 i**7/3780 + i**6/2160 + i**4/24 + 2*i**2. Let b(g) be the second derivative of q(g). Solve b(y) = 0 for y.
0, 1
Let o(j) be the third derivative of -j**5/20 + j**4/4 - j**3/2 + 18*j**2. Find z such that o(z) = 0.
1
Let w(u) be the third derivative of -u**7/105 + u**6/60 + u**5/30 - u**4/12 + 2*u**2. Let w(r) = 0. What is r?
-1, 0, 1
Let o(n) be the third derivative of 0*n - 1/3*n**3 + 0 - 8*n**2 - 1/30*n**5 - 1/6*n**4. Suppose o(t) = 0. Calculate t.
-1
Suppose 0*b - 4 = -2*b. Suppose 0*f**3 - 6*f**3 + 3*f - 5*f**2 - 4 - f + 13*f**b = 0. What is f?
-2/3, 1
Let v(m) = 21*m**2 - 12. Let s(f) = 2*f - 1. Let w be s(-4). Let j(r) = -5*r**2 + 3. Let x(q) = w*j(q) - 2*v(q). Factor x(a).
3*(a - 1)*(a + 1)
Let g(u) be the first derivative of 3*u**4/8 + u**3/2 + 5. Let g(r) = 0. What is r?
-1, 0
Let a(n) = -2*n. Let u be a(0). Let y be (6/(-30))/((-4)/10). Let u + 1/2*f**4 + 0*f**2 + y*f**5 + 0*f**3 + 0*f = 0. What is f?
-1, 0
Let x(v) be the third derivative of -v**6/240 - v**5/120 + 5*v**4/48 - v**3/4 + v**2. Let x(a) = 0. What is a?
-3, 1
Let c be 23/90 + (-2)/10. Let z(f) be the second derivative of 0*f**2 - c*f**4 + f + 0 - 1/9*f**3. Factor z(q).
-2*q*(q + 1)/3
Suppose 2*p = -2*p + 4*b - 24, -10 = 4*p + 3*b. Let a = p - -6. Factor 2*o**5 + 2*o**a - 9*o**3 + 7*o**3 - 5*o**4 + 3*o**4.
2*o**2*(o - 1)**2*(o + 1)
Let c be 8 - 0 - (-240)/(-32). Factor 19/2*j**3 + 1 - 15/2*j**2 + c*j - 7/2*j**4.
-(j - 1)**3*(7*j + 2)/2
Let l(y) = -3*y**4 - 12*y**3 - 6*y**2 + 12*y + 9. Let z(r) = -30*r**4 - 120*r**3 - 60*r**2 + 120*r + 90. Let m(n) = 21*l(n) - 2*z(n). Factor m(d).
-3*(d - 1)*(d + 1)**2*(d + 3)
Suppose -2*p**4 - 3*p**3 + p**3 + 2*p**5 + 6*p**4 - 4*p**2 + 0*p**3 = 0. Calculate p.
-2, -1, 0, 1
Let i(c) be the third derivative of 0 + 0*c + 1/165*c**5 - 3*c**2 - 1/660*c**6 + 0*c**3 - 1/132*c**4. Factor i(u).
-2*u*(u - 1)**2/11
Let o = 63 - 313/5. Factor 0*t**3 + 2/5*t + 4/5*t**4 - 4/5*t**2 + 0 - o*t**5.
-2*t*(t - 1)**3*(t + 1)/5
Let f = 57 + -55. Let y(u) be the third derivative of 0 + 1/180*u**5 - 2*u**f - 1/360*u**6 + 0*u + 0*u**4 + 0*u**3. Factor y(h).
-h**2*(h - 1)/3
Let a be 0 - 1 - (-8)/4. Let g be (0 + 1)*(1 + a). Factor -2 - t - t**3 + 2*t + 4*t**2 - g*t**2.
-(t - 2)*(t - 1)*(t + 1)
Let a be 45/(-5)*2/(-3). Let h be (a/(-4))/((-15)/4). Factor 2/5 - h*i + 2/5*i**3 - 2/5*i**2.
2*(i - 1)**2*(i + 1)/5
Let x(h) be the third derivative of -h**5/60 + h**4/24 + 3*h**2. What is l in x(l) = 0?
0, 1
Let x be 4/10 - 2/5. Factor 2*d**3 + x*d - 6*d**2 + 5*d**4 - 4*d + d**4 + 2*d**3.
2*d*(d - 1)*(d + 1)*(3*d + 2)
Let i(b) = b**3 - b**2 - 4*b. Let p be i(3). Suppose 3*c = 5*c + w, w = -5*c + p. Factor 0 + 0*f**c + 0*f + 2/7*f**4 - 2/7*f**3.
