(q) be the third derivative of q**6/8 + 5*q**5/3 + 65*q**4/8 + 15*q**3 - 164*q**2. Find i, given that w(i) = 0.
-3, -2/3
Solve 1/7*s**2 + 117/7*s + 0 = 0 for s.
-117, 0
Let q(u) = -80*u + 643. Let v be q(8). Let o(y) be the third derivative of 5*y**2 + 0*y**v - 1/150*y**5 + 0*y + 1/60*y**4 + 0. Find k, given that o(k) = 0.
0, 1
Let n(w) be the second derivative of -w**4/36 + 34*w**3/9 - 67*w**2/6 - 27*w. Factor n(h).
-(h - 67)*(h - 1)/3
Let g(o) be the first derivative of -o + 0*o**2 + 14 + 1/12*o**3. Let g(u) = 0. Calculate u.
-2, 2
Let o be (-1)/((-84)/344) - 4. Let r(k) be the first derivative of 2/7*k - 2 + o*k**3 + 2/7*k**2. Suppose r(y) = 0. What is y?
-1
Let s = 2 - -62. Let w = s - 38. Let 4*m**2 + 24*m - 3 - 8 + 6*m**3 + 3 - w*m**2 = 0. What is m?
2/3, 1, 2
Let i(d) be the second derivative of -d**8/192 - d**7/56 + d**6/12 + d**5/6 - 2*d**4/3 + 13*d. Let z(h) be the third derivative of i(h). Solve z(n) = 0.
-2, -2/7, 1
Let l(k) be the first derivative of k**6/40 + k**5/15 - 5*k**4/24 - k**3/3 - 12*k**2 - 3. Let v(i) be the second derivative of l(i). Factor v(b).
(b - 1)*(b + 2)*(3*b + 1)
Suppose 648*r + 225 = 1964 + 1501. Factor 0*s + 4/3*s**4 - 16/3*s**2 - 8/3*s**3 + 0 + 2/3*s**r.
2*s**2*(s - 2)*(s + 2)**2/3
Let j(y) = y**3 + y**2 + y - 1. Suppose -8*l = -13*l + 110. Let u(g) = 16*g + 5*g**2 - 12 + l*g**2 - 9*g**2 + 14*g**3. Let k(r) = 12*j(r) - u(r). Factor k(o).
-2*o*(o + 1)*(o + 2)
Let r = 13 + -12. Suppose 0 = -5*n - j + 7, -n + 4*j + 13 = -r. Factor -n*w - 8*w**2 + 12*w**3 - 2*w - 3 + 3.
4*w*(w - 1)*(3*w + 1)
Suppose -98/5 - 2/5*r**2 + 28/5*r = 0. Calculate r.
7
Let y(p) = -321*p - 3. Let r be y(-3). Suppose -84 - 604*g**3 + 37 - 36*g**5 - 11*g**2 - 97 + 372*g**4 - r*g - 1817*g**2 = 0. What is g?
-1, -1/3, 6
Let q(z) be the third derivative of -z**7/105 + z**6/15 - z**5/10 - z**4/3 + 4*z**3/3 + 61*z**2 - 1. What is g in q(g) = 0?
-1, 1, 2
What is z in 9*z + 51/2*z**2 + 3/4*z**5 - 21/4*z**3 - 54 - 3*z**4 = 0?
-2, 2, 3
Let b(q) be the first derivative of 12*q - 17 - 3/5*q**5 - 6*q**2 - 3*q**3 + 3*q**4. Factor b(a).
-3*(a - 2)**2*(a - 1)*(a + 1)
Let u(a) = -24*a**3 + 26*a**2 - 61*a + 40. Let r(n) = 10*n**3 - 13*n**2 + 30*n - 20. Let g(l) = 10*r(l) + 4*u(l). Suppose g(v) = 0. What is v?
2, 5/2
Let y(v) be the first derivative of 0*v + 16/27*v**3 + 1/9*v**2 - 5. Find b such that y(b) = 0.
-1/8, 0
Find x, given that -32/3*x + 0 + x**4 - 43/3*x**3 - 26*x**2 = 0.
-1, -2/3, 0, 16
Let -28/5*g**2 - 36/5*g**3 + 0 - 4/5*g**5 - 8/5*g - 4*g**4 = 0. What is g?
-2, -1, 0
Let k(b) be the third derivative of 1/1365*b**7 + 1/156*b**4 + 0*b + 0 + 0*b**3 + 1/260*b**6 + 1/130*b**5 + 15*b**2. Solve k(z) = 0.
-1, 0
Factor 53*m - 180 + 22*m - 34*m + 51*m + 83*m + 5*m**2.
