he second derivative of v(u). Suppose c(g) = 0. What is g?
-1, 1
Suppose -10 + 2 = -c. Let z be 9/(-24)*c/(-12). Let 0*b**2 - 1/4*b**3 + z*b + 0 = 0. Calculate b.
-1, 0, 1
Suppose -19 - 1 = -4*d. Factor -3/2*l**d + 3/2*l**4 + 0*l**2 + 0 + 0*l**3 + 0*l.
-3*l**4*(l - 1)/2
Suppose 2*m + 2 = -0. Let l be m + (4 - 10/4). Factor -1/4 + 0*n + 0*n**3 + l*n**2 - 1/4*n**4.
-(n - 1)**2*(n + 1)**2/4
Let y(v) be the second derivative of -v**7/840 + v**6/180 + v**3/3 + 2*v. Let q(o) be the second derivative of y(o). Determine h, given that q(h) = 0.
0, 2
Let s(t) be the second derivative of t**6/6 + t**5/2 - 5*t**4/12 - 5*t**3/3 + 17*t. Find r, given that s(r) = 0.
-2, -1, 0, 1
Let s(n) be the first derivative of -n**2 + 0*n + 0*n**4 + 1 - 1/120*n**5 + 1/12*n**3. Let b(a) be the second derivative of s(a). Let b(y) = 0. Calculate y.
-1, 1
Let s be (18/14)/(15/10). Factor -6/7*o**4 - s*o**3 - 2/7*o**2 + 0 + 0*o - 2/7*o**5.
-2*o**2*(o + 1)**3/7
Let 20*u**2 - 4*u**2 + 28*u**3 + 16*u + 48*u**2 = 0. Calculate u.
-2, -2/7, 0
Let k be (-4)/(-6) + (-44)/99. Find d such that -2/9*d**3 + 0*d - k*d**4 + 0 + 0*d**2 = 0.
-1, 0
Let u(v) be the third derivative of -v**6/160 + v**5/24 - 3*v**4/32 + v**3/12 - 4*v**2. Factor u(p).
-(p - 2)*(p - 1)*(3*p - 1)/4
Factor 7*w**2 - 7*w**4 - 2*w**3 + 3 + 8*w**3 - 2*w**4 - w**2 - 9*w + 3*w**5.
3*(w - 1)**4*(w + 1)
Let a(y) be the first derivative of y**3/7 - 3*y/7 + 2. Determine u, given that a(u) = 0.
-1, 1
Let c be 4/14*(0 + (0 - -2)). Factor -2/7*n**2 - 2/7 - c*n.
-2*(n + 1)**2/7
Let c(i) be the third derivative of i**8/40320 - i**6/1440 + i**5/10 + 3*i**2. Let g(t) be the third derivative of c(t). Factor g(r).
(r - 1)*(r + 1)/2
Suppose 4*n = p - 10, 2*p + 7*n = 5*n. Factor 1/2*o**p + 0 - 1/6*o**3 + 0*o.
-o**2*(o - 3)/6
Let h(t) be the second derivative of -t**5/20 + t**4/6 - t**3/3 + 2*t**2 - t. Let m(n) = -n**2 + n - 1. Let j(d) = h(d) + 3*m(d). Factor j(b).
-(b - 1)*(b + 1)**2
Let a = 151/525 + -6/25. Let l(w) be the second derivative of -1/10*w**5 - 1/15*w**6 + 1/6*w**4 + a*w**7 + 0*w**2 + 0 - 2*w + 0*w**3. Let l(t) = 0. What is t?
-1, 0, 1
Let z(p) be the second derivative of p**4/42 - p**3/21 - 6*p**2/7 - 13*p. What is i in z(i) = 0?
-2, 3
Suppose -4*y - 4 = -4*o, -5 = -3*y - 5*o + 16. Factor -4*g**y + 3*g - 3*g**2 + g + 5*g**2.
-2*g*(g - 2)
Let p(x) = -10*x**4 + 5*x**3 + 5*x**2 - 10*x. Let o(a) = a**5 + 10*a**4 - 6*a**3 - 4*a**2 + 11*a. Let g(h) = 5*o(h) + 6*p(h). Let g(i) = 0. What is i?
-1, 0, 1
Suppose -2*u - f = 11, -4*f = -3 - 1. Let z be (1/(-6))/(u/12). Let -z*k**2 - 2/3*k - 1/3 = 0. What is k?
-1
Let l be ((-3)/(-4))/((-18)/(-48)). Suppose l*z = -d + 4, 3 + 17 = z - 4*d. What is t in -2/9*t**3 - 2/3*t**z + 2/9*t + 2/3*t**2 + 0 = 0?
-1, -1/3, 0, 1
Factor 0*w - 5/2*w**2 - 95/4*w**3 - 55*w**4 + 0.
