2 - 24*y + 19. Let m(w) be the first derivative of x(w). Factor m(j).
-4*(j - 3)*(j + 1)**2
Let s(v) = 3*v**5 - 23*v**4 - 5*v**3 + 23*v**2 + 2*v + 2. Let h(r) = -12*r**5 + 93*r**4 + 21*r**3 - 93*r**2 - 9*r - 9. Let n(p) = 2*h(p) + 9*s(p). Factor n(f).
3*f**2*(f - 7)*(f - 1)*(f + 1)
Determine g so that 19/8*g**2 + 9/8 + 3/8*g**3 + 33/8*g = 0.
-3, -1/3
Let w(i) be the third derivative of i**6/120 + i**5/40 - 11*i**3/6 + 8*i**2. Let k(v) be the first derivative of w(v). Factor k(u).
3*u*(u + 1)
Suppose -57 = -2*x - 7. Let c be 50/x*(-4)/(-10). Factor 0*w + 6/5*w**3 - c*w**2 + 0 - 2/5*w**4.
-2*w**2*(w - 2)*(w - 1)/5
Let v(y) = -y**3 + 4*y**2 + 5*y - 4. Let m be v(4). What is k in 2 + 4 - 18*k**2 - 9*k**5 + 12*k**4 - 19*k + 0 + m*k + 12*k**3 = 0?
-1, -2/3, 1
Let z(j) be the first derivative of -2*j**3/21 - 4*j**2/7 - 6*j/7 + 81. Factor z(t).
-2*(t + 1)*(t + 3)/7
Let f(n) be the second derivative of -n**6/60 + 41*n**5/40 + 7*n**4/4 + 292*n + 2. Factor f(y).
-y**2*(y - 42)*(y + 1)/2
Let h(k) be the third derivative of -k**6/200 + k**5/75 + k**4/24 - k**3/15 + 27*k**2 + 2. Solve h(w) = 0 for w.
-1, 1/3, 2
What is u in 0 - u**4 + 21/2*u**3 + 19*u**2 - 12*u = 0?
-2, 0, 1/2, 12
Let q = -116 - -243. Let j = q + -632/5. Factor 2/5*c**3 + j*c**2 - 3/5*c**4 - 2/5*c + 0.
-c*(c - 1)*(c + 1)*(3*c - 2)/5
Let y(k) = 3*k**2 + 4. Let d(r) = r**2 + 1. Suppose -7*a = -13*a - 42. Let t(x) = a*d(x) + 2*y(x). Let t(v) = 0. Calculate v.
-1, 1
Let z(l) be the third derivative of -l**7/1008 + l**6/144 + l**5/16 + 5*l**4/12 + 9*l**2. Let m(b) be the second derivative of z(b). Factor m(o).
-5*(o - 3)*(o + 1)/2
Let s(n) = -6*n**2 - 41*n + 462. Let j be s(6). Factor j*l**2 + 0*l**3 + 0*l + 0 + 2/15*l**4.
2*l**4/15
Solve 20/3*f - f**2 + 7/3 = 0 for f.
-1/3, 7
Let p(b) be the second derivative of b**7/168 - b**5/40 + b**3/24 + 7*b + 2. Factor p(f).
f*(f - 1)**2*(f + 1)**2/4
Solve -21/2*y**3 + 3/8*y**4 - 177/8*y**2 - 45/4*y + 0 = 0.
-1, 0, 30
Let d be (-4)/16*(8 - 8). Let o(b) be the second derivative of -4/3*b**2 + d + b + 2*b**3 - 5/12*b**5 - 5/6*b**4. Let o(a) = 0. What is a?
-2, 2/5
Let z(q) be the third derivative of -q**5/135 + 16*q**4/27 - 40*q**3/9 + 7*q**2 + 2. Let z(n) = 0. Calculate n.
2, 30
Let i(q) be the first derivative of -1/12*q**3 + 0*q**2 + 0*q + 0*q**4 + 1/20*q**5 - 20. Factor i(z).
z**2*(z - 1)*(z + 1)/4
Let b be (-5)/(-20) - (1001/(-140) + 7). Determine d so that -4/5*d - 2/5*d**4 - b*d**5 + 2/5*d**2 + 6/5*d**3 + 0 = 0.
-2, -1, 0, 1
Let d(i) = 4*i**2 + i - 2*i**2 - i**2. Let v(m) be the second derivative of m**4/4 + m**3/3 - 4*m. Let b(j) = 5*d(j) - 2*v(j). Let b(p) = 0. What is p?
0, 1
Let x(o) be the first derivative of o**4/24 + 10*o**3/9 + 77*o**2/12 - 121*o/3 - 63. Factor x(i).
