p) be the first derivative of p**7/525 + p**6/150 + p**5/150 + p**2/2 - 2. Let y(q) be the second derivative of r(q). Let y(v) = 0. Calculate v.
-1, 0
Let c(s) be the third derivative of 4/3*s**3 + 0 - 1/2*s**4 - s**2 + 1/15*s**5 + 0*s. Factor c(h).
4*(h - 2)*(h - 1)
Let a = -5/13 + 77/65. Solve 4/5 + 1/5*c**2 - a*c = 0 for c.
2
Factor 1/5*s - 1/5*s**3 - 1/5*s**2 + 1/5.
-(s - 1)*(s + 1)**2/5
Let z(j) = -11*j - 9. Let w be z(-1). Let 0*n + 2/13*n**4 + 2/13*n**3 - 2/13*n**w + 0 - 2/13*n**5 = 0. What is n?
-1, 0, 1
Factor 2/3*w**3 + 2/3*w - 4/3*w**2 + 0.
2*w*(w - 1)**2/3
Suppose d + 2 = w, -d = -5*w - 0*w + 22. Let m(j) be the third derivative of 0 - 1/150*j**w + 0*j**3 - 2*j**2 - 1/60*j**4 + 0*j. Determine q so that m(q) = 0.
-1, 0
Let u = -49 + 52. Let p(y) be the first derivative of -4*y + 8*y**2 + 3 - 7/4*y**4 - 5/3*y**u. Find t, given that p(t) = 0.
-2, 2/7, 1
Let f(i) = -i**2 - 6*i - 4. Let v be f(-4). Let m(q) be the third derivative of 0 + 0*q**v + 0*q**3 + 1/30*q**5 + 1/120*q**6 + 0*q + 3*q**2. Factor m(r).
r**2*(r + 2)
Let q(o) be the third derivative of -o**6/360 + o**5/45 - 5*o**4/72 + o**3/9 + 4*o**2. Factor q(j).
-(j - 2)*(j - 1)**2/3
Let h(a) be the first derivative of -3/8*a**4 + 1 + 2/3*a**3 - a + 1/4*a**2. Factor h(v).
-(v - 1)**2*(3*v + 2)/2
Find q such that 6 + 2*q**2 - 5*q**2 - 18 + 6 - 9*q = 0.
-2, -1
Let r be (85/350 - 2/14)*4. Determine v, given that -r*v - 4/5*v**2 + 0 - 2/5*v**3 = 0.
-1, 0
Let c(r) = 10*r**5 + 12*r**4 + 14*r**3 - 8*r**2 - 18*r - 10. Let b(x) = -x**5 - x**3 + x + 1. Let l(p) = -6*b(p) - c(p). What is o in l(o) = 0?
-1, 1
Let f(p) be the second derivative of 0 + 1/33*p**3 - 6*p + 0*p**2 - 1/66*p**4. Solve f(o) = 0.
0, 1
Let q be (-10)/(-24)*30/100. Let k(u) be the first derivative of -q*u**4 + 1/10*u**5 + 1/12*u**6 + 0*u + 0*u**2 + 1 - 1/6*u**3. Let k(o) = 0. What is o?
-1, 0, 1
Let p(d) = -12*d**2 + 33*d - 15. Let c(u) = u**3 + 12*u**2 - 33*u + 16. Let b(x) = -3*c(x) - 2*p(x). Determine g so that b(g) = 0.
-6, 1
Let h(o) be the first derivative of o**3/12 - 7*o**2/2 + 49*o - 23. Find b, given that h(b) = 0.
14
Let a(v) = -3*v**4 - 9*v**3 - 15*v**2 + 3*v. Let t(m) = -m**2 + m. Let b(f) = -a(f) + 6*t(f). Factor b(q).
3*q*(q + 1)**3
Let i(j) be the third derivative of 0*j + 0*j**5 - 1/60*j**6 + 1/12*j**4 + 1/6*j**3 + 4*j**2 + 0 - 1/210*j**7. Find h such that i(h) = 0.
-1, 1
Let x(q) = 4*q - 5. Let j be x(2). Let w(b) be the second derivative of 1/80*b**5 + 1/4*b**2 + 0*b**4 + 2*b + 0 - 1/8*b**j. Factor w(c).
(c - 1)**2*(c + 2)/4
Let z(x) be the first derivative of -x**7/294 - x**6/105 + x**4/42 + x**3/42 - 2*x + 8. Let o(u) be the first derivative of z(u). Determine a so that o(a) = 0.
-1, 0, 1
Factor 4*w + 12 - 4*w**2 - 3*w + 2*w + 5*w.
-4*(w - 3)*(w + 1)
Let h(y) = -2*y**4 - 7*y**3 + 11*y**2 + 15*y + 4. Let n(m) = 3*m**4 + 11*m**3 - 17*m**2 - 23*m - 6. Let b(o) = 8*h(o) + 5*n(o). Solve b(l) = 0.