2*f**3*(f - 1)/7
Let z(m) be the first derivative of m**6/1080 + m**5/180 + m**4/72 + 5*m**3/3 - 2. Let a(s) be the third derivative of z(s). Factor a(h).
(h + 1)**2/3
Determine q so that 6/5*q**2 - 4/5*q + 0 + 4/5*q**3 - 6/5*q**4 = 0.
-1, 0, 2/3, 1
Let k(w) be the second derivative of -w**9/10584 + w**8/5880 + w**7/2940 - w**6/1260 - w**3/3 + 6*w. Let n(o) be the second derivative of k(o). Factor n(z).
-2*z**2*(z - 1)**2*(z + 1)/7
Let d be (-6)/33 + 10/55. Let v(x) be the first derivative of 0*x + d*x**2 + 1/4*x**4 + 2 + 1/12*x**6 - 1/12*x**3 - 1/4*x**5. Factor v(m).
m**2*(m - 1)**2*(2*m - 1)/4
Suppose -12*f + 8 = -11*f. Let l be ((-2)/3)/(f/(-6)). Factor -1/2*b**5 + 0*b**2 + b**3 + 0 + 0*b**4 - l*b.
-b*(b - 1)**2*(b + 1)**2/2
Let k(v) be the third derivative of -v**5/40 + v**4/2 - 4*v**3 - 10*v**2. Factor k(o).
-3*(o - 4)**2/2
Let f(i) be the first derivative of 8/5*i**5 + 3/2*i**4 - 10/3*i**3 - 3*i**2 + 2*i + 4. Factor f(b).
2*(b - 1)*(b + 1)**2*(4*b - 1)
Let r(a) be the second derivative of -a**2 - 1/30*a**5 + 0*a**3 + 1/105*a**7 + 0*a**4 + 0*a**6 - 2*a + 0. Let o(w) be the first derivative of r(w). Factor o(b).
2*b**2*(b - 1)*(b + 1)
Let q = 21 - 12. Let d = q + -4. Determine n so that -3/2*n**4 + n**2 + 1/2 + n**3 - 3/2*n + 1/2*n**d = 0.
-1, 1
Let t(p) be the first derivative of p**6/2 - 3*p**4/4 - 22. Factor t(i).
3*i**3*(i - 1)*(i + 1)
Let h be 2/(-4) + (-10)/(-4). Let n(y) = -y**2 + y + 2. Let c be n(h). Factor 1/3*i**4 + 0*i - 1/3*i**2 + c - 1/3*i**3 + 1/3*i**5.
i**2*(i - 1)*(i + 1)**2/3
Let x(i) be the third derivative of 0 + 0*i + 0*i**4 + 1/30*i**5 - i**2 - 1/60*i**6 + 0*i**3. Factor x(t).
-2*t**2*(t - 1)
Let j be 7/(-14) + 10*1/4. Factor -2/3 + 4/3*z**j + 0*z - 2/3*z**4 + 0*z**3.
-2*(z - 1)**2*(z + 1)**2/3
Let z(d) = -d**2 - 7*d + 5. Let a be z(-7). Suppose -5*j + c = -11, a*c + 0*c + 5 = 0. Solve -14*x**4 + x**5 - 16*x**3 + 0*x**5 - 4*x**2 + 4*x + j - 5*x**5 = 0.
-1, 1/2
Let f be (-1 - -9)*(-1)/(-2). Factor 2*s**3 + 0*s**3 + 4*s**2 - f*s**2 + 2*s**2.
2*s**2*(s + 1)
Let j be 3/(((-8)/6)/(-4)). Let a be -1 - (-6)/j - -2. Factor -2/3 + 7/3*b**4 + 3*b - 3*b**3 - a*b**2.
(b - 1)**2*(b + 1)*(7*b - 2)/3
Let w(u) be the second derivative of -u**7/8820 + u**5/420 + 5*u**4/12 + u. Let a(b) be the third derivative of w(b). Factor a(h).
-2*(h - 1)*(h + 1)/7
Let a(h) = -6. Let m(l) = -1. Let w(r) = -a(r) + 5*m(r). Let c(v) = v**2 - v + 1. Let z(k) = 2*c(k) - 6*w(k). Find p such that z(p) = 0.
-1, 2
Let h(j) be the second derivative of 1/8*j**4 - 1/20*j**5 + 4*j + 0 + 1/2*j**2 + j**3. Let q(p) be the first derivative of h(p). Factor q(f).
-3*(f - 2)*(f + 1)
Determine p, given that 10*p**2 + 15/2 - 65/2*p = 0.
