 -l*b**3 + 2*b**3 + 5*b**5 - 3*b**5 = 0.
-1, 0, 1
Let v(q) be the third derivative of 4*q**8/7 + 24*q**7/5 + 15*q**6/2 - 361*q**5/20 + 51*q**4/4 - 9*q**3/2 + q**2. Factor v(p).
3*(p + 3)**2*(4*p - 1)**3
Find t, given that -24/5*t**2 + 8/15*t + 0 + 54/5*t**3 = 0.
0, 2/9
Determine h so that -4*h**2 - 18*h + 3*h**3 - h**2 + 8*h**2 = 0.
-3, 0, 2
Let r(s) be the third derivative of s**6/300 - s**5/50 + s**4/30 - 17*s**2. Suppose r(y) = 0. What is y?
0, 1, 2
Let t(m) = -m**3 + m - 1. Let p(a) = -7*a**3 - 2*a**2 + 15*a - 11. Let l(z) = 2*p(z) - 10*t(z). Suppose l(j) = 0. What is j?
-3, 1
Let w(q) = -5*q**3 + 9*q**2 + 2*q. Let d(m) = 9*m**3 - 17*m**2 - 4*m. Let b(y) = -6*d(y) - 11*w(y). Determine n, given that b(n) = 0.
-2, -1, 0
Suppose 2*y + 4 = -0, -5*y = 5*h - 5. Let t(b) be the first derivative of -4/3*b**h + 5*b**2 - 1 - 4*b. Find k such that t(k) = 0.
1/2, 2
Let f = -96 + 96. Factor 1/2*c**4 + 0 + f*c + 0*c**3 + 0*c**2.
c**4/2
Suppose -q = 3*q + 4. Let d = q + 3. Find m such that -2 + 9*m + m**2 - 2*m**2 - 6*m**d = 0.
2/7, 1
Let o(f) be the second derivative of -6*f**7/35 - 58*f**6/75 - 33*f**5/25 - f**4 - 4*f**3/15 - 5*f. Let o(a) = 0. What is a?
-1, -2/9, 0
Let l(v) be the first derivative of v**4/6 - 2*v**3/9 - v**2/3 + 2*v/3 + 16. Find g, given that l(g) = 0.
-1, 1
Let -2/9*h + 2/9*h**2 - 4/9 = 0. What is h?
-1, 2
Let k(y) = y**2 - 26*y - 87. Let a be k(29). Let v(o) be the first derivative of 1 + 1/12*o**6 + 0*o**2 + 0*o**3 + a*o + 1/5*o**5 + 1/8*o**4. Factor v(m).
m**3*(m + 1)**2/2
Suppose 0*s = s + 7. Let p(v) = -5*v**3 - 3*v**2 + v - 5. Suppose -1 + 9 = 2*w. Let c(r) = -9*r**3 - 5*r**2 + 2*r - 9. Let k(a) = s*p(a) + w*c(a). Factor k(h).
-(h - 1)**2*(h + 1)
Let c(v) be the third derivative of v**7/420 + v**6/40 + 11*v**5/120 + v**4/8 - 11*v**2. Factor c(s).
s*(s + 1)*(s + 2)*(s + 3)/2
Let m(x) be the first derivative of x**6/1440 - x**5/80 + 3*x**4/32 + x**3/3 - 1. Let f(r) be the third derivative of m(r). Factor f(h).
(h - 3)**2/4
Let j(g) be the second derivative of -g**7/2520 + g**6/432 - g**5/180 + g**4/6 - 2*g. Let y(b) be the third derivative of j(b). Suppose y(x) = 0. What is x?
2/3, 1
Let a(f) be the second derivative of f**7/126 - f**5/20 + f**4/18 - 3*f + 12. Solve a(g) = 0.
-2, 0, 1
Let f(g) be the first derivative of 0*g - 1/2*g**6 + 2*g**3 + 0*g**4 - 6 - 6/5*g**5 + 3/2*g**2. Solve f(o) = 0.
-1, 0, 1
Suppose -3*a + 4*x = 0, 4*a + 2*x = -0*a. Suppose -o - 1 = a, 5*o + 0 = -3*q + 1. Find i, given that 1/2*i - 1 + 1/2*i**q = 0.
-2, 1
Let k(v) = v - 9*v**3 + 5*v**4 + 6*v**4 + 4 - 9*v**2 + 4 - 2*v**4. Let s(f) = -f**4 + f**3 + f**2 - 1. Let m(n) = -3*k(n) - 24*s(n). Factor m(o).
-3*o*(o - 1)**2*(o + 1)
Let y(j) = -3*j - 9. Let s be y(-3). Let m(t) be the first derivative of 0*t + 1/15*t**6 + 2 - 2/25*t**5 + 0*t**3 + 0*t**4 + s*t**2. Factor m(u).
