/9*w**2 + 0*w**4. Factor f(o).
-2*(o - 1)*(o + 1)**3/9
Let v(j) be the first derivative of 6*j**5/85 - 7*j**4/34 + 10*j**3/51 - j**2/17 - 10. Factor v(p).
2*p*(p - 1)**2*(3*p - 1)/17
Factor 3/2*c**4 + 0 + 0*c**2 + 0*c - 1/2*c**5 - c**3.
-c**3*(c - 2)*(c - 1)/2
Let d(o) be the third derivative of o**9/181440 + o**8/30240 + o**7/15120 - o**5/30 + 2*o**2. Let c(b) be the third derivative of d(b). Factor c(t).
t*(t + 1)**2/3
Suppose -19*g**3 - 17*g**4 - 6*g**3 + 25*g**5 - 20*g**3 + 20*g + 57*g**4 - 40*g**2 = 0. What is g?
-2, -1, 0, 2/5, 1
Let -4/7*z**2 - 2*z + 2/7*z**3 - 8/7 = 0. What is z?
-1, 4
Let q be 2 + (-10)/4 + (-2)/(-4). Let s(u) be the second derivative of 0*u**2 - u + q*u**3 + 0 + 1/12*u**4. Factor s(x).
x**2
Determine v, given that -1/3*v**3 + 0 + 0*v + 1/3*v**5 + 1/3*v**4 - 1/3*v**2 = 0.
-1, 0, 1
Let k(g) be the first derivative of -g**3/3 + 5*g**2/2 - 4*g - 2. Let w be k(4). Factor -4/5*u**2 + w + 2/5*u.
-2*u*(2*u - 1)/5
Let j = 9 + -17. Let c(z) = -z**4 + 7*z**3 + z**2 - 7*z - 3. Let q(k) = 4*k**4 - 20*k**3 - 4*k**2 + 20*k + 8. Let s(r) = j*c(r) - 3*q(r). Solve s(i) = 0 for i.
-1, 0, 1
Let y(v) be the second derivative of 0 + 3/2*v**2 - 1/2*v**4 + 0*v**5 + 1/10*v**6 - 4*v + 0*v**3. Factor y(m).
3*(m - 1)**2*(m + 1)**2
Let q(o) = -4*o**2 + 4*o + 4. Let s(l) = 18*l - 12*l**2 - 4*l - l**3 + 12 - 2*l. Let d(k) = 11*q(k) - 4*s(k). Factor d(v).
4*(v - 1)*(v + 1)**2
Suppose -6*s = -4*s - 8. Factor -v**5 + s*v**5 + v**4 + v**4 - 4*v**3 - v**5.
2*v**3*(v - 1)*(v + 2)
Let f = -4 + 5. Let d be 27/(-15) - (-3 + f). Let 2/5*h**3 + 0*h + 0 - 1/5*h**4 - d*h**2 = 0. What is h?
0, 1
Let k(h) be the third derivative of 0*h**3 + 49/660*h**6 + 0*h + h**2 + 0 + 1/33*h**4 + 14/165*h**5. Suppose k(v) = 0. Calculate v.
-2/7, 0
Let j(x) be the first derivative of x**6/9 - 4*x**5/15 + x**4/6 + 4. Solve j(o) = 0.
0, 1
Let f(q) be the second derivative of q**7/2100 - 2*q**3/3 + 3*q. Let u(h) be the second derivative of f(h). Suppose u(c) = 0. Calculate c.
0
Suppose 4*n = r + 6 - 2, -4*r + 26 = 5*n. Let t be 5 + -2 + (1 - 2). Determine u so that -u + u**3 - n*u**3 + t*u = 0.
-1, 0, 1
Determine o so that o**5 + 1 - 1/2*o - 1/2*o**3 - 7/2*o**2 + 5/2*o**4 = 0.
-2, -1, 1/2, 1
Let f(x) = 3*x**5 + 2*x**4 - 8*x**3 - 2*x**2 + 5*x + 2. Let a(r) = -3*r**5 - 3*r**4 + 9*r**3 + 3*r**2 - 6*r - 3. Let g(w) = 2*a(w) + 3*f(w). Factor g(q).
3*q*(q - 1)**2*(q + 1)**2
Solve 64/9*t**3 - 18*t**5 - 10*t**4 + 0 - 8/9*t**2 + 0*t = 0.
-1, 0, 2/9
Let l(s) = -5*s**2 - 2*s. Let t(i) = -24*i**2 - 10*i. Let q(a) = 28*l(a) - 6*t(a). What is f in q(f) = 0?
-1, 0
Let k be (-16)/2 - (-384)/44. Factor 2/11*x**2 + k*x + 8/11.
2*(x + 2)**2/11
Let r be 2*(-9)/12*-2. Suppose -5*d + r*j = -1, -j + 2 = -d + 1. Factor -2/9 + 0*g + 2/9*g**d.
2*(g - 1)*(g + 1)/9
Let p(t) be the third derivative of t**8/112 - 3*t**6/40 - t**5/10 - 55*t**2. What is z in p(z) = 0?