(i - 2)*(i + 11)**2/6
Let i(q) be the second derivative of -q**7/21 + q**6/15 + 6*q**5/5 + 2*q**4/3 - 16*q**3/3 - 120*q - 1. Determine m, given that i(m) = 0.
-2, 0, 1, 4
Let a(v) be the first derivative of v**5/5 - 10*v**4 + 148*v**3/3 - 72*v**2 - 423. Find n, given that a(n) = 0.
0, 2, 36
Let x(v) be the second derivative of v**6/6 + 2*v**5 - 75*v**4/4 + 30*v**3 + 156*v + 1. Let x(b) = 0. Calculate b.
-12, 0, 1, 3
Solve -32/7*w**2 - 1/7*w**5 - 192/7*w + 36/7*w**3 + 0 + 0*w**4 = 0 for w.
-6, -2, 0, 4
Suppose -z + 129 = 5*s, -2*z - 3*s - s + 246 = 0. Factor -g**2 - z*g + 6*g**2 - 10 + 114*g.
5*(g - 2)*(g + 1)
Let n(u) be the first derivative of u**8/336 - u**7/56 + u**5/6 + 22*u**3/3 + 42. Let i(h) be the third derivative of n(h). Factor i(v).
5*v*(v - 2)**2*(v + 1)
Suppose 2*m + 5*o - 5 = 0, 37*m + 4*o - 4 = 33*m. Factor m - 8/9*h**2 + 2/9*h**3 + 0*h.
2*h**2*(h - 4)/9
Let p(s) be the first derivative of 0*s**2 - 1/60*s**4 - 2 + 1/15*s**3 - s. Let f(a) be the first derivative of p(a). Suppose f(w) = 0. Calculate w.
0, 2
Let c = -662/7 + 95. Determine o, given that -12/7*o + 12/7 + c*o**2 = 0.
2
Solve -u - 11*u + 23*u - 4*u**2 + u + 16 = 0.
-1, 4
Suppose 0*d = -3*a + 2*d + 10, 15 = -3*d. Let i be 442/(-104) + (a - -5). Factor -3/2 + 3/4*p + 3/2*p**2 - i*p**3.
-3*(p - 2)*(p - 1)*(p + 1)/4
Suppose 5*m + 2 + 0 = 4*z, 0 = -2*m + 4*z - 8. Suppose -7 = m*s - 8*p + 3*p, 0 = -3*s + 3*p + 3. Factor -u**2 + 4*u**4 + 3*u**3 - 3*u**s + 3*u**2.
u**2*(u + 1)*(u + 2)
Suppose -5*l - 3*p - p + 8 = 0, -l + 5*p = 10. Determine d, given that 7/6*d**2 + 1/3*d + l + 5/6*d**3 = 0.
-1, -2/5, 0
Let s(w) be the first derivative of 1/9*w**3 + 5/6*w**2 + 4/3*w + 16. Find d, given that s(d) = 0.
-4, -1
Let w(q) = 2*q - 47. Let k be w(26). Let x be 4/k + (-93)/(-15). Let x*o**4 - 2*o - 2*o**5 + 1/4 + 25/4*o**2 - 19/2*o**3 = 0. What is o?
1/2, 1
Factor 405*l**3 - 635*l - 1800*l**2 - 80 + 653*l + 722*l.
5*(l - 4)*(9*l - 2)**2
Let v = -20 + -14. Let b = 39 + v. Solve -s**b + 0 - 1/2*s**3 + 3/2*s**4 + 0*s + 0*s**2 = 0.
0, 1/2, 1
Let t(o) = -o + 8. Let n be t(-7). Suppose -10*j = -n*j. Let -4/3*f - 16/3*f**2 + j - 4*f**3 = 0. What is f?
-1, -1/3, 0
Let w(t) be the first derivative of t**3/3 - 5*t**2 + 25*t - 126. Suppose w(a) = 0. Calculate a.
5
Suppose 0*h**4 + 0*h**2 - 2/7*h**5 - 2/7*h + 0 + 4/7*h**3 = 0. Calculate h.
-1, 0, 1
Let o(w) = -13*w**4 + 15*w**3 + 10*w**2 - 15*w - 12. Let n(b) = 5*b**4 - 7*b**3 - 5*b**2 + 7*b + 6. Let h(s) = -10*n(s) - 4*o(s). Suppose h(k) = 0. Calculate k.
-3, -2, -1, 1
Let l be (11/3)/(8/240*55). Solve 2/5*v**3 + 64/5 + 4*v**l + 64/5*v = 0.
-4, -2
Let y(n) = 7*n**2 + 25*n - 1 - 2 - 15*n + 6. Let o(q) = 8*q**2 + 10*q + 2. Let a(z) = -2*o(z) + 3*y(z). Let a(g) = 0. Calculate g.
