**5/20 - 33*h**4/4 - 15*h**3/2 - 3*h**2 + 2*h - 4. Let q(x) be the first derivative of f(x). Factor q(v).
-3*(v + 1)**3*(9*v + 2)
Factor -8/9*u**2 + 0*u - 44/9*u**3 + 0 - 20/9*u**4.
-4*u**2*(u + 2)*(5*u + 1)/9
Let t = -18 + 24. Factor 0*m**2 + 6*m**2 + 2*m**2 - t*m**3 - 2*m.
-2*m*(m - 1)*(3*m - 1)
Let d(g) be the second derivative of 3*g**5 - 58*g**4/3 + 74*g**3/3 + 12*g**2 - 23*g. Determine s, given that d(s) = 0.
-2/15, 1, 3
Let p(j) be the third derivative of -j**6/360 - j**5/180 + j**4/72 + j**3/18 + 10*j**2. Factor p(v).
-(v - 1)*(v + 1)**2/3
Let c(p) = 7*p**2 - 3*p + p + 5*p - 3*p**2. Let n(y) = y**2 + y. Let t(r) = c(r) - 3*n(r). Determine d, given that t(d) = 0.
0
Suppose -10*k + 9*k = -6. Let z(b) be the second derivative of 0*b**3 + 1/70*b**5 + 0 + 1/42*b**4 + 0*b**2 - 1/147*b**7 - 1/105*b**k + b. Factor z(x).
-2*x**2*(x - 1)*(x + 1)**2/7
Let i = -24 + 27. Let c(d) be the second derivative of 0*d**i + 0*d**4 + 0*d**2 - 4/3*d**6 + 2/5*d**5 + 25/21*d**7 + 0 - 2*d. Factor c(w).
2*w**3*(5*w - 2)**2
Let c(f) be the first derivative of -f**4/42 - f**3/21 + 2*f**2/7 + 4*f - 2. Let w(z) be the first derivative of c(z). Determine j, given that w(j) = 0.
-2, 1
Let c(r) be the second derivative of 3*r**4/20 + 4*r**3/5 - 9*r**2/10 + 5*r. Factor c(a).
3*(a + 3)*(3*a - 1)/5
Let z = 11 - 6. Suppose b = -b + 3*x + 16, z*x = -5*b - 10. Factor 0*u**b + 0*u - 1/2*u**3 + 0.
-u**3/2
Let u = -2 + 7. Let k be (3 - u) + 1 - -1. What is h in 0 + k*h + 1/5*h**3 - 1/5*h**2 = 0?
0, 1
Let m(f) be the second derivative of -2*f + 0*f**3 + 1/6*f**4 + 1/5*f**5 + 0*f**2 + 0 + 1/15*f**6. Find j, given that m(j) = 0.
-1, 0
Suppose 4*u - 240 = -72. Let q be (8/(-6))/(u/(-9)). Let -q + 2/7*g + 4/7*g**2 = 0. Calculate g.
-1, 1/2
Let d(a) = -7*a**2 - 13*a - 3. Let y be -2 - ((0 - -6) + -2). Suppose 3*f = 4*f + 5. Let r(z) = 8*z**2 + 14*z + 2. Let w(b) = f*r(b) + y*d(b). Factor w(l).
2*(l + 2)**2
Let w be 3/(-9) + 2/6. Find b such that b**3 + 0*b**3 - 4*b + 3*b + w*b**3 = 0.
-1, 0, 1
Factor -6*m - 4*m**4 - 6*m + 8*m + 4*m**3 + 4*m**2.
-4*m*(m - 1)**2*(m + 1)
What is r in 2 - 1/2*r**4 - r**3 + 3/2*r**2 + 4*r = 0?
-2, -1, 2
Let l = 356/21 - 50/3. Let u(f) be the first derivative of -1/7*f**4 + 2/7*f**2 + 2/35*f**5 + 0*f**3 - l*f - 2. Let u(q) = 0. Calculate q.
-1, 1
Let p(y) = -2*y**2 + 7*y. Let r be p(-3). Let z be (-12)/(-10)*(-26)/r. Determine m so that 0*m + 0*m**2 - 2*m**4 + 0 + z*m**3 = 0.
0, 2/5
Let a(h) be the third derivative of -h**6/180 - h**3/3 + 3*h**2. Let m(t) be the first derivative of a(t). Let m(p) = 0. Calculate p.
0
Let r(h) be the second derivative of -3*h**5/20 + h**4 + 5*h**3/2 - 48*h. Factor r(a).
-3*a*(a - 5)*(a + 1)
Let r = -7 + 10. Determine v so that 3*v**3 - 9*v + 4*v**r - 6*v**2 + 2*v**3 + 6 = 0.
