culate j.
-1, -1/3
Let b(n) be the first derivative of n**7/560 + n**6/240 + n**3 - 2. Let v(y) be the third derivative of b(y). Factor v(q).
3*q**2*(q + 1)/2
Let j(s) = -3*s**4 - 7*s**3 - 7*s**2 + 2*s + 2. Let r(b) = b**4 + b**2 - b. Let z(w) = -5*j(w) - 5*r(w). Find l, given that z(l) = 0.
-2, -1, 1/2
Let y(k) = -17*k**2 + 23*k + 40. Let l(z) = -8*z**2 + 12*z + 20. Let d(v) = 7*l(v) - 3*y(v). Solve d(o) = 0 for o.
-1, 4
What is h in 7*h**4 + 69*h**2 + 29*h**3 + 28*h**3 + 5*h**4 + 15*h - 14 + 5 = 0?
-3, -1, 1/4
Factor -4*j + 0*j**2 - 3*j**2 + 8*j**3 + 3*j**4 + 3*j**4 + j**2.
2*j*(j + 1)**2*(3*j - 2)
Let k(w) be the second derivative of -w**7/11340 - w**6/1620 - w**4/12 - 2*w. Let c(v) be the third derivative of k(v). Find l such that c(l) = 0.
-2, 0
Solve 3*m**3 - 5*m**2 - 4*m**2 + 9*m**2 = 0.
0
Find m, given that -2/9*m**2 + 2/3 + 4/9*m = 0.
-1, 3
Let j(k) be the first derivative of 0*k**2 + 0*k - 1/3*k**3 + 5. Find m, given that j(m) = 0.
0
Let m(v) be the second derivative of v**7/1680 - v**6/120 + v**5/20 + 2*v**4/3 + 2*v. Let l(h) be the third derivative of m(h). Factor l(d).
3*(d - 2)**2/2
Let b(w) = 11*w**2 - 5*w - 16. Let d(s) = -10*s**2 + 5*s + 15. Let i(h) = -5*b(h) - 6*d(h). Factor i(g).
5*(g - 2)*(g + 1)
Let w = 145 + -1013/7. Factor w*v**2 - 2/7 + 2/7*v - 2/7*v**3.
-2*(v - 1)**2*(v + 1)/7
Let c be 4/(-6) + 68/12. Factor c*r + 3*r**4 + 9*r**2 + 9*r**3 - r - r.
3*r*(r + 1)**3
Let d(x) be the second derivative of 2*x + x**2 - 1/2*x**3 + 0 + 1/12*x**4. Factor d(s).
(s - 2)*(s - 1)
Let s = 20 - -11. Suppose -v + 2*b = -14, 9*v - 3*b - s = 5*v. Let 2*z - 2 + 4*z**2 + 1 - v*z**3 - 2*z**4 - 1 + 2*z**5 = 0. What is z?
-1, 1
Suppose 5*r + 2 = x - 0*x, -3*x + 6 = -4*r. Let n(z) be the first derivative of -2/15*z**3 + 1/10*z**4 - 3 + r*z + 0*z**2. Let n(s) = 0. Calculate s.
0, 1
Let w(r) = r**3 - r**2 - 2*r + 4. Let h(d) = 2*d**3 - 2*d**2 - 4*d + 9. Suppose -5 = 5*l + 15. Let o(f) = l*h(f) + 9*w(f). Factor o(u).
u*(u - 2)*(u + 1)
Let v(u) = -9*u**2 - 4*u + 5. Let x(a) = -a**2 + 1. Let d(f) = 7*f**2 + 6*f - 1. Let q(j) = -d(j) + 6*x(j). Let c(w) = 5*q(w) - 7*v(w). Solve c(b) = 0.
-1, 0
Let x be (-4)/11*(-3)/6. Let r = 233 - 2561/11. Determine p so that -x + 4/11*p - r*p**2 = 0.
1
Factor 15/4*i**2 + 9/4 + 21/4*i + 3/4*i**3.
3*(i + 1)**2*(i + 3)/4
Let n be 4/14 - (13 - (-1096)/(-84)). Factor 2/3 - n*a - 1/3*a**2.
-(a - 1)*(a + 2)/3
Suppose 16/15 + 2/5*j**3 - 44/15*j**2 + 2/3*j**4 - 8/5*j = 0. What is j?
-2, -1, 2/5, 2
Let p = -22 + 23. Let f(i) = -i**4 - 21*i**3 - 39*i**2 - 3. Let x(o) = o**4 + o**3 - o**2 - 1. Let n(m) = p*f(m) - 3*x(m). Factor n(s).
-4*s**2*(s + 3)**2
Let j(p) = 3*p**5 - 4*p**4 - 21*p**3 - 12*p**2 - 2*p. Let m(t) = -6*t**5 + 7*t**4 + 42*t**3 + 24*t**2 + 5*t. Let c(b) = -5*j(b) - 2*m(b). Factor c(w).
