2*u**4/3 + 8*u**3/3 + 13*u**2. Determine z so that c(z) = 0.
-2
Let v(c) be the third derivative of -c**5/150 + c**4/30 - c**3/15 - 5*c**2. Factor v(o).
-2*(o - 1)**2/5
Suppose 2*d + 2*d = 0, 2*d = -4*c + 16. Let f(r) be the third derivative of -r**2 - 1/6*r**3 - 1/24*r**5 + 7/48*r**c + 0*r + 0. Solve f(a) = 0 for a.
2/5, 1
Let k(w) be the second derivative of w**7/63 - 4*w**6/45 + w**5/6 - w**4/9 - 51*w. Find p such that k(p) = 0.
0, 1, 2
Let u(j) be the second derivative of 1/8*j**3 + 0 - 3*j - 1/48*j**4 + 0*j**2. Factor u(o).
-o*(o - 3)/4
Let 20/3*t + 4*t**3 - 2 - 8*t**2 - 2/3*t**4 = 0. What is t?
1, 3
Let a(x) be the third derivative of x**7/4200 + x**6/900 - x**3/6 - 2*x**2. Let b(s) be the first derivative of a(s). Suppose b(g) = 0. What is g?
-2, 0
Let a(q) be the third derivative of 0 - 1/40*q**6 + 0*q + 2/105*q**7 - 1/336*q**8 + 0*q**3 - 1/15*q**5 - 3*q**2 + 1/6*q**4. Factor a(z).
-z*(z - 2)**2*(z - 1)*(z + 1)
Let m = 472 - 89. Let g = m - 1523/4. Factor -27/4 - g*h**2 - 1/4*h**3 - 27/4*h.
-(h + 3)**3/4
Let o(z) = z + 6. Let p be o(-5). Let r(w) = 4*w - 1. Let l be r(p). Factor -3*k + 6*k + l*k**2 - 4*k**2 - 2.
-(k - 2)*(k - 1)
Let w be 241/(-4) + 1/4. Let u be (-4)/10 + (-64)/w. Let -2/3*t**2 - 2/3*t**3 + u*t + 2/3 = 0. What is t?
-1, 1
Let z(o) be the third derivative of -o**7/210 + o**6/40 - o**5/20 + o**4/24 + 11*o**2. Factor z(u).
-u*(u - 1)**3
Let a(y) = -2*y**5 - y**4 + y**3 - 3*y**2 - 3*y. Let n(t) = 9*t**5 + 5*t**4 - 4*t**3 + 13*t**2 + 13*t. Let i(l) = 26*a(l) + 6*n(l). Factor i(j).
2*j**3*(j + 1)**2
Let z be -46 + 47 + (-6)/9*1. Let -z*b**2 - 1/6*b**5 + 1/2*b - 1/6 - 1/3*b**3 + 1/2*b**4 = 0. Calculate b.
-1, 1
Let z(c) = -20*c. Let d be z(-1). Suppose d = 8*s - 4*s. Factor 3 + 16*i**4 - 6*i**3 - 3*i + i**s + 8*i**5 - 18*i**2 - i**4.
3*(i - 1)*(i + 1)**3*(3*i - 1)
Let a(n) be the second derivative of -n**6/300 + n**5/100 + n**4/120 - n**3/30 + 11*n. Factor a(l).
-l*(l - 2)*(l - 1)*(l + 1)/10
Let b(d) = -2*d**2 + 6*d - 4. Let g(w) = 2*w**2 - 6*w + 4. Let c(n) = -4*b(n) - 3*g(n). Factor c(t).
2*(t - 2)*(t - 1)
Let w(p) be the second derivative of -p**4/8 + p**3/2 - 3*p**2/4 - 6*p. Suppose w(f) = 0. Calculate f.
1
Let j be 10/35 - (-40)/7. Let z = 9 - j. Let -3*t**z + 13*t**2 + 4 - 4*t**3 + t**4 + t**3 - 12*t = 0. Calculate t.
1, 2
Let h(d) be the first derivative of d**7/231 - 2*d**6/165 + d**4/33 - d**3/33 + 3*d + 1. Let c(r) be the first derivative of h(r). Suppose c(o) = 0. What is o?
-1, 0, 1
Let d = -23101 - -114387/5. Let i = -222 - d. Determine q so that -24/5*q + i - 14/5*q**2 = 0.
-2, 2/7
Let t(y) be the third derivative of y**6/40 + 7*y**5/20 - 17*y**4/8 + 9*y**3/2 - 8*y**2. Factor t(j).
3*(j - 1)**2*(j + 9)
Let j(w) be the first derivative of -w**6/15 + w**5/4 - 5*w**3/6 + w**2 + 5*w - 3. Let o(m) be the first derivative of j(m). Determine f so that o(f) = 0.