1/4, 3
Let r(k) = -9*k**4 - 5*k**3 - k**2 + 7*k - 3. Let j(g) = -19*g**4 - 9*g**3 - 3*g**2 + 15*g - 7. Let o(u) = 6*j(u) - 14*r(u). Factor o(y).
4*y*(y + 1)**2*(3*y - 2)
Let o(a) be the second derivative of a**7/63 - 4*a**6/45 + a**5/6 - a**4/9 - 11*a. Determine c so that o(c) = 0.
0, 1, 2
Let m(g) be the third derivative of g**5/330 + g**4/33 - 27*g**2. Solve m(n) = 0.
-4, 0
Let b(d) be the third derivative of d**8/20160 - d**7/7560 - d**6/2160 + d**5/360 + d**4/12 + 2*d**2. Let q(s) be the second derivative of b(s). Factor q(v).
(v - 1)**2*(v + 1)/3
Let i(j) be the third derivative of 2*j**7/105 - 2*j**6/15 + j**5/5 + 2*j**4/3 - 8*j**3/3 - 26*j**2. Find q, given that i(q) = 0.
-1, 1, 2
Let 0 + 3/5*g**3 - 4/5*g**2 - 4/5*g + 1/5*g**5 + 4/5*g**4 = 0. Calculate g.
-2, -1, 0, 1
Let l(q) be the second derivative of 19/70*q**5 + 1/15*q**6 + 0 + 16/21*q**3 + 4/7*q**2 + 25/42*q**4 - 3*q + 1/147*q**7. What is u in l(u) = 0?
-2, -1
Let t(o) be the first derivative of -o**4/3 + o**3/3 + o**2/6 - 25. Factor t(x).
-x*(x - 1)*(4*x + 1)/3
Let r = 1/4 - -5/12. Factor -4/3*m**2 + 0*m - r*m**3 + 2/3*m**4 + 0.
2*m**2*(m - 2)*(m + 1)/3
Let q(z) = 5*z**5 + 2*z**4 + z**3 - 4. Let h(t) = -39*t**5 - 15*t**4 - 9*t**3 + 33. Suppose -3*k - 163 = -64. Let m(r) = k*q(r) - 4*h(r). What is v in m(v) = 0?
-1, 0, 1/3
Let n(z) = 3*z**2 - 19*z - 7. Let o(l) = -4*l + 2*l**2 + 9 - 5 + 14*l - 4*l**2. Let f(x) = 4*n(x) + 7*o(x). Solve f(s) = 0.
-3, 0
Let j(b) be the second derivative of -b**4/60 + b**3/5 - 2*b. Factor j(t).
-t*(t - 6)/5
Let w(h) be the first derivative of h**6/30 + h**5/10 - h**3/3 - h**2/2 - h - 3. Let i(f) be the first derivative of w(f). Find y such that i(y) = 0.
-1, 1
Let j(u) be the first derivative of -2*u**3 - 8*u**2 - 32*u/3 - 9. Factor j(c).
-2*(3*c + 4)**2/3
Let m(j) be the third derivative of j**6/15 + 3*j**5/10 + j**4/2 + j**3/3 + j**2 + 3*j. Suppose m(s) = 0. What is s?
-1, -1/4
Let z(x) = -x + 13. Let k be z(11). Let j be ((-80)/108*-3)/k. Solve 0 + 14/9*n**3 - j*n**2 - 4/9*n = 0 for n.
-2/7, 0, 1
Let y(b) be the second derivative of b**4/108 - 7*b**3/18 - 64*b. Factor y(v).
v*(v - 21)/9
Let x(v) = -2*v - 11. Let s be x(-7). What is t in t**s - 6 - 5*t**3 + 2 + 4*t**2 + 4*t = 0?
-1, 1
Let z(p) be the second derivative of 3*p + 0 - 49/6*p**4 - 4*p**2 + 28/3*p**3. Factor z(a).
-2*(7*a - 2)**2
Let z(j) = -6*j**2 - 6*j + 6. Let u = -153 + 90. Let o be 18/u + (-16)/(-7). Let d(y) = 7*y**2 + 5*y - 6. Let q(b) = o*z(b) + 3*d(b). Factor q(x).
3*(x + 1)*(3*x - 2)
Let f(b) be the third derivative of -b**7/60 + b**6/120 + 7*b**5/120 - b**4/24 - 19*b**2. Determine z, given that f(z) = 0.
-1, 0, 2/7, 1
Let c(g) = -g**3 + 6*g**2 - 5*g + 2. Let s be c(5). Suppose 0 = -3*o + 6*o. Factor o*w - 1/3 + 1/3*w**s.
(w - 1)*(w + 1)/3
Let i(g) be the second derivative of 1/16*g**4 - 1/6*g**3 + 1/8*g**2 - g + 0. Determine z, given that i(z) = 0.
1/3, 1
