5*y(r). What is s in o(s) = 0?
-2/5, 2
Factor 980 + 16*p**3 - 43*p**3 + 17*p**3 + 840*p - 135*p**2 + 15*p**3.
5*(p - 14)**2*(p + 1)
Let q(t) = t**5 + 3*t**4 - t**3. Let y(z) = -3*z**5 + 7*z**4 + 99*z**3 + 5*z**2 - 396*z - 324. Let b(m) = 4*q(m) + y(m). Suppose b(g) = 0. Calculate g.
-9, -2, -1, 2
Let g(t) be the second derivative of -2*t - 2*t**3 + 2*t**2 - 7/12*t**4 + 0. Factor g(b).
-(b + 2)*(7*b - 2)
Let o(i) be the second derivative of -i**6/30 - 9*i**5/4 - 203*i**4/12 - 37*i**3/2 + 180*i**2 - 35*i. Factor o(t).
-(t - 1)*(t + 3)**2*(t + 40)
Let h = -3 - -16. Suppose -17*i = -h*i. Factor 0*y**2 - 1/2*y**3 + i*y + 0 - 1/2*y**4.
-y**3*(y + 1)/2
Let 18/5*b**2 - 2*b**3 + 27/5*b - 1/5*b**5 - 27/5 - 7/5*b**4 = 0. Calculate b.
-3, 1
Suppose 0 = 4*a + 5*a. Suppose a*b**2 + 3/7 - 6/7*b**3 - 3/7*b**4 + 6/7*b = 0. What is b?
-1, 1
Let l be 4/2 + 48/6. Determine x so that 14*x**2 - 22*x**5 - 9*x**2 + 2*x**5 - 35*x**4 - l*x**3 = 0.
-1, 0, 1/4
Solve 6/5*d**2 + 6/5 - 2/5*d**4 + 3/5*d**3 - 13/5*d = 0 for d.
-2, 1, 3/2
Suppose 23 + 12*l**4 - 94*l**2 + 2*l**3 + 41 - 2*l**5 + 18*l**2 = 0. What is l?
-2, -1, 1, 4
Let y = 251 - 751/3. Let i = -106/21 - -40/7. What is a in -i + y*a**2 + 0*a = 0?
-1, 1
Let p be (-180)/(-330)*(-11)/(-13). Suppose -10/13*a**2 - 4/13*a + p*a**4 + 0 + 8/13*a**3 = 0. Calculate a.
-2, -1/3, 0, 1
Suppose -23*o - 68 = -5*b - 24*o, b + 4*o = 25. Let a(x) be the second derivative of -1/8*x**3 - 1/4*x**2 - 1/48*x**4 + 0 - b*x. Factor a(m).
-(m + 1)*(m + 2)/4
Let v(l) be the second derivative of -l**6/120 + l**5/40 + l**4/16 - l**3/3 + l**2/2 - 3*l + 95. Determine s so that v(s) = 0.
-2, 1, 2
Let f be (-2)/4 - 1/(-2). Suppose -2*o + 9*o - 28 = f. Find u such that 1/2*u - u**2 + u**o - 1/2*u**5 + 0*u**3 + 0 = 0.
-1, 0, 1
Let m be (-160)/(-15)*(-1 + 153/156). Let q = m + 73/39. Factor l + 3 + 1/3*l**3 - q*l**2.
(l - 3)**2*(l + 1)/3
Let i(q) be the first derivative of 27*q + 9*q**2 - 3/5*q**5 - 8*q**3 - 31 - 9/2*q**4. Factor i(m).
-3*(m - 1)*(m + 1)*(m + 3)**2
Let g(m) be the third derivative of -1/30*m**5 - 1/6*m**3 + 0*m**4 + 0*m - 6*m**2 - 1/90*m**6 + 0. Let t(a) be the first derivative of g(a). Factor t(k).
-4*k*(k + 1)
Let x(f) be the second derivative of 0*f**2 + 6/49*f**7 - 7/15*f**6 + 0 - 17*f + 2/21*f**3 + 23/35*f**5 - 17/42*f**4. Find d, given that x(d) = 0.
0, 2/9, 1/2, 1
Solve -48*c + 58*c**3 + 64*c**2 + 1/2*c**5 + 27/2*c**4 - 88 = 0.
-22, -2, 1
Suppose 0*t + 18*t = 378. Let x be (10/t)/((-1)/(-7)). Factor -8/9 + 8/3*v + 8/9*v**3 + x*v**2.
2*(v + 2)**2*(4*v - 1)/9
Let a(j) be the second derivative of -j**6/160 - 11*j**5/160 + j**4/8 + 8*j**3/3 - 26*j. Let u(m) be the second derivative of a(m). Factor u(n).
-3*(n + 4)*(3*n - 1)/4
Let w(n) be the third derivative of 2*n**7/105 - 3*n**6/5 + 109*n**5/15 - 42*n**4 + 392*n**3/3 - 2*n**2 - 2. Factor w(t).