-1, 1/2, 1, 2
Let r = -1081/5 + 217. Factor 0 - 2/5*w**2 - 2/5*w**3 + r*w.
-2*w*(w - 1)*(w + 2)/5
Let t(w) = 186*w**5 - 266*w**4 + 138*w**3 - 33*w**2 + 2*w - 6. Let g(y) = y**5 - y**4 - y**3 + y**2 + 1. Let a(s) = -6*g(s) - t(s). Factor a(v).
-v*(3*v - 2)*(4*v - 1)**3
Let a(m) be the third derivative of -1/35*m**7 + 0 + 2/15*m**6 + 0*m - 7/30*m**5 + 1/6*m**4 + 0*m**3 + 2*m**2. Find d, given that a(d) = 0.
0, 2/3, 1
Factor 4*z + 4*z**2 + 24*z**3 + 8*z**2 - 19*z**3.
z*(z + 2)*(5*z + 2)
Let s be 6/(-10) - (-4036)/60. Let l(x) be the first derivative of s*x**3 + 49/2*x**6 - 16*x + 108*x**4 - 24*x**2 - 553/5*x**5 + 4. Let l(z) = 0. Calculate z.
-2/7, 1/3, 2
Let h be (4 - 2)*6/4. Let i(d) be the first derivative of -1/3*d**2 - 1/9*d**3 + 0*d - h. Determine l so that i(l) = 0.
-2, 0
Let q(s) = 36*s - 2. Let z be q(-9). Let o = z + 988/3. Solve -o*n**4 - 4/3*n**2 + 14/3*n**3 + 0 + 0*n = 0 for n.
0, 2/5, 1
Factor -1 - 9*z + 6 + 1 + 3*z**2.
3*(z - 2)*(z - 1)
Let m be -1 - 3/(6/(-10)). Suppose -2*b + 26 = 4*a, a - m*b = b - 21. Factor 1/3*c**2 + 3*c**a + 4/3*c**5 + 0 + 2*c**3 + 0*c.
c**2*(c + 1)**2*(4*c + 1)/3
Let k(m) be the third derivative of -1/30*m**5 - 1/180*m**6 - 1/3*m**3 + 0*m + 0*m**4 + 0 + m**2. Let h(a) be the first derivative of k(a). Factor h(u).
-2*u*(u + 2)
Let t be 6 + (-18)/24*6. Factor -o + 1/6*o**2 + t.
(o - 3)**2/6
Suppose -8/3*h + 1/3*h**2 + 16/3 = 0. What is h?
4
Let y be ((-26)/(-4) + -5)*(1 + 2). Suppose -y - 3*t + 3/2*t**2 = 0. What is t?
-1, 3
Let k be (-3332)/105 + (-2)/(-5). Let c = -31 - k. Determine f, given that -1/3 + c*f**3 + 1/3*f**2 - 1/3*f = 0.
-1, 1
Let h = 1904/5 + -380. Factor h*u + 6/5*u**5 - 22/5*u**4 - 18/5*u**2 + 0 + 6*u**3.
2*u*(u - 1)**3*(3*u - 2)/5
Let z(b) = b**3 - 4*b**2 - 4*b + 6. Let r be z(4). Let g be (r/6)/((-25)/30). Let -8/3 - 2/3*f**g + 8/3*f = 0. Calculate f.
2
Let j(c) be the first derivative of -c**4/22 - 2*c**3/11 - 3*c**2/11 - 2*c/11 + 15. Factor j(k).
-2*(k + 1)**3/11
Factor -n - 19*n + 2*n**2 + 57 - 7.
2*(n - 5)**2
Let q(i) be the second derivative of -5*i**5/14 - 5*i**4/6 - 11*i**3/21 - i**2/7 + 5*i. Suppose q(r) = 0. What is r?
-1, -1/5
Let j be 1/(-2)*198/(-27). Factor 2/3 + j*s**2 - 13/3*s.
(s - 1)*(11*s - 2)/3
Let c(z) = -10*z**2 + 65*z - 90. Let l(y) = 15*y**2 - 98*y + 135. Let s(g) = 8*c(g) + 5*l(g). Solve s(n) = 0 for n.
3
Let t(v) be the second derivative of 1/110*v**5 - 1/11*v**3 - 2*v + 0*v**2 - 1/33*v**4 + 0. Factor t(i).
2*i*(i - 3)*(i + 1)/11
Let b(p) be the second derivative of -p**2 + 2*p + 1/2*p**3 + 0 - 1/12*p**4. Factor b(n).
-(n - 2)*(n - 1)
Suppose 1 = 4*l - 15. Let x(r) be the second derivative of 2*r - 1/30*r**l + 1/5*r**2 + 0 + 0*r**3. Factor x(m).
