9
Let r be 63/36 - (4 - 3). Determine p so that -r - 9/4*p**3 + 9/4*p + 3/4*p**2 = 0.
-1, 1/3, 1
Let p be 6*(33/6 + -2). Suppose -5*l + p = 1. Solve 0*r**2 + r - r**3 + 1/2*r**l - 1/2 = 0.
-1, 1
Let d(a) be the second derivative of -a**4/4 - 2*a**3 - 9*a**2/2 + 17*a. Factor d(s).
-3*(s + 1)*(s + 3)
Let u(d) be the second derivative of -d**5/5 - 2*d**4/3 + 2*d**3/3 + 4*d**2 + 16*d. Factor u(k).
-4*(k - 1)*(k + 1)*(k + 2)
Let g = 3 + -1. Let z(c) = 2*c**2 - 2*c - 3. Let k(b) = -b**2 + 1. Let m(o) = g*z(o) + 6*k(o). Let m(n) = 0. What is n?
-2, 0
Let u be 55/150 + (-4)/(-30). Suppose 4*i + 4 = 2*z, 6*z = z - i + 10. Determine c so that 1/2*c**z + u + c = 0.
-1
Let c(f) = -5*f - f**2 + 4*f**2 + f**2 - f. Let m(d) = -5*d**2 + 7*d. Suppose 0 = 3*u + 12 + 9. Let r(x) = u*c(x) - 6*m(x). Factor r(n).
2*n**2
Let b(q) be the second derivative of -5*q - 1/4*q**4 + 0*q**2 + 1/3*q**3 + 0. Suppose b(s) = 0. What is s?
0, 2/3
Let o(c) be the first derivative of 2*c**5/5 + c**4 + 2*c**3/3 + 6. Let o(y) = 0. What is y?
-1, 0
Let o(y) be the first derivative of -13/25*y**5 + 1/15*y**3 + 9/20*y**4 - 2 - 1/5*y**2 + 1/6*y**6 + 0*y. Factor o(q).
q*(q - 1)**3*(5*q + 2)/5
Factor -7/4*z**3 + 2*z + 3/4*z**2 - 1 + 1/2*z**4.
(z - 2)**2*(z + 1)*(2*z - 1)/4
Let w(d) be the first derivative of d**4/10 + 2*d**3/5 + 2*d**2/5 + 36. Factor w(j).
2*j*(j + 1)*(j + 2)/5
Factor 24*x**5 + 7*x**3 - 19*x**5 - 2*x**3 + 10*x**4.
5*x**3*(x + 1)**2
Let i(s) be the third derivative of -s**5/20 + 6*s**2. Let i(u) = 0. What is u?
0
Let k = -270 + 17548/65. Let o = k - -28/65. Find z such that -o*z**3 - 2/5*z**4 + 0 + 0*z + 0*z**2 = 0.
-1, 0
Let z(t) be the first derivative of -t**9/1512 + t**7/420 + 4*t**3/3 + 6. Let b(f) be the third derivative of z(f). Factor b(y).
-2*y**3*(y - 1)*(y + 1)
Let w(n) be the first derivative of 32*n**5/35 + 20*n**4/7 + 22*n**3/7 + 10*n**2/7 + 2*n/7 + 13. Let w(r) = 0. Calculate r.
-1, -1/4
Let k(o) be the second derivative of -o**4/18 + 8*o**3/3 - 48*o**2 - 53*o. Let k(n) = 0. Calculate n.
12
Let g = -1/5 - -7/10. Find f, given that -1/4*f**3 + 0 + g*f**2 + 1/4*f**5 + 0*f - 1/2*f**4 = 0.
-1, 0, 1, 2
Let o be -2 + 2 - (-70)/(-45). Let b = 20/9 + o. Factor b*m**2 + 0 - 4/3*m.
2*m*(m - 2)/3
Determine z, given that -14/9*z**4 + 4/9*z - 4/9*z**5 - 16/9*z**3 - 4/9*z**2 + 2/9 = 0.