5*(m - 1)*(m + 36)
Let o(p) be the first derivative of p**6/40 + p**5/20 - 5*p**2 - 19. Let t(v) be the second derivative of o(v). Factor t(w).
3*w**2*(w + 1)
Let o(n) = -n**4 - n**2 + 1. Suppose -4*j + 84 = 3*l, -l - 4*l = 0. Let u(r) = 8*r**4 - 9*r**3 + 34*r**2 - 27*r - 7. Let c(d) = j*o(d) + 3*u(d). Factor c(q).
3*q*(q - 3)**3
Let y(a) be the first derivative of 19 + 3*a**3 - 63/2*a**2 - 3/28*a**4 + 147*a. Factor y(c).
-3*(c - 7)**3/7
Let p(q) be the second derivative of 0*q**3 - 1/9*q**4 + 0 + 0*q**2 + 1/30*q**5 - 8*q + 1/45*q**6. Solve p(j) = 0 for j.
-2, 0, 1
Factor 3/8*f**2 + 9/4 + 15/8*f.
3*(f + 2)*(f + 3)/8
Suppose -27*b + 3*b**2 + 0*b**3 + 30*b**3 + 31*b**3 - 34*b**3 - 3*b**4 = 0. Calculate b.
-1, 0, 1, 9
Let s(w) be the first derivative of -1/12*w**4 - 25 - 1/15*w**5 + 4/9*w**3 + 0*w + 2/3*w**2. Factor s(o).
-o*(o - 2)*(o + 1)*(o + 2)/3
Let c = -39 - -23. Let j be (16/10)/(-4) + c/(-15). Find r such that 2/3*r**2 + j*r + 0 = 0.
-1, 0
Let y be (-5 + 4)*-1 - -3. Factor 9*t - 3*t + 0*t + y*t**2 - 3*t**2 + 9.
(t + 3)**2
Let t(b) be the first derivative of -b**6/15 - 8*b**5/25 - 3*b**4/10 + 8*b**3/15 + 4*b**2/5 + 55. Suppose t(q) = 0. Calculate q.
-2, -1, 0, 1
Let g(l) be the second derivative of -l**6/15 - 13*l**5/10 - 11*l**4/3 - 98*l - 2. What is s in g(s) = 0?
-11, -2, 0
Factor -3/2*u**2 + 15/2*u - 9.
-3*(u - 3)*(u - 2)/2
Let j(s) be the third derivative of -s**5/60 - 55*s**4/24 - s**2 - 92*s. Factor j(i).
-i*(i + 55)
Let a(j) = j**3 - j + 2. Let q(g) = -2*g**3 + g**2 - 14*g + 9. Let t(w) = -3*a(w) - q(w). Suppose t(n) = 0. What is n?
-5, 1, 3
Let w(p) be the third derivative of -p**4/24 - p**3/3 - 3*p**2. Let y be w(-7). Factor -9*x**2 + 3*x**4 + x**3 - 15*x - 1 + 2*x**3 - y.
3*(x - 2)*(x + 1)**3
Suppose -292*c + 876 = 292. Factor 4/13*g + 2/13*g**c + 0.
2*g*(g + 2)/13
Let x(a) be the first derivative of 2*a**3/3 + 54*a**2 - 110*a + 158. Factor x(q).
2*(q - 1)*(q + 55)
Suppose 2*s + 2*s = -7*s. Factor 0 + h**4 - 1/2*h**2 + s*h + 1/2*h**3.
h**2*(h + 1)*(2*h - 1)/2
Suppose 19*h - 140 = -7. Let b be ((-2)/42)/(h/(-84)). Factor 2/7*m**5 + 8/7*m**3 - 8/7*m**4 + b*m**2 + 4/7 - 10/7*m.
2*(m - 2)*(m - 1)**3*(m + 1)/7
Suppose -3*m + 12 = 2*n - m, -5*n + 9 = -2*m. Let o(l) be the first derivative of -1/18*l**4 + 2/27*l**n + 7 + 0*l**2 + 0*l. Factor o(y).
-2*y**2*(y - 1)/9
Let m = -446 - -2234/5. Solve 0 - m*p**2 - 4/5*p = 0 for p.
-1, 0
Let z be (5/(90/24) - 1)*20/5. What is u in 22/9*u - 2/9*u**3 + 8/9*u**2 + z = 0?
-1, 6
Let y(t) be the third derivative of t**5/20 + 41*t**4/4 + 1681*t**3/2 + 170*t**2. Factor y(c).
3*(c + 41)**2
Suppose 0 = -9*r + 5*r - 72. Let m = 22 + r. What is w in m*w**4 + 5*w**2 - 3*w**4 + 2*w**4 - 6*w**3 - 2*w**2 = 0?