2*u**4*(u - 1)/5
Let h(u) be the third derivative of -u**6/120 - u**5/60 + u**4/12 - u**2. Let r be h(-2). Factor -2 - 2*a**2 + r + 4.
-2*(a - 1)*(a + 1)
Let w(t) be the second derivative of t**5/20 + t**4/12 - t**3/3 - 5*t. Let w(y) = 0. Calculate y.
-2, 0, 1
Let x(f) be the third derivative of 0*f**3 + 0 + 1/90*f**5 + 0*f**4 - 1/360*f**6 + 0*f - 1/630*f**7 + 2*f**2. Factor x(n).
-n**2*(n - 1)*(n + 2)/3
Suppose -3*b + b + 4*o + 50 = 0, 95 = 3*b + 4*o. Suppose s + 8*s = 18. Factor -d**4 - 13*d**3 + 24*d**2 - b*d**2 + s*d + 4*d**5 + d**3.
d*(d - 2)*(d + 1)**2*(4*d - 1)
Let q(m) be the first derivative of 3/4*m**4 - 4 + 0*m**2 + 0*m - 1/2*m**3. Factor q(c).
3*c**2*(2*c - 1)/2
Let b(n) = 7*n**2 + 12*n + 5. Let g be b(-1). Factor 0 + 4/3*s**3 + 0*s + 2*s**4 + g*s**2 + 2/3*s**5.
2*s**3*(s + 1)*(s + 2)/3
Let d(m) be the first derivative of -8 + 2/27*m**3 + 1/3*m**2 + 0*m. Factor d(w).
2*w*(w + 3)/9
Suppose -2 = -z + 2*w, 3*z + 2*w + 2 = -0*w. Suppose -4*c + c + 9 = z. Find v, given that -1 + 0*v**4 + 4*v**4 + v**5 + 2*v**3 - 2*v**2 - c*v - v**4 = 0.
-1, 1
Let x(f) be the first derivative of 1/6*f**4 - 2*f**3 + 1 - 3*f + 9*f**2. Let n(t) be the first derivative of x(t). Let n(o) = 0. What is o?
3
Let g(r) = r**3 + 15*r**2 + 16*r + 19. Let f be g(-14). Let s be (-3)/(f/(-6) - 3). Let 2/9*m**s + 0 - 4/9*m = 0. Calculate m.
0, 2
Suppose 13*h = 11*h + 8. Let p(s) be the first derivative of 2*s**3 + 0*s**2 + 0*s + 3/5*s**5 + 9/4*s**h + 3. Factor p(b).
3*b**2*(b + 1)*(b + 2)
Let r(a) be the first derivative of -1/3*a**3 + a**2 + 3 + 0*a. Let r(d) = 0. What is d?
0, 2
Suppose m = 3*f + 2*f - 29, f - 2 = 4*m. Let o(g) = g - f - 2*g**2 - g**3 + 11 + 2*g**2. Let j(w) = -1. Let h(l) = -10*j(l) - 2*o(l). Factor h(x).
2*x*(x - 1)*(x + 1)
Let b(j) be the second derivative of -2/3*j**3 + 0 + 0*j**2 + 3*j - 1/6*j**4. Determine z so that b(z) = 0.
-2, 0
Factor -2*l**3 - 9*l + 5*l + 4*l**2 + 6*l**3 - 4*l**4.
-4*l*(l - 1)**2*(l + 1)
Suppose 4*i = n + 9 - 25, -n - 5*i - 2 = 0. Factor 2 + 5 + t**2 - n.
(t - 1)*(t + 1)
Let m(q) be the first derivative of -1/2*q**2 + 1/3*q**3 + 1/4*q**4 + 5 - q. Solve m(i) = 0.
-1, 1
Let n(a) = -9*a + 59. Let m be n(6). Let q = -4/7 - -15/14. Let 3/2*r**3 + 3/2*r**4 + 1/2*r**2 + q*r**m + 0 + 0*r = 0. Calculate r.
-1, 0
Let a(s) be the second derivative of s + 4*s**2 - 1/15*s**6 - 1/2*s**4 - 2/5*s**5 + 0 + 4/3*s**3. Solve a(u) = 0 for u.
-2, -1, 1
Let x(v) be the first derivative of 2*v**3/3 - v**2 + 6*v + 6. Let c(g) = -3*g**2 + 3*g - 7. Let d(a) = 6*c(a) + 7*x(a). Factor d(m).
-4*m*(m - 1)
Let h(w) = w**3 + 5*w**2 - 2*w - 7. Let v be h(-5). Factor -1/2*i**5 - 1/2*i**2 + 0 + 0*i + 1/2*i**4 + 1/2*i**v.