-1, 1/2
Let m = -1 - -3. Let n be (m/(-6))/((-5)/30). Let k(d) = d**2 + d + 1. Let r(c) = 4*c**3 + 14*c**2 + 2*c + 13. Let q(g) = n*r(g) - 22*k(g). Factor q(y).
2*(y - 1)*(y + 2)*(4*y - 1)
Let g(d) = -d**2 + 7*d - 7. Let w be g(5). Let r be (w/6)/(1/6). Factor 4*x**r + 0*x**4 - x**4 + x**2 - 2*x**3 - 2*x.
-x*(x - 2)*(x - 1)*(x + 1)
Let p be (-10 - -7)*(-8)/60. Determine f, given that 0*f + 0 - 2/5*f**2 - p*f**3 = 0.
-1, 0
Suppose 1/3 - 1/3*q**2 + 0*q = 0. What is q?
-1, 1
Let b(t) = -t**2 - 8*t + 13. Let c be b(-10). Let j be (-10 - c)/(-1*9). Determine h, given that j - 2/3*h + 1/3*h**2 = 0.
1
Suppose 0 = 6*p - 15 - 9. Factor -1/2*r**2 + 0 + 1/2*r**p - 1/2*r**3 + 1/2*r**5 + 0*r.
r**2*(r - 1)*(r + 1)**2/2
Let x = 133/2 + -66. Let t(s) be the first derivative of -1 + 3/4*s**4 + 0*s + x*s**2 + s**3 + 1/5*s**5. Determine z, given that t(z) = 0.
-1, 0
Let p(j) = -9*j**3 - 20*j**2 + 11*j + 11. Suppose 9*n = 4*n + 20. Let f(h) = -3*h**3 - 7*h**2 + 4*h + 4. Let m(l) = n*p(l) - 11*f(l). Factor m(s).
-3*s**2*(s + 1)
Let a = 13 + -13. Let x(r) be the second derivative of 0*r**2 + 1/10*r**5 - r + 1/45*r**6 + a + 1/9*r**3 + 1/6*r**4. Solve x(z) = 0.
-1, 0
Let t(a) be the second derivative of -3/20*a**5 + 3*a + 0*a**2 + 0 + 0*a**3 + 1/2*a**4 + 1/14*a**7 - 1/5*a**6. Find b, given that t(b) = 0.
-1, 0, 1, 2
Let j = 22 - 20. Let y(c) be the third derivative of 0*c + 2*c**j + 0 + 1/6*c**4 - 1/30*c**5 - 1/3*c**3. Factor y(d).
-2*(d - 1)**2
Let z = 120/7 + -572/35. Factor -z + 2/5*l**2 - 2/5*l.
2*(l - 2)*(l + 1)/5
Let k(b) be the third derivative of 2*b**7/105 + 2*b**6/15 + 4*b**5/15 - b**2. Let k(j) = 0. Calculate j.
-2, 0
Let k = 15 - 10. Factor -6*d**3 + 2*d**5 + d**5 - 6*d**k + 8*d**4 + d.
-d*(d - 1)**3*(3*d + 1)
Let j = -2 - -5/2. Let c(s) be the first derivative of -2 + j*s**2 - 1/6*s**3 + 0*s. Factor c(g).
-g*(g - 2)/2
Let s = -61 - -36. Let g = s + 76/3. Factor 0*c**2 - 2/3 - g*c**3 + c.
-(c - 1)**2*(c + 2)/3
Let s(g) be the third derivative of -g**8/504 + 2*g**7/45 - 13*g**6/30 + 12*g**5/5 - 33*g**4/4 + 18*g**3 + 10*g**2. Let s(n) = 0. Calculate n.
2, 3
Let y = 352/537 - -2/179. Factor y*c**3 + 0 + 2/9*c**4 + 2/3*c**2 + 2/9*c.