-1, 2
Let c(i) = i**3. Let p(r) be the first derivative of r**5/5 - r**4 + 13*r**3/3 - 6*r**2 + 4*r - 3. Let s(f) = 2*c(f) - p(f). Solve s(j) = 0.
1, 2
Factor 32/11*i**2 + 2/11*i**3 + 0 + 128/11*i.
2*i*(i + 8)**2/11
Let n(p) = -p**2 - p. Let d(j) = -4*j. Let z(m) = -d(m) + 2*n(m). Solve z(g) = 0 for g.
0, 1
Let h = 1 + 3. Suppose -f + 6*f + h*b - 19 = 0, 0 = -2*f + 5*b + 1. Determine t, given that 2 + 3*t**4 - 3*t**4 - f - t**4 + 2*t**2 = 0.
-1, 1
Suppose -35 = -9*l + 4*l - 5*t, 0 = 5*l + 2*t - 38. Suppose 14 = -3*a + 4*d, a + l - 35 = -5*d. What is h in -h + 0*h + h**2 + a*h = 0?
-1, 0
Let t(z) = -8*z**4 - 43*z**3 - 85*z**2 - 63*z - 12. Let a(m) = -8*m**4 - 44*m**3 - 86*m**2 - 62*m - 12. Let g(n) = -5*a(n) + 4*t(n). Factor g(q).
2*(q + 2)*(q + 3)*(2*q + 1)**2
Suppose 20*z - 43*z + 6 + 3*z**2 + 14*z = 0. Calculate z.
1, 2
Let q(o) be the second derivative of -o**7/70 - o**6/25 + o**4/10 + o**3/10 + 48*o. Factor q(y).
-3*y*(y - 1)*(y + 1)**3/5
Let u be ((-10)/18)/(42/(-504)). Factor -u*m + 5/3*m**2 + 5.
5*(m - 3)*(m - 1)/3
Suppose -3*r - 8 = 4. Let l be (-30)/(-5)*r/(-6). Factor -3*q**l + q**3 - q + 4*q**2 + 4*q**4 - 4*q**2 - q**2.
q*(q - 1)*(q + 1)**2
Let w(k) be the second derivative of 2*k**6/105 - k**5/35 - k**4/21 + 2*k**3/21 - 9*k. Find f, given that w(f) = 0.
-1, 0, 1
Let y(m) be the third derivative of 0*m - 1/672*m**8 + 1/210*m**7 + 0 + 0*m**3 + 0*m**6 + 4*m**2 + 1/48*m**4 - 1/60*m**5. Factor y(n).
-n*(n - 1)**3*(n + 1)/2
Let o be (-18)/(-4)*(-36)/(-81). Let 0 - 2/5*l - 6/5*l**3 - 2/5*l**4 - 6/5*l**o = 0. What is l?
-1, 0
Let r = 46761/70 + -668. Let u(o) be the third derivative of -1/420*o**6 + 2/21*o**3 + 5/84*o**4 + r*o**5 + 3*o**2 + 0 - 1/735*o**7 + 0*o. Factor u(s).
-2*(s - 2)*(s + 1)**3/7
Let o(l) be the first derivative of l**6/180 - l**5/60 + l**3/3 + 1. Let q(k) be the third derivative of o(k). Factor q(m).
2*m*(m - 1)
Let j be 4*1 - 1/1. Let k = -18 + 18. Suppose 2/5*v**2 + 0*v - 2/5*v**j + k = 0. Calculate v.
0, 1
Let g(x) be the first derivative of -x**4/24 - x**3/12 - x - 1. Let y(w) be the first derivative of g(w). Factor y(l).
-l*(l + 1)/2
Let o(d) be the third derivative of d**5/180 + d**4/24 + d**3/9 + 2*d**2. Find a, given that o(a) = 0.
-2, -1
Factor 0 - 1/2*i**3 - 1/2*i**2 + 0*i.
-i**2*(i + 1)/2
What is n in -3/5*n**5 - 12/5*n**4 + 6/5*n**2 + 3*n + 6/5 - 12/5*n**3 = 0?
-2, -1, 1
Let 0*i**2 + 8/7*i**4 + 0 + 0*i - 8/7*i**3 - 2/7*i**5 = 0. What is i?
0, 2
Let i(q) be the third derivative of 0 + 7/8*q**4 - q**3 + 6*q**2 + 3/40*q**6 - 2/5*q**5 + 0*q. Find c such that i(c) = 0.
2/3, 1
Let g(v) = 3*v - 17. Let n be g(6). Suppose 1/2*o**2 - n - 1/2*o = 0. What is o?
-1, 2
Let u(v) = -2*v**2 + 2*v + 4. Let s(z) = -4*z**2 + 4*z + 8. Let j(k) = 4*s(k) - 9*u(k). Factor j(i).
2*(i - 2)*(i + 1)
Let h(q) = 4*q**2 + 16*q + 21. Let g(x) = 2*x**2 + 8*x + 10. Let n(r) = -5*g(r) + 2*h(r). Find p, given that n(p) = 0.
-2
Factor 0 + 3/4*q**4 + 3/4*q**3 - 3/2*q**2 + 0*q.
3*q**2*(q - 1)*(q + 2)/4
Let 3/4*w - 1/4*w**2 + 5/2 = 0. What is w?
-2, 5
Let y(n) = n**2 - 2*n - 3. Suppose 2*d - 2 - 4 = 0. Let x(j) = -j**2 + 2*j + 2. Let r(u) = d*y(u) + 4*x(u). Find o such that r(o) = 0.
1
Let z(m) be the second derivative of m**9/20160 - m**8/8960 - m**7/3360 + m**6/960 + m**4/12 + 2*m. Let g(n) be the third derivative of z(n). Factor g(c).
3*c*(c - 1)**2*(c + 1)/4
Let y(v) = -2*v**5 + 7*v**4 - 5*v**2 - v. Let a(d) = -d**5 + d**2 + d. Let o(f) = 4*a(f) + 4*y(f). Solve o(n) = 0 for n.
-2/3, 0, 1, 2
Let w(l) be the second derivative of -l**6/10 + 9*l**5/10 - 13*l**4/4 + 6*l**3 - 6*l**2 + 16*l. Factor w(j).
-3*(j - 2)**2*(j - 1)**2
Let r(h) = -2*h**3 - 2*h**2 + 3*h. Let n(s) = -s**3 - s**2 + 2*s. Let y(p) = -3*n(p) + 2*r(p). Factor y(c).
-c**2*(c + 1)
Let g be (2/24 - (-3)/18)/1. Let u(f) be the first derivative of 1/4*f - 1 + 1/12*f**3 - g*f**2. Factor u(k).
(k - 1)**2/4
Let t be 0 + 0 + (3 - 6). Let k be (-1 + 4)/t + 4. Suppose 6/7*v + 6/7*v**2 + 2/7*v**k + 2/7 = 0. What is v?
-1
Suppose -r = -5*r - 24. Let u be ((-2)/(-6))/((-1)/r). Factor 0 + 1/3*k**u + 0*k + 1/3*k**3.
k**2*(k + 1)/3
Let f(m) be the first derivative of -m**6/9 - 2*m**5/5 - m**4/2 - 2*m**3/9 - 25. Factor f(j).
-2*j**2*(j + 1)**3/3
Factor l**2 + 8 + 7*l**2 - 5*l**2 - 4*l**4 - 7*l**2 - 12*l**3 + 12*l.
-4*(l - 1)*(l + 1)**2*(l + 2)
Suppose -4*x + 23 = -a - 1, -3*x = -4*a - 18. Suppose -16*r - 2*r**2 + 0*r**4 - x - 2*r**5 - 2 + 10*r**3 + 2*r**4 = 0. Calculate r.
-1, 2
Find h, given that -27*h**2 + 67*h**3 - 6*h**4 + 7*h**4 - 19*h**4 + 2 - 17*h**4 - 7*h = 0.
-2/7, 1/5, 1
Suppose -2*a + 1 + 3 = 0. Let i(n) be the second derivative of -1/4*n**4 - 1/16*n**5 - 1/4*n**2 - 3/8*n**3 - a*n + 0. Factor i(g).
-(g + 1)**2*(5*g + 2)/4
Let b be (-4)/(-14) - 66/(-14). Let g be b*1 + -4 + 5. Find d such that -6 + 2*d + g + 2*d - 2*d**2 = 0.
0, 2
Factor -12*r**4 - 4*r**3 - 2*r**4 + 14*r**2 - 8*r**5 - 12*r**2.
-2*r**2*(r + 1)**2*(4*r - 1)
Let y(v) be the second derivative of 0 + 0*v**3 + 1/4*v**5 - 2*v + 0*v**2 + 7/30*v**6 - 1/6*v**4. Suppose y(l) = 0. Calculate l.
-1, 0, 2/7
Determine n, given that -1 - 14*n**3 - 9*n + 31*n**3 + 6*n**2 - 18*n**3 + 5 = 0.
1, 4
Let q(v) be the second derivative of -3*v - 1/5*v**2 + 0 - 1/5*v**3 - 1/50*v**5 - 1/10*v**4. Factor q(o).
-2*(o + 1)**3/5
Let w = -4 - -7. Suppose 5*j = w*j - 5*i + 26, -4*j + 24 = -4*i. Suppose -2*s**2 - 13*s**2 +