-3*w**2*(w - 4)*(w + 1)**2
Let r(c) = c**3 + 6*c**2 + 6*c + 12. Let f be r(-5). Find g such that -f*g - 6*g + 11*g + 2*g**3 = 0.
-1, 0, 1
Let l(b) = 6*b**2 + 5*b + 6. Let k(j) = j**2 + j + 1. Let g(o) = 21*k(o) - 3*l(o). Solve g(m) = 0 for m.
-1
Suppose -2*r - 10 = 3*r. Let o be 3 - (r/(-4) - -2). Factor 1/2*z**4 + 1/2*z**3 - o*z - 1/2*z**2 + 0.
z*(z - 1)*(z + 1)**2/2
Let b(t) be the second derivative of -1/21*t**4 + 0 - 8/7*t**2 + 8/21*t**3 + 8*t. Determine c so that b(c) = 0.
2
Let f(m) be the third derivative of -m**6/10 - 7*m**5/15 - 5*m**4/6 - 2*m**3/3 - m**2. Factor f(l).
-4*(l + 1)**2*(3*l + 1)
Let w(b) be the third derivative of b**7/42 - b**6/4 + 2*b**5/3 + 5*b**4/4 - 15*b**3/2 - b**2. Suppose w(z) = 0. What is z?
-1, 1, 3
Let n = -8 + 8. Let a be n/(-2) + 10/5. Factor 1/2*x**4 - 1/2*x**a + 0 - 1/2*x**3 + 1/2*x.
x*(x - 1)**2*(x + 1)/2
Let y = 9 + -21. Let j(a) = a**3 + 1. Let q(s) = -14*s**3 - 2*s**2 + 2*s - 10. Let i(w) = y*j(w) - q(w). Find p, given that i(p) = 0.
-1, 1
Factor 4/7*r**2 + 1/7*r**5 + 3/7*r**3 - 4/7*r**4 - 4/7*r + 0.
r*(r - 2)**2*(r - 1)*(r + 1)/7
Let x(d) = -8*d**2 - 20*d - 7. Let k(j) = 9*j**2 + 21*j + 6. Let i(h) = -5*k(h) - 6*x(h). Let i(s) = 0. Calculate s.
-4, -1
Let g(j) be the second derivative of -1/8*j**4 + 9/80*j**5 - 5*j + 3/4*j**2 - 3/8*j**3 + 0. Find f such that g(f) = 0.
-1, 2/3, 1
Suppose 0 = -4*x + 5*x. Suppose -3*h + 9 - 3 = x. Factor -p**2 + h*p**2 + p + p.
p*(p + 2)
Let s(p) be the third derivative of p**6/240 - p**5/60 - 8*p**2. Factor s(k).
k**2*(k - 2)/2
Solve 0 - 3/2*y**3 + 3/2*y**2 - 1/2*y + 1/2*y**4 = 0.
0, 1
Let o(k) be the second derivative of -3*k + 0*k**2 - 1/36*k**4 + 0 + 1/18*k**3 - 1/30*k**5. Factor o(z).
-z*(z + 1)*(2*z - 1)/3
Let n(w) be the first derivative of -2*w**6/3 + 6*w**5/5 + w**4 - 8*w**3/3 + 2*w - 1. Solve n(u) = 0.
-1, -1/2, 1
Let p(h) be the second derivative of 5*h**4/12 + 5*h**3/6 - 5*h**2 + 7*h. Determine u, given that p(u) = 0.
-2, 1
Suppose 25 = 5*p - 5*m, -m + 11 - 22 = -3*p. Factor 0*a - 3/7*a**p + 3/7*a**2 + 0.
-3*a**2*(a - 1)/7
Let c(h) be the third derivative of 0*h + 0*h**3 + 2*h**2 + 1/16*h**4 + 1/80*h**5 + 0. Factor c(d).
3*d*(d + 2)/4
Determine i so that -2/3*i**4 - 4/3*i**3 + 0*i**2 + 0 + 0*i = 0.
-2, 0
Let i(k) be the third derivative of 3*k**6/20 - k**5/10 - 5*k**4/12 - k**3/3 + k**2. Factor i(u).
2*(u - 1)*(3*u + 1)**2
Determine u so that -10/11*u - 4/11 - 8/11*u**2 - 2/11*u**3 = 0.
-2, -1
Let f be (8/(-14))/((-4)/14). Factor -3*y**3 + f*y**3 + y**5 + 4 - 4.
y**3*(y - 1)*(y + 1)
Let k(n) = n**2 - n + 1. Let o(h) = h**3 + h**2 - 2*h + 2. Let r(v) = -2*k(v) + o(v). Find m such that r(m) = 0.