-5*w**2*(4*w + 1)*(11*w + 2)/4
Let f be (-3)/(-1) - 1*(-1 + 4). Let t(d) be the first derivative of 10/3*d**3 - 4*d**4 - 2/3*d**2 + f*d - 32/15*d**5 + 3. Factor t(b).
-2*b*(b + 2)*(4*b - 1)**2/3
Let i(f) be the first derivative of -10/27*f**3 + 4/9*f**2 + 2 + 2/9*f. Let i(v) = 0. What is v?
-1/5, 1
Let n(k) = k**3 + 4*k**2 + k - 3. Let c be n(-3). Suppose -2*j - 12 + 4 = -4*x, -j - 1 = -x. Factor 5 - 4*p**j - 3*p**3 + 2*p**c - 6 - 5*p - 1.
-(p + 1)**2*(p + 2)
Factor -9/4*a**3 + 0 - 3*a - 6*a**2.
-3*a*(a + 2)*(3*a + 2)/4
Let g(q) be the first derivative of -q**8/840 + 2*q**7/525 - q**5/75 + q**4/60 - 3*q**2/2 - 1. Let s(d) be the second derivative of g(d). Factor s(t).
-2*t*(t - 1)**3*(t + 1)/5
Let h be -8 - (3/(-3) - -3). Let g be (4/h)/((-24)/40). Suppose 0*p - 1/3*p**3 + g*p**2 + 0 = 0. What is p?
0, 2
Find n, given that -13*n - 60*n**2 - 13*n**4 - 8*n**4 + 6*n**3 + 3*n**5 + 37*n + 48*n**3 = 0.
0, 1, 2
Let z(v) be the third derivative of -2/15*v**5 + 1/15*v**6 + 10*v**2 + 0 + 0*v + 2/35*v**7 + 1/84*v**8 - 1/2*v**4 - 2/3*v**3. What is g in z(g) = 0?
-1, 1
Let z(b) be the first derivative of -3*b**5/5 - 3*b**4/4 + 3*b**3 + 3*b**2/2 - 6*b - 10. What is m in z(m) = 0?
-2, -1, 1
Let p(n) be the first derivative of 3*n**6 - 4*n**5/5 - 18*n**4 + 16*n**3/3 - 31. Suppose p(r) = 0. What is r?
-2, 0, 2/9, 2
Suppose -31 - 1 = -8*z. Let m(n) be the third derivative of 1/120*n**5 - n**2 + 0*n + 0*n**z + 0 + 0*n**3. What is v in m(v) = 0?
0
Let o(h) be the second derivative of -2*h**6/15 + 4*h**5/5 - h**4 - 8*h**3/3 + 8*h**2 - 15*h. Determine t, given that o(t) = 0.
-1, 1, 2
Find w, given that -63*w - 6 - 1725/4*w**3 - 1125/4*w**4 - 495/2*w**2 = 0.
-2/5, -1/3
Let c = -7564/19 + 398. Let b = 44/57 + c. Determine q so that b*q**2 + 2/3*q + 0 = 0.
-1, 0
Let a(x) be the second derivative of 0 + 32/27*x**3 + 74/45*x**5 + 10/63*x**7 - 4/9*x**2 - 11/6*x**4 + 7*x - 107/135*x**6. Find y such that a(y) = 0.
2/5, 1/2, 2/3, 1
Suppose 5*d - i - 7 = 0, 0 = 2*d - 6*d + 2*i + 2. Factor 7 - 7 + 2*g**d + 2*g.
2*g*(g + 1)
Suppose -2*l - 3*k + 9 = -2*k, 5*k - 9 = 2*l. Let n(h) be the first derivative of 1/3*h**l + 3 - 1/2*h**2 + 0*h. Factor n(g).
g*(g - 1)
Let n(t) = -7*t**2 - 19*t - 15. Let u(v) = 20*v**2 + 56*v + 44. Let b(i) = 8*n(i) + 3*u(i). Factor b(c).
4*(c + 1)*(c + 3)
Let o(h) be the second derivative of h**6/60 + h**5/20 - h**4/8 - h**3/3 + h**2 - 16*h. Let o(g) = 0. What is g?
-2, 1
Let f(p) be the third derivative of -p**6/1440 + p**5/480 + p**4/48 - 2*p**3/3 + 2*p**2. Let n(q) be the first derivative of f(q). Factor n(v).
-(v - 2)*(v + 1)/4
Let r(o) = 15*o**2 - 1. Let t be r(-1). Factor 8 - t*x + 16*x**2 - 6*x**3 + 0 - 4.
-2*(x - 1)**2*(3*x - 2)
Suppose 3*u + 8 = 3*m + 5, -3*m + 27 = 5*u. Find d, given that 10/9*d + 2*d**u + 32/9*d**2 - 4/9 = 0.