-1, 2/3, 1
Determine q, given that 9*q**2 - 2*q**4 + 2*q**4 - 12 + 6*q**3 - 3*q**4 - 12*q = 0.
-1, 2
Factor -x**3 + 12*x - 3*x**3 - 1340*x**2 + 1332*x**2.
-4*x*(x - 1)*(x + 3)
Suppose -i = -2*i + 5*z + 7, z = -3*i + 5. Factor 60*m**2 - 65*m**2 - i - m**3 - 8*m - 2.
-(m + 1)*(m + 2)**2
Let w(n) = -n**2 + n + 2. Let l(o) = 5*o**2 - 4*o - 9. Let p(t) = 2*l(t) + 9*w(t). Solve p(b) = 0.
-1, 0
Factor 2*t - t + 13*t**3 - 2*t**2 - 12*t**3.
t*(t - 1)**2
Let b = 175 - 699/4. Let u = -2/7 - -11/14. Determine r so that -u + 3/4*r**5 - r**3 + b*r - r**4 + 3/2*r**2 = 0.
-1, -2/3, 1
Suppose 2*a - 4 = -2. Suppose 0 = -x + a + 1. Suppose -4*g**x + 4*g**3 - 43*g**4 + 2*g**3 + 53*g**4 = 0. What is g?
-1, 0, 2/5
Let c(k) be the third derivative of -k**2 + 1/20*k**5 + 0 + 0*k + 0*k**3 - 1/24*k**4. Factor c(q).
q*(3*q - 1)
Let i(y) = 2*y**2 + 4*y + 3. Let b be i(-2). Suppose 0 = -8*j + b*j. Factor j*n - 10/7*n**3 - 4/7*n**2 + 0.
-2*n**2*(5*n + 2)/7
Let q be (-3 + 3)/7 - 2/(-6). Factor 1/3*b**4 + 0 - 1/3*b + 1/3*b**3 - q*b**2.
b*(b - 1)*(b + 1)**2/3
Let w(a) be the first derivative of 1/4*a**2 + 0*a - 2 + 1/6*a**3. Solve w(n) = 0.
-1, 0
Let h(d) = -3*d**2 - 5*d - 2. Let b(m) = m**2 + m. Let z(g) = -2*b(g) - h(g). Factor z(x).
(x + 1)*(x + 2)
Let i(n) be the first derivative of n**3/5 - 9*n**2/5 + 27*n/5 + 4. Find s such that i(s) = 0.
3
Let j be (-6 + 3 - -3)*-1. Suppose -3*o - 4*d + 20 = 0, 5*o - 5 = -d - j*d. Find p such that 0*p + 0 - 1/4*p**4 + o*p**3 + 0*p**2 = 0.
0
Let x(h) be the third derivative of -h**5/150 + h**4/10 - 13*h**2. Factor x(u).
-2*u*(u - 6)/5
Let -4/11 + 10/11*h + 0*h**2 - 10/11*h**3 + 4/11*h**4 = 0. What is h?
-1, 1/2, 1, 2
Let v(g) = g**4 - g**2 - 2. Let s(q) = 8*q**4 + q**3 - 9*q**2 - 17. Let d(l) = -6*s(l) + 51*v(l). Factor d(b).
3*b**2*(b - 1)**2
Suppose 2*n + 5*r = 21, 4*n + 0*r = -4*r + 48. Determine h so that -n*h - h**3 + 3*h**3 + 11*h = 0.
-1, 0, 1
Let r(g) be the first derivative of g**6/36 + g**5/15 - g**3/9 - g**2/12 - 1. Determine b, given that r(b) = 0.
-1, 0, 1
Let a = -11 + 13. Suppose -5*f + 1 = -9. Factor 6*r**3 + 0*r**a - 3*r**4 - 3*r**4 - 2*r**f + 2*r**5.
2*r**2*(r - 1)**3
Let x(w) be the third derivative of -w**5/15 + 7*w**4/3 - 98*w**3/3 - 2*w**2. Factor x(f).
-4*(f - 7)**2
Let j(n) be the third derivative of 5*n**6/48 + n**5/12 + n**4/48 - 3*n**2. Factor j(f).
f*(5*f + 1)**2/2
Let p(c) be the third derivative of 0*c**7 - 3*c**2 + 1/336*c**8 + 0*c**3 + 1/24*c**4 + 0*c + 0 - 1/60*c**6 + 0*c**5. Solve p(u) = 0.
-1, 0, 1
Let n = 3377/38790 + -4/431. Let d(h) be the third derivative of -h**2 + 1/18*h**4 - 1/9*h**3 + n*h**5 + 1/45*h**6 + 0 + 0*h. Solve d(t) = 0.
-1, 1/4
Let z(m) be the first derivative of -m**3/8 + 3*m/8 - 13. Suppose z(j) = 0. Calculate j.