0, 1
Suppose 3*i = -4*i. Let w(r) be the first derivative of i*r + 6 - 5/3*r**3 + r**2 + r**4 - 1/5*r**5. Factor w(j).
-j*(j - 2)*(j - 1)**2
Let w(q) be the first derivative of -2*q - 3/2*q**2 + 0*q**5 - 8 + 2/3*q**3 - 1/6*q**6 + q**4. Find p such that w(p) = 0.
-1, 1, 2
Let a(m) be the second derivative of -1/3*m**4 + 12*m**2 + 2/3*m**3 + 30*m + 0. Factor a(p).
-4*(p - 3)*(p + 2)
Let l(s) be the second derivative of -3/2*s**2 - 1/4*s**4 - 41*s - s**3 - 2. Factor l(m).
-3*(m + 1)**2
Let b(x) be the first derivative of x**4/3 + 13*x**3/9 + x**2/2 - 88. Factor b(f).
f*(f + 3)*(4*f + 1)/3
Let d = -164 - -171. Let v be ((-56)/(-26))/d*4. Determine b, given that 32/13 + 2/13*b**2 - v*b = 0.
4
Let z(k) be the first derivative of -1/3*k**3 - 8 - 6*k + 1/24*k**4 + k**2. Let q(o) be the first derivative of z(o). Factor q(l).
(l - 2)**2/2
Let r be 7 + -11 + 7 + 2. Let v(m) = 13*m**2 + 3*m - 21. Let u(c) = 20*c**2 + 4*c - 32. Let g(n) = r*u(n) - 8*v(n). Let g(x) = 0. Calculate x.
-2, 1
Suppose -9 = -3*n + 15*c - 11*c, -n = c - 3. Let w(f) be the first derivative of 0*f + 1/4*f**4 + 4/9*f**n - 1 + 1/6*f**2. Factor w(s).
s*(s + 1)*(3*s + 1)/3
Let g(z) be the second derivative of -1/36*z**4 + 0*z**3 + 1/6*z**2 + 21*z + 0. Factor g(h).
-(h - 1)*(h + 1)/3
Let p(w) be the second derivative of -32/45*w**6 + 0*w**3 - 2/9*w**4 + 2/9*w**7 + 11/15*w**5 + 11*w + 0*w**2 + 0. Find o, given that p(o) = 0.
0, 2/7, 1
Suppose -m = 2*m - 3, -5*a - 4*m + 4 = 0. Suppose -3*o + 24 + 72 = a. Suppose 0*d - 4*d - 36*d**2 + o*d**2 = 0. What is d?
-1, 0
Find n, given that 18*n - 28*n + 20*n + 18*n + n**2 + 3*n**2 = 0.
-7, 0
Let p = 5 - 3. Let z be (20/12 - p)*-21. Let 6*s**3 - 3*s**2 + 2*s**2 - z*s + 4*s**2 - 3*s**4 + s = 0. Calculate s.
-1, 0, 1, 2
Let c(w) = 9*w**3 + 5*w. Let v(h) = -1 + 10*h**3 + 1 + 6*h. Suppose 38 = 5*i + 2*k, i + 5*k = -i + 32. Let u(f) = i*c(f) - 5*v(f). Find b such that u(b) = 0.
0
Let u(c) = 9*c**4 + 2*c**3 - 5*c**2 + 2. Let r(m) = 47*m**4 + 11*m**3 - 25*m**2 + 11. Let a(f) = 2*r(f) - 11*u(f). Factor a(w).
-5*w**2*(w - 1)*(w + 1)
Let z = 973/12 + -81. Let y(m) be the second derivative of 1/42*m**7 + 3*m - 1/30*m**6 + 0*m**2 + 0*m**3 - 1/20*m**5 + 0 + z*m**4. Factor y(j).
j**2*(j - 1)**2*(j + 1)
Let s(a) be the first derivative of -a**3/12 - 3*a**2/8 + 5*a/2 - 19. Factor s(n).
-(n - 2)*(n + 5)/4
Let w(g) be the second derivative of 0 - 3/20*g**5 + 0*g**2 + 0*g**3 + 37*g - 1/4*g**4. Suppose w(s) = 0. Calculate s.
-1, 0
Suppose 3*f + 5*o + 3 = 5*f, -o = -5. Suppose f = 7*n - 0*n. Solve -1/6*x**n + 0 - 1/6*x**3 + 0*x = 0 for x.
-1, 0
Let m be (30/(-25))/(8/(-20)). Let c(f) be the second derivative of 0 + 0*f**2 + 49/10*f**6 + 21/5*f**5 - 3*f + 0*f**m + f**4. Factor c(v).
3*v**2*(7*v + 2)**2
Suppose -22 + 57 = 7*w. Factor -1/8*t**3 - 1/2*t**w + 0*t + 0 + 5/8*t