-1, 2/9
Suppose -3*y + y**2 - 2 + 2 - 4*y**2 = 0. Calculate y.
-1, 0
Let w(j) be the second derivative of -j**6/90 - j**5/15 - j**4/6 - 2*j**3/9 - j**2/6 - 9*j. Find o such that w(o) = 0.
-1
Factor 0 + 1/7*g**3 + 0*g**2 - 1/7*g.
g*(g - 1)*(g + 1)/7
Suppose 4*m - 11*m + 14 = 0. Let b(f) be the third derivative of -1/42*f**4 - m*f**2 + 0*f + 1/210*f**5 + 0 + 1/21*f**3. Suppose b(y) = 0. What is y?
1
Let s(r) be the second derivative of r**6/240 + r**5/160 - r**4/32 - 5*r**3/48 - r**2/8 + 20*r. Factor s(x).
(x - 2)*(x + 1)**3/8
Let n(q) be the third derivative of q**5/90 - q**4/18 - q**3/3 + 13*q**2. Solve n(h) = 0.
-1, 3
Suppose 3*n - n + 4 = 0. Let t = n - -4. Factor 1/2*k + 1/4*k**t + 0.
k*(k + 2)/4
Let 0 - 2/5*f**3 + 0*f**2 + 0*f = 0. Calculate f.
0
Let a(h) be the first derivative of 1/8*h**4 + 0*h**2 + 1/3*h**3 + 0*h + 3. Let a(l) = 0. Calculate l.
-2, 0
Factor -1/2*f**3 + 0 - 1/2*f**4 + 2*f**2 + 2*f.
-f*(f - 2)*(f + 1)*(f + 2)/2
Let q be (((-18)/(-20))/9)/((-2)/(-5)). Factor 0*f**3 + 0 + 0*f + q*f**4 + 1/4*f**5 + 0*f**2.
f**4*(f + 1)/4
Let b(r) = 3*r**4 + 9*r**3 + 6. Let v(l) = -l**4 - l**2 - 1. Let z(o) = b(o) + 6*v(o). What is h in z(h) = 0?
0, 1, 2
Let a(o) be the second derivative of -o**4/12 + o**3/6 + 11*o. What is j in a(j) = 0?
0, 1
Factor 0 - 1/2*r + 0*r**2 + 1/2*r**3.
r*(r - 1)*(r + 1)/2
Let p(t) = 5*t**3 - 4*t**2 + 16*t. Let v(o) = 6*o**3 - 3*o**2 + 16*o. Let c(b) = 5*p(b) - 4*v(b). Factor c(j).
j*(j - 4)**2
Let g = 148 + -83. Let f be (-1)/3 - g/(-105). Factor -2/7*c**2 + 2/7 + 2/7*c**3 - f*c.
2*(c - 1)**2*(c + 1)/7
Let f(s) be the second derivative of s**8/3360 + s**7/1260 - s**6/180 - s**4/2 + s. Let g(a) be the third derivative of f(a). Factor g(x).
2*x*(x - 1)*(x + 2)
Let h = 88 - 84. Solve 0 + 0*s + 0*s**3 - 3/5*s**h + 1/5*s**2 - 2/5*s**5 = 0 for s.
-1, 0, 1/2
Let f(a) = 21*a**2 - 1. Let i = 10 - 9. Let x be f(i). Factor u**2 + x*u - 18*u + 3*u**2.
2*u*(2*u + 1)
Let s(y) be the third derivative of -y**6/120 + 3*y**5/80 + 5*y**4/48 - y**3/8 - 11*y**2. Solve s(g) = 0.
-1, 1/4, 3
Let h(t) be the first derivative of 2*t**3/33 + 3*t**2/11 + 4*t/11 - 3. Factor h(r).
2*(r + 1)*(r + 2)/11
Suppose 3*g + 24 - 9 = 0. Let z = -3 - g. Determine x so that 7*x**5 + 2 + 8*x**4 + 2*x - z*x**5 - 2*x**2 - 3*x - 4*x**3 - 8*x**2 = 0.
-1, 2/5, 1
Let n(h) be the second derivative of -h**7/6300 - 7*h**4/12 + 8*h. Let z(o) be the third derivative of n(o). Factor z(r).
-2*r**2/5
Let f(a) = a**3 - a**2 - 4*a + 4. Let p be f(1). Factor 4/5*j**3 + 0*j**4 - 2/5*j**5 - 2/5*j + 0*j**2 + p.
-2*j*(j - 1)**2*(j + 1)**2/5
Find u such that 4/9*u - 2/9 - 4/9*u**3 + 0*u**2 + 2/9*u**4 = 0.
-1, 1
Suppose 2/5*q - 3/5*q**