-1, 1
Find g, given that 2*g**4 - 13 + 5 + 6*g**2 - 13*g - 8*g**3 + 21*g = 0.
-1, 1, 2
Let g(v) be the third derivative of v**7/105 - v**6/30 - 2*v**5/5 + 10*v**4/3 - 32*v**3/3 + 21*v**2. Factor g(y).
2*(y - 2)**3*(y + 4)
Let w be 7*(0 - 303/(-6)). Let f = 378 - w. Determine x so that 2 + 16*x + 77/2*x**2 + f*x**3 = 0.
-1, -2/7
Let n(k) be the first derivative of -2*k**5/55 - k**4/22 + 2*k**3/33 + k**2/11 + 5. Factor n(l).
-2*l*(l - 1)*(l + 1)**2/11
Suppose -4*u = -u - 5*z, -z = 3*u. Let w(i) be the first derivative of -1 + 0*i**3 + 0*i**2 + u*i + 1/14*i**4. Factor w(c).
2*c**3/7
Let j = 791/6150 - 5/41. Let h(t) be the third derivative of -1/30*t**4 + 0*t**3 - 2*t**2 - j*t**5 + 0 + 0*t. Solve h(c) = 0 for c.
-2, 0
Let a(y) be the first derivative of -6*y - 3/2*y**6 - 5 - 24/5*y**5 + 0*y**4 + 10*y**3 + 9/2*y**2. Suppose a(w) = 0. What is w?
-2, -1, 1/3, 1
Let q(h) be the third derivative of -h**7/105 - 6*h**2. Factor q(k).
-2*k**4
Factor 0 + 0*w + 1/2*w**2 + 49/8*w**4 + 7/2*w**3.
w**2*(7*w + 2)**2/8
Let y(b) be the second derivative of -b**5/130 + 2*b**4/39 + 11*b**3/39 + 6*b**2/13 + 2*b. Factor y(w).
-2*(w - 6)*(w + 1)**2/13
Let o(t) = -t**3 - t**2 + 2*t - 2. Let a be o(-3). Let i be 38/171 + a/9. Factor 2/3 + i*l + 2/3*l**2.
2*(l + 1)**2/3
Factor -5/6*z**3 + 0*z + 0 - 1/3*z**2 - 1/6*z**5 - 2/3*z**4.
-z**2*(z + 1)**2*(z + 2)/6
Suppose -5*f + 5*d + 5 + 10 = 0, 4*d - 12 = -2*f. Suppose 0 = -2*j - 4*q + f, 0*j = 3*j + 5*q - 6. Factor 4*x**j + 32/3*x**5 + 2/3*x + 0 + 2/3*x**3 - 16*x**4.
2*x*(x - 1)**2*(4*x + 1)**2/3
Let a(m) = m**3 + 5*m**2 + 4*m - 3. Let d be a(-3). Let i(f) be the first derivative of -1/10*f**4 + 2 + 0*f + 0*f**2 + 0*f**d. Factor i(u).
-2*u**3/5
Let x(n) be the first derivative of 2*n**3/33 + 2*n**2/11 - 6*n/11 + 2. Factor x(q).
2*(q - 1)*(q + 3)/11
Let w be (-3)/15*-2*(-5)/(-9). Find x, given that 0 + 0*x - w*x**2 = 0.
0
Factor 66*t**2 - 2*t + 44*t**3 + 2*t - 50*t**2 - 12*t**4.
-4*t**2*(t - 4)*(3*t + 1)
Let c be 20/(-40) + (-5)/2. Let f(z) = z + 3. Let t be f(c). Let t + j + 1/2*j**2 = 0. What is j?
-2, 0
Suppose 0 = 3*z - 5*i + 5 + 9, 4*z + 5*i = 28. Suppose -2*m + 16 = 2*m. Let m*r + z*r**2 + 2*r**2 - 10*r**2 = 0. Calculate r.
0, 2/3
Suppose -4*s + 10 = 5*m, 4*s = -5*m + s + 15. Let r(w) = w**2 - 8. Let h be r(m). What is z in 5*z**2 - 81 + 3*z**3 - h*z**2 + 81*z - 4*z**2 = 0?
3
Suppose 9 = -z - 3*v, 2*z + 16 = -4*v + 6. Solve d**2 - 8*d**z - 9*d**5 + 8*d**5 + 5*d**4 + 3*d**2 = 0 for d.
0, 1, 2
Suppose 15 = 5*c - 20. Let q(a) = a**2 - 6*a - 5. Let p be q(c). Factor -1 - v**4 + 2*v**4 - 2*v**4 + p*v**2.
-(v - 1)**2*(v + 1)**2
Let t(l) be the second derivative of l**7/735 + l**6/210 + l**5/210 + l**2/2 + 3*l. Let h(j) be the first derivative of t(j). Factor h(k).