4*(t - 7)**2*(t - 2)**2
Let u(p) be the second derivative of -p**6/255 - 7*p**5/170 + p**4/6 - 3*p**3/17 - 92*p. Suppose u(d) = 0. What is d?
-9, 0, 1
Let n(x) be the third derivative of -x**6/240 - x**5/12 - 23*x**4/48 - 7*x**3/6 + 662*x**2. Factor n(f).
-(f + 1)*(f + 2)*(f + 7)/2
Suppose 0 = 10*l - 8 - 32. What is d in 0*d - 34*d**2 + d**3 - d**5 + 0*d - d**l + 35*d**2 = 0?
-1, 0, 1
Factor -1/2*f**3 - 1/4*f**4 + 1/4*f - 1/4 + 1/4*f**5 + 1/2*f**2.
(f - 1)**3*(f + 1)**2/4
Factor -h**2 + 155 - 7492*h - 4*h**2 + 7342*h.
-5*(h - 1)*(h + 31)
Let l(x) be the second derivative of -x**4/54 + 11*x**3/27 + 26*x + 3. Factor l(n).
-2*n*(n - 11)/9
Let k(a) be the first derivative of -49*a**5/150 + 7*a**4/30 - a**3/15 - 5*a**2/2 + 7. Let m(p) be the second derivative of k(p). Factor m(i).
-2*(7*i - 1)**2/5
Suppose 12*n**3 - 1 + 144 + 2*n**3 - 3 - 160*n**2 + n**3 + 365*n = 0. Calculate n.
-1/3, 4, 7
Suppose 0 = -6*c - 18, -5*h = c - 2*c - 18. Factor -20/7*a**h - 92/7*a - 24/7 - 88/7*a**2.
-4*(a + 1)*(a + 3)*(5*a + 2)/7
Let y(a) = -a**3 + 5*a**2 + 8*a - 9. Let i be y(-2). Factor 0 + 1/2*s**5 - 1/2*s**4 - 5/2*s**i - 3/2*s**2 + 0*s.
s**2*(s - 3)*(s + 1)**2/2
Let j(m) be the second derivative of m**7/210 - m**6/24 + m**5/10 + m**4/6 - 4*m**3/3 - m**2 + 3*m. Let q(l) be the first derivative of j(l). Factor q(y).
(y - 2)**3*(y + 1)
Find s such that -5*s**5 - 24*s**4 + 21*s - 115*s**3 + 0*s**2 - 35*s**2 - 21*s**4 + 80 + 99*s = 0.
-4, -1, 1
Let u = -1692 - -1694. Solve -2*l**u + 18/5 + 6/5*l + 2/5*l**3 = 0.
-1, 3
What is k in 4*k**4 + 2*k**2 + 585*k**3 - 2*k**4 + 0*k**2 - 581*k**3 = 0?
-1, 0
Let y(c) = -c**3 - 3*c**2 + c. Let u(p) = 3*p**3 + 24*p**2 - 3*p - 12. Let v(t) = u(t) + 4*y(t). What is z in v(z) = 0?
-1, 1, 12
Let s = 17 - 11. Suppose -16*v + 17*v = 2. Solve 3*u**3 + 9*u**v - 15*u + 1 + 5 + 3*u**4 - s*u**4 + 0*u**4 = 0 for u.
-2, 1
Let j(a) = 3*a**2 + 7*a + 7. Let i be j(7). Let o = -1014/5 + i. Factor 2/5*s + o*s**2 + 0.
s*(s + 2)/5
Suppose -2*b + 0*x - 6 = 5*x, 4*b + 2 = -5*x. Suppose -5*a + 1 = 3*u + b, -3*u - 2*a = -5. Factor -2*g**3 - 3*g**3 + 3*g**3 - 6*g + 5*g**u - 3*g**2.
3*g*(g - 2)*(g + 1)
Let p be -10 - -3 - (-1 + (-222)/30). Factor p*v + 2/5 + v**2.
(v + 1)*(5*v + 2)/5
Let k be (2/1)/((-35)/(-10)). Let n(v) be the first derivative of -k*v + 2 - 11/7*v**2 - 6/7*v**3. Solve n(h) = 0.
-1, -2/9
Let j = 3277 - 3275. Factor 4/3*c - 1/3*c**3 + 2/3*c**j - 1/6*c**4 + 0.
-c*(c - 2)*(c + 2)**2/6
Let h(n) be the first derivative of 1 + 0*n - 1/360*n**6 - 1/24*n**4 + 3*n**2 + 1/60*n**5 + 1/18*n**3. Let a(w) be the second derivative of h(w). Factor a(q).