2*c*(c + 1)**3/9
Let n be ((-1)/(-2))/(10/(-240)). Let i be (n/(-15))/((-2)/(-5)). Factor -2/5*m**i - 4/5*m - 2/5.
-2*(m + 1)**2/5
Factor 6/7*s**2 + 15/7*s**4 + 0 + 3*s**3 + 0*s.
3*s**2*(s + 1)*(5*s + 2)/7
Let a(t) be the second derivative of -t**10/105840 + t**8/23520 + t**4/2 + 6*t. Let c(v) be the third derivative of a(v). Solve c(o) = 0.
-1, 0, 1
Let m(v) be the second derivative of -1/2*v**3 + 1/2*v**4 - 3*v**2 + 3/20*v**5 + 7*v + 0. Determine p, given that m(p) = 0.
-2, -1, 1
Let n = -145 - -148. Factor -1/2 + 1/2*y**2 - 1/2*y + 1/2*y**n.
(y - 1)*(y + 1)**2/2
Suppose -128/7 + 32/7*b - 2/7*b**2 = 0. Calculate b.
8
Suppose 0 = o + 4*j + 18, 2*o + 2*j = 6*o - 18. Factor -2*x + 5*x**2 + 2*x - x**2 - o*x - 2*x**3.
-2*x*(x - 1)**2
Let j(z) be the second derivative of -z**6/50 - 9*z**5/100 - z**4/10 + 3*z. Let j(y) = 0. Calculate y.
-2, -1, 0
Suppose -x - 7 = 2. Let r be 3 + (x/3)/1. Solve -2/5*l**2 + r + 0*l = 0 for l.
0
Let o be ((-4)/12)/((-2)/12). Solve -4*b**2 + b**3 - b**o + 7*b**2 + b = 0.
-1, 0
Let a = 1835/13 - 141. Suppose -2/13*o + 4/13 - 4/13*o**2 + a*o**3 = 0. What is o?
-1, 1, 2
Let i = -4 + 10. Suppose c + c = i. Solve 2/9*f**c + 2/9*f - 4/9*f**2 + 0 = 0.
0, 1
Let p(r) be the third derivative of -r**8/420 - r**7/105 - r**6/90 + r**3 - 5*r**2. Let j(z) be the first derivative of p(z). Factor j(u).
-4*u**2*(u + 1)**2
Let h = 437/369 - 3/41. Factor 4/9*w**4 + 2/9 + h*w + 2*w**2 + 14/9*w**3.
2*(w + 1)**3*(2*w + 1)/9
Factor -4/3*o**3 - 144*o + 24*o**2 + 288.
-4*(o - 6)**3/3
Let j = 1022/15 - 68. Factor 4/5*c - j*c**2 - 6/5.
-2*(c - 3)**2/15
Let p(d) = -12*d**5 + 16*d**4 - 20*d**3 + 18*d**2 + 9*d. Let o(t) = t**5 - t**4 + t**3 - t**2 - t. Let v(z) = 44*o(z) + 4*p(z). Factor v(l).
-4*l*(l - 2)*(l - 1)**3
Let r(z) be the third derivative of 0*z - 1/420*z**6 - 5*z**2 - 1/21*z**4 + 2/105*z**5 + 0 + 0*z**3. Suppose r(a) = 0. What is a?
0, 2
Let y(m) = -2*m**5 + 7*m**4 + 8*m**3 - m**2 + 3. Let v(k) = 5*k**5 - 15*k**4 - 17*k**3 + 3*k**2 - 7. Let r(i) = -6*v(i) - 14*y(i). Let r(p) = 0. What is p?
-2, -1, 0
Let d(a) = 21*a**3 - 48*a**2 - 33*a. Let b(r) = -5*r**3 + 12*r**2 + 8*r. Let k(s) = 15*b(s) + 4*d(s). What is l in k(l) = 0?
-2/3, 0, 2
Let n = 612/1555 + 2/311. Factor -2/5*a**3 + n*a**4 - 4/5*a**2 + 0 + 0*a