-1
Let w(o) be the third derivative of 0*o + 16*o**2 + 1/36*o**4 + 0 + 1/45*o**5 - 1/9*o**3. Factor w(r).
2*(r + 1)*(2*r - 1)/3
Let o be 0 - 0*(-1 - 0). Let k be (-68 + 64)/(2 - 3). Factor 0 + 0*q**2 + o*q + 0*q**3 - 2/5*q**k.
-2*q**4/5
Let u(n) be the second derivative of -11/60*n**6 + 4*n - 1/28*n**7 + 7/24*n**4 + n**3 + n**2 + 0 - 9/40*n**5. Solve u(o) = 0.
-2, -1, -2/3, 1
Let g = 4708 - 108282/23. Factor -g*p**2 + 0 - 10/23*p.
-2*p*(p + 5)/23
Let i be (-1)/8 + 3/((-24)/71). Let b(l) = -l**2 - 11*l - 16. Let y be b(i). Factor 7/3*r**y + r**3 + 1/3 + 5/3*r.
(r + 1)**2*(3*r + 1)/3
Let n(u) be the second derivative of -1/132*u**4 - 1/22*u**2 + 39*u + 0 - 1/33*u**3. Find c, given that n(c) = 0.
-1
Let v(d) = d**2 - 3. Let k be v(3). Suppose -k = -2*m + 4. Factor 2*y**5 - 8*y**3 + 10*y**3 - y**m - 3*y**5.
-2*y**3*(y - 1)*(y + 1)
Let m(r) be the third derivative of r**7/1344 + r**6/2880 - r**3 - 16*r**2. Let q(y) be the first derivative of m(y). Let q(p) = 0. Calculate p.
-1/5, 0
Let r = -6661 - -46630/7. Suppose 1/7*i**2 + r - 1/7*i**3 + 5/7*i = 0. Calculate i.
-1, 3
Let u be (-38)/(-8) - (175/20 - 9). Let n(k) be the second derivative of 0 + 0*k**3 + 0*k**2 - 2/105*k**7 + 0*k**u + 0*k**4 - k - 1/75*k**6. Factor n(a).
-2*a**4*(2*a + 1)/5
Let u(g) be the third derivative of 2/525*g**7 + 1/300*g**6 + 0*g**3 + g**2 + 0*g**4 + 0*g**5 + 1/840*g**8 + 0*g + 0. Let u(n) = 0. Calculate n.
-1, 0
Let q(r) be the second derivative of r**5/20 + 5*r**4/2 + 50*r**3 + 13*r**2 - 4*r. Let v(h) be the first derivative of q(h). Factor v(z).
3*(z + 10)**2
Let p(g) be the first derivative of -3/4*g**4 + 12 - 3*g - 9/2*g**2 - 3*g**3. Solve p(t) = 0.
-1
Let z(g) be the second derivative of 3*g**5/20 - 15*g**4/4 + 750*g**2 - 4*g - 34. Factor z(q).
3*(q - 10)**2*(q + 5)
Let q(y) be the first derivative of -y**6/180 - y**5/60 + 21*y - 42. Let p(l) be the first derivative of q(l). Factor p(g).
-g**3*(g + 2)/6
Let g(u) = -2*u**2 + 8*u - 4. Let j(p) = p**3 - p + 1. Let c(n) = 2*n**2 + 25*n + 10. Let v be c(-12). Let r(y) = v*j(y) + g(y). Factor r(x).
-2*(x - 1)**2*(x + 3)
Let j(d) = -3*d**2 + 2*d - 1. Let o(w) = -w**2 - w - 1. Let l(n) = j(n) - 4*o(n). Let h be l(-6). Factor -2*r**h - 2*r + r**3 + 3*r - 1 + r**2.
-(r - 1)**2*(r + 1)
Suppose 3*m + 18 = a, 28 = 3*a - 5*m - 6. Let v be ((-3)/9)/(2/(-12)). Factor -u**2 + a*u**v - 5*u**2.
-3*u**2
Let f(a) = a**2 + 5*a**2 - 7*a**2 + 2*a**2. Let m(w) = -4*w**2 + 1. Let h(k) = -6*f(k) - 2*m(k). Factor h(d).
2*(d - 1)*(d + 1)
Let v(x) be the third derivative of x**7/4200 - x**5/200 - x**4/60 + 17*x**3/3 + 15*x**2. Let l(w) be the first derivative of v(w). What is d in l(d) = 0?
-1, 2
Let l(c) be the first derivative of c**4/6 - 4*c**3/9 - 20*c**2/3 - 16*c + 30. Factor l(g).
2*(g - 6)*(g + 2)**2/3