-(q - 1)**3/3
Let l(d) = d**4 + 4*d**3 + 2*d**2 + d. Let w(u) = u**3 + 6*u**2 - 5*u + 16. Let h be w(-7). Let v(c) = c**4 - c. Let k(q) = h*l(q) + 2*v(q). Factor k(y).
4*y**2*(y + 1)**2
Let h(f) = 15*f**4 - 35*f**3 - 10*f**2 + 32*f + 12. Let y(b) = -16*b**4 + 36*b**3 + 11*b**2 - 29*b - 13. Let j(w) = -5*h(w) - 4*y(w). Factor j(x).
-(x - 2)**2*(x + 1)*(11*x + 2)
Let d be (-6)/48*(-1 - 1). Let r(w) be the second derivative of -w + d*w**4 - 7/30*w**6 + 1/14*w**7 + 0 - 1/3*w**3 + 3/20*w**5 + 0*w**2. Factor r(f).
f*(f - 1)**3*(3*f + 2)
What is i in 0 + 2/9*i**5 + 8/9*i**4 + 2/3*i**3 - 8/9*i**2 - 8/9*i = 0?
-2, -1, 0, 1
Suppose -8/9 - 14/9*l**5 - 38/9*l**4 - 2/9*l**3 + 16/9*l + 46/9*l**2 = 0. Calculate l.
-2, -1, 2/7, 1
Let f(u) be the second derivative of u**7/168 - u**6/18 + 5*u**5/24 - 5*u**4/12 - 5*u**3/2 + 6*u. Let h(z) be the second derivative of f(z). Solve h(i) = 0.
1, 2
Suppose 0 = -4*l + j + 23, -7*l + 2*l - 5*j = -10. Let i(n) = -n - 5. Let x be i(-7). Suppose -4 + l*k**2 - x + 50 - 40*k + 36 = 0. What is k?
4
Determine q so that -2/5*q**2 - 72/5 - 6*q = 0.
-12, -3
Let y(q) be the first derivative of 7*q**6/90 + q**5/12 - q**4/4 - 5*q**3/18 + q**2/3 + 38*q - 5. Let r(h) be the first derivative of y(h). Factor r(t).
(t - 1)*(t + 1)**2*(7*t - 2)/3
Let n(v) be the third derivative of 0*v + 1/14*v**7 + 1/2*v**3 + 1/112*v**8 + 5/8*v**4 + 1/4*v**6 + 1/2*v**5 + 0 + 25*v**2. Solve n(d) = 0.
-1
Factor 3/5*q**4 + 0*q + 0 + 3/5*q**2 + 6/5*q**3.
3*q**2*(q + 1)**2/5
Suppose 29*j - 46 - 12 = 0. Let p(m) be the second derivative of 2/39*m**3 + 1/26*m**4 + 7/195*m**6 - 6/65*m**5 + 0 + 0*m**2 - j*m. Factor p(k).
2*k*(k - 1)**2*(7*k + 2)/13
Factor 32/7 + 30/7*v - 2/7*v**2.
-2*(v - 16)*(v + 1)/7
Let g(y) = 3 + 3 - 9*y**2 - 2*y - y. Let q(m) = -m - 8*m**2 - 2*m + 18 - 18*m**2 - 5*m + 0*m**2. Let j(x) = -17*g(x) + 6*q(x). Factor j(f).
-3*(f - 2)*(f + 1)
Let c = 27/34 + -121/238. Let f be (-26)/(-7) - (1 - -1). Find m, given that -18/7 - c*m**2 - f*m = 0.
-3
Solve 8/7*w - 18/7*w**2 + 0 = 0 for w.
0, 4/9
Let r(p) be the third derivative of p**8/336 - 2*p**7/105 - p**6/20 + p**5/15 + 5*p**4/24 + 56*p**2. Determine x so that r(x) = 0.
-1, 0, 1, 5
Let s = -624 + 3745/6. Let c(j) be the second derivative of 3/40*j**6 + 0 - s*j**3 + 1/3*j**4 - 11*j - 21/80*j**5 + 0*j**2. Determine b, given that c(b) = 0.
0, 2/3, 1
Let j(p) be the third derivative of -p**7/30 - 557*p**6/40 - 20063*p**5/12 - 23443*p**4/8 + 14161*p**3/3 + 453*p**2 - 2. Determine x, given that j(x) = 0.
-119, -1, 2/7
Let x(p) = -3*p**2 - p + 2. Let n be x(3). Let d be (-24)/36 + n/(-30). Suppose d*k**2 - 2/15*k**4 - 2/15 + 0*k**3 + 0*k = 0. Calculate k.
-1, 1
Factor 72 - 16*s**2 - 4*s - 8*s - 248*s**3 + 252*s**3.
4*(s - 3)**2*(s + 2)
Factor 26 + 5*b**3 - 3*b - 38 + 10*b**2 + 12 - 37*b.
5*b*(b - 2)*(b + 4)
Le