-i**2*(i - 1)**2*(i + 1)/2
Let c(i) be the first derivative of -i**4/24 + i**2/12 + 63. Determine w, given that c(w) = 0.
-1, 0, 1
Let q(z) be the first derivative of -z**3/3 + 10*z**2 - 100*z + 40. Let q(t) = 0. Calculate t.
10
Let s be -2 - (-4 - 0/(-1)). Find i, given that 0*i + 2*i - 2*i - s*i**2 = 0.
0
Factor -h**4 - 2*h**2 + 2*h**3 - 4*h**3 + 2*h**5 + 3*h**4 + 0*h**2.
2*h**2*(h - 1)*(h + 1)**2
Factor 2*o**2 - 4*o**4 - 2*o**4 + 4*o**4 + 2*o**5 + 0*o**3 - 2*o**3.
2*o**2*(o - 1)**2*(o + 1)
Let c(i) = 5*i**2 + 33*i - 32. Let p(f) = f + 1. Let x(d) = -c(d) + 3*p(d). Find b, given that x(b) = 0.
-7, 1
Let d be -6 + (-3 - -2) + 2. Let g = d + 12. Let -g*n + 9*n**2 + n**2 + 8 + 23*n + 2*n**3 = 0. Calculate n.
-2, -1
Suppose -21*n + 36 = -9*n. Find j, given that 0 + 0*j**2 - 1/5*j**n + 0*j**4 + 0*j + 1/5*j**5 = 0.
-1, 0, 1
Let d(l) = 4*l + 15. Let n be d(-3). Factor -2*q - 1/3*q**2 - n.
-(q + 3)**2/3
Factor -2*i + 3134 - 3134 - i**2.
-i*(i + 2)
Let c be (-603)/6*(-6)/9. Factor -f**2 - 67 + c + 6*f - f**2.
-2*f*(f - 3)
Let q(w) = -10*w**2 + 14*w + 6. Let n(o) = -51*o**2 + 70*o + 31. Suppose -a - k = 12, 0*k + k = -1. Let x(u) = a*q(u) + 2*n(u). Suppose x(f) = 0. What is f?
-1/4, 2
Let v(g) be the second derivative of -g**6/10 - 3*g**5/20 + 6*g. What is i in v(i) = 0?
-1, 0
Let x(i) = -i + 1. Let d(t) = -2*t**2 + 5*t. Let f(a) = d(a) + 4*x(a). Let n(s) = 3*s**2 - s - 7. Let o(p) = -5*f(p) - 3*n(p). Determine l, given that o(l) = 0.
1
Let g(u) be the second derivative of -u**9/378 + u**8/210 + u**7/140 - u**6/90 - u**5/60 - u**3/2 - 3*u. Let i(k) be the second derivative of g(k). Factor i(j).
-2*j*(j - 1)**2*(2*j + 1)**2
Suppose 4*v = 5 + 7. Factor -6*c**v + 2*c**3 - c**3 + 3*c**3 + 5*c + c**2 + 2.
-(c - 2)*(c + 1)*(2*c + 1)
Suppose 6*d**2 + 14*d + 3 - 14 - 1 = 0. Calculate d.
-3, 2/3
Let i(a) be the second derivative of a**5/40 - a**4/12 + 23*a. Solve i(x) = 0.
0, 2
Let m(p) = p**4 - 4*p**3 - p**2 + 4*p - 4. Let j(w) = 2*w**4 - 9*w**3 - 2*w**2 + 9*w - 9. Let i(d) = 4*j(d) - 9*m(d). Determine f so that i(f) = 0.
-1, 0, 1
Let c = 1 + 4. Suppose 5*r + 5*x - 5 = 0, -4*x - 9 = 2*r - 3. Find y, given that -y**4 - y**5 + 0*y**4 + c*y**r = 0.
0, 1/4
Let t(w) be the first derivative of w**4/12 - w**3/3 + 2. Solve t(l) = 0 for l.
0, 3
Let g(p) be the second derivative of p**7/168 + p**6/40 - 3*p**5/80 - 7*p**4/48 + p**3/4 + 30*p. Determine q so that g(q) = 0.
-3, -2, 0, 1
Let n(y) be the third derivative of -y**6/80 + 3*y**4/16 + y**3/2 + 2*y**2. Factor n(f).
-3*(f - 2)*(f + 1)**2/2
Suppose 4*a - 6 = 6. Suppose -a*j - j + 3*j**2 + 7*j - 3*j**3 - 3 = 0. Calculate j.
-1, 1
Let v = 223 - 2005/9. Determine b, given that -4/9 + 2/3*b**3 + 8/9*b**2 - v*b = 0.
-1, 2/3
Let g be 3 - (-26 - -3) - 1. Let j be