-1, 0, 2
Let q = -6 + 13. Suppose -3*s + q = 1. Suppose -z - 4*z**3 + s*z + 3*z**3 = 0. Calculate z.
-1, 0, 1
Let t(j) = -j**4 - 1 + 1 + j**3 + 4*j - 5*j - 2*j**2. Let k(a) = a**3 + a**2 + a. Let c(i) = -k(i) - t(i). Factor c(b).
b**2*(b - 1)**2
Factor 2/7*g**4 - 38/7*g**2 + 0 - 16/7*g**3 - 20/7*g.
2*g*(g - 10)*(g + 1)**2/7
Determine q, given that 8/11*q**2 - 2/11*q**4 - 16/11*q + 4/11*q**3 + 0 = 0.
-2, 0, 2
Let j(h) = h**2 - 8*h + 5. Let u(l) be the first derivative of 2*l**3/3 - 10*l**2 + 12*l + 3. Let r(m) = 12*j(m) - 5*u(m). Suppose r(b) = 0. What is b?
-2, 0
Suppose 5 = 6*t - t. Factor -s**2 + 4*s**2 + t - 3 - 5*s.
(s - 2)*(3*s + 1)
Let x(c) = c**3 - 4*c**2. Let o be x(4). Let y(n) be the third derivative of 1/90*n**5 - 3*n**2 - 1/9*n**4 + o + 0*n + 4/9*n**3. Solve y(t) = 0.
2
Let q = -12 - -12. Let n = -6/119 + 304/1309. Let -n*o**4 + 0 - 8/11*o**2 + q*o + 8/11*o**3 = 0. What is o?
0, 2
Let o(p) be the first derivative of p**4/12 + 2*p**3/9 + p**2/6 - 8. Suppose o(m) = 0. Calculate m.
-1, 0
Factor -1 - 2*d**2 + d**4 + 0 + 2.
(d - 1)**2*(d + 1)**2
Let c(p) be the second derivative of -2*p**6/105 + 2*p**4/7 + 16*p**3/21 + 6*p**2/7 - 18*p. Factor c(k).
-4*(k - 3)*(k + 1)**3/7
Suppose 0 = 4*s - 8, 8 = -5*r - 2*s - 3. Let a be r*(8/(-12) - 0). What is v in -1/2*v**3 - 1/2*v + 0 - v**a = 0?
-1, 0
Let n(c) = 8*c**5 + 80*c**4 - 36*c**3 - 10*c**2 + 80*c + 8. Let o(x) = x**5 + 9*x**4 - 4*x**3 - x**2 + 9*x + 1. Let f(b) = -6*n(b) + 52*o(b). Factor f(a).
4*(a - 1)**4*(a + 1)
Let w(f) be the first derivative of 0*f + 1/48*f**6 + 3/16*f**4 + f**2 + 2 - 1/10*f**5 - 1/6*f**3. Let j(s) be the second derivative of w(s). Factor j(b).
(b - 1)**2*(5*b - 2)/2
Let q(m) be the first derivative of 4*m**3/9 - 2*m**2/3 - 8*m + 23. Suppose q(z) = 0. What is z?
-2, 3
Let v be ((-2)/6)/((-11)/61). Let i = v - -9/11. Let -22/3*s**2 - 1/3 + 4/3*s**5 + i*s - 17/3*s**4 + 28/3*s**3 = 0. What is s?
1/4, 1
Suppose 2*s = -a - s + 4, 3*s + 16 = -5*a. Let j = a - -8. Suppose 2*r + 2*r - j*r**2 + r**3 - 1 - r = 0. Calculate r.
1
Let d(a) = -4*a + 2. Suppose -4*q + 3*f - 29 = 0, -3*q - 2 - 10 = f. Let r(h) = -h**2 - 7*h + 3. Let s(t) = q*d(t) + 2*r(t). What is x in s(x) = 0?
1, 2
Let m(r) be the second derivative of -r**7/168 + r**6/24 + r**5/40 - 5*r**4/24 - r**3/24 + 5*r**2/8 - r - 28. Let m(l) = 0. What is l?
-1, 1, 5
Factor 4/5 + 4*t**4 + 4/5*t**5 + 8*t**3 + 8*t**2 + 4*t.
4*(t + 1)**5/5
Suppose 5*g - 7 = 3. Let s(r) = -r**2 - 10*r + 13. Let c be s(-11). Factor 0*d**3 + c*d**g - 2*d**4 - 7*d**3 + 7*d**4.
d**2*(d - 1)*(5*d - 2)
Solve -101 + 203 - 4*p - 104 + 6*p**2 = 0.
-1/3, 1
Factor -q**2 + 3/2*q**3 + 0*q**4 - 1/2*q**5 + 0 + 0*q.
-q**2*(q - 1)**2*(q + 2)/2
Let c(p) = 12*p**2 - 30*p + 25. Let t(g) = -4*g**2 + 10*g - 8. Let f(m) = -4*c(m) - 14*t(m). Factor f(r).
4*(r - 1)*(2*