-2*(m - 1)*(m + 1)/5
Let i(x) be the second derivative of x**7/126 - x**6/90 - x**5/30 + x**4/18 + x**3/18 - x**2/6 + 8*x. Factor i(a).
(a - 1)**3*(a + 1)**2/3
Suppose -5*m + 7 = 2*p + 5, -p + 1 = 0. Let d(v) = v**3 + 2*v**2 + v + 2. Let a be d(-2). Suppose a + m*j + 1/3*j**4 - 2/3*j**2 + 1/3*j**3 = 0. Calculate j.
-2, 0, 1
Suppose 2*n + 4*r = 4, -3*r = n - 0*r - 2. Solve 2/3*l**5 + 8/3*l**3 + 8/3*l**4 - 4/3 - 4/3*l**n - 10/3*l = 0.
-2, -1, 1
Let a(x) be the first derivative of 49*x**6/18 - 14*x**5/3 - x**4/4 + 20*x**3/9 + 2*x**2/3 - 14. Factor a(c).
c*(c - 1)**2*(7*c + 2)**2/3
Suppose -2*n + 134 - 864 = 0. Let h = 1473/4 + n. Let a**4 + 0 + 1/2*a + 11/4*a**2 + h*a**3 = 0. What is a?
-2, -1, -1/4, 0
Let x(f) be the third derivative of -f**2 + 0*f - 1/15*f**5 + 0*f**3 + 1/336*f**8 + 1/24*f**4 + 1/20*f**6 - 2/105*f**7 + 0. Factor x(j).
j*(j - 1)**4
Let y(w) = 0 - 9*w - 1 + 7*w - 7. Let x be y(-5). Factor -1/3*g**x - 5/3*g**4 + 2/3*g + 0 - 8/3*g**3.
-g*(g + 1)**2*(5*g - 2)/3
Suppose -11 - 13 = -4*g - 4*v, 0 = g + 5*v + 6. Suppose -g = -2*a + j - 2, -12 = -3*a + 2*j. Determine z so that -2/7*z + 0 - 2/7*z**a = 0.
-1, 0
Let t(w) be the third derivative of 0*w**4 + 0*w**5 + 0 + 1/210*w**7 + 2*w**2 + 0*w + 0*w**3 + 1/240*w**6 + 1/672*w**8. Find a such that t(a) = 0.
-1, 0
Suppose -2*y = -0*y - 32. Suppose -2*g + 40 = 4*k, 0*k + 4*k - 4*g - y = 0. Factor 8*m + 2*m**3 + 0 - k*m**2 + 0.
2*m*(m - 2)**2
Let x be 5 - 2 - (6 - 3). What is g in -g**2 + x*g**2 - 3 - 2 + 6 = 0?
-1, 1
Let i be (-20)/6 + 3/(3/4). Factor -o + 1/3*o**2 + i.
(o - 2)*(o - 1)/3
Let a(k) be the first derivative of 3 + 0 - 5 - k**3. Factor a(y).
-3*y**2
Let m(i) = -4*i**2 - 9*i - 7. Suppose 0 - 2 = -2*z. Let w(u) be the first derivative of u - 1. Let n(k) = z*m(k) + 5*w(k). Suppose n(r) = 0. Calculate r.
-2, -1/4
Let a(h) be the second derivative of -5*h + 2/25*h**6 + 0*h**2 + 0 + 0*h**3 + 2/15*h**4 - 1/5*h**5. Find l, given that a(l) = 0.
0, 2/3, 1
Let a(v) be the first derivative of v**8/5040 - v**6/540 + v**4/72 + 2*v**3 - 5. Let k(n) be the third derivative of a(n). Factor k(d).
(d - 1)**2*(d + 1)**2/3
Let p(r) be the second derivative of -2*r**7/21 + 7*r**6/15 - 9*r**5/10 + 5*r**4/6 - r**3/3 + 4*r. Suppose p(z) = 0. Calculate z.
0, 1/2, 1
Let u(o) = o**3 + 5*o**2 + 2*o + 13. Let m be u(-5). Factor 0 - 1/2*c**2 - 1/4*c - 1/4*c**m.
-c*(c + 1)**2/4
Let j(m) be the second derivative of m**7/147 + 4*m**6/105 + 2*m**5/35 - m**4/21 - 5*m**3/21 - 2*m**2/7 - 6*m. Factor j(y).
2*(y - 1)*(y + 1)**3*(y + 2)/7
Let x(n) = -3*n**2 + 20*n + 100. Let d(l) = 2*l**2 - 20*l - 100. Let b(q) = 4*d(q) + 3*x(q). Factor b(f).
-(f + 10)**2
Let c(a) be the first derivative of 7/2*a**2 - 1/5*a**5 - 2*a