0, 1
Let t(d) be the third derivative of -d**6/30 + 3*d**5/5 - 9*d**4/2 + 18*d**3 + 2*d**2. Factor t(b).
-4*(b - 3)**3
Let v be 6/3 + (-3 - 6). Let w = v + 7. Determine a so that w*a - 1/4*a**2 - 1/4*a**3 + 0 = 0.
-1, 0
Let m(h) be the second derivative of 0 - 1/3*h**3 + 7*h + 2*h**2 - 1/2*h**4. Suppose m(r) = 0. Calculate r.
-1, 2/3
Let j(f) be the third derivative of f**5/120 + f**4/24 + 2*f**2. What is l in j(l) = 0?
-2, 0
What is i in -3/2*i**2 + 0 - 21/2*i = 0?
-7, 0
Let x(b) be the second derivative of -b**7/70 + b**6/25 - b**4/10 + b**3/10 - 6*b. What is t in x(t) = 0?
-1, 0, 1
Let c be (-5212)/45 + 22/99. Let r = -114 - c. Factor r*u - 2/5*u**2 - 8/5.
-2*(u - 2)**2/5
Let l(c) be the first derivative of -c**6/9 + 2*c**5/5 - c**4/2 + 2*c**3/9 - 43. Suppose l(m) = 0. What is m?
0, 1
Factor -5*w**2 + 9*w**2 + 12*w + 0*w**2.
4*w*(w + 3)
Let k(s) be the second derivative of -s + 0*s**3 + 0 - 1/20*s**4 + 0*s**2. Factor k(w).
-3*w**2/5
Let n(l) be the first derivative of l**6/33 + 4*l**5/55 - l**4/11 - 16*l**3/33 - 7*l**2/11 - 4*l/11 - 52. Let n(c) = 0. Calculate c.
-1, 2
Suppose -4*q - 2*s = 20, -13 - 11 = 4*q + 3*s. Let m be (-2 + 2)/((-3)/q). Factor m*g - 1/4*g**2 + 1/4.
-(g - 1)*(g + 1)/4
Let m(g) be the second derivative of -g + 0 + 1/120*g**5 + 1/72*g**4 + 0*g**2 + 0*g**3. Factor m(s).
s**2*(s + 1)/6
Let h(n) be the first derivative of 0*n**3 + 0*n + 2 + 3/16*n**4 - 3/8*n**2. Suppose h(a) = 0. What is a?
-1, 0, 1
Let w(x) be the first derivative of 2*x**3/3 + x**2 - 4*x + 24. Factor w(q).
2*(q - 1)*(q + 2)
Let d be (-2)/20 + 8/80. Let m(q) be the second derivative of 0*q**2 - 1/126*q**7 + 1/30*q**6 + 0 + 0*q**4 + d*q**3 - 2*q - 1/30*q**5. Factor m(a).
-a**3*(a - 2)*(a - 1)/3
Let x(d) be the second derivative of -1/18*d**4 + 1/60*d**5 + 0 - 4*d + 1/18*d**3 + 0*d**2. Factor x(k).
k*(k - 1)**2/3
Let j(c) be the third derivative of -1/240*c**5 + 0*c + 0*c**3 + 0 - 2*c**2 - 1/96*c**4. Solve j(d) = 0 for d.
-1, 0
Suppose -5*h + 20*h = 9*h. Factor h*s - 2/11 + 2/11*s**2.
2*(s - 1)*(s + 1)/11
Let h(x) = -7*x**2 + 6*x + 10. Let b(k) = 6*k**2 - 5*k - 9. Let r(v) = -6*b(v) - 5*h(v). Let r(l) = 0. Calculate l.
-2, 2
Suppose -2*a + 2 = -16. Suppose 5*r - 2*r + 3*p - a = 0, -2*r + 9 = 3*p. Solve -4/3*z + 2*z**4 + 4/3*z**3 + r - 2*z**2 = 0.
-1, -2/3, 0, 1
Let l be (0 + 1)/((-13)/(-26)). Solve -30*s**3 + l*s**4 + 14*s**3 + 12*s**3 = 0 for s.
0, 2
Let z(a) be the third derivative of -a**5/5 - a**4/3 + 2*a**3/3 - 8*a**2. Let z(i) = 0. Calculate i.
-1, 1/3
Let h(u) = -u - 3. Let s be h(-4). Let a = s + 1. Factor 2*i**a + i**3 + i**3 - i**4 - 2*i**2 - i**2.
-i**2*(i - 1)**2
Let w(o) be the second derivative of -o**6/24 + 17*o**5/80 - o**4/8 + 11*o. Determine y, given that w(y) = 0.
0, 2/5, 3
Let a(u) = 23*u**4 + 11*u**3 - 5*u**2 + 7*u. Let c(b) = -70*b**4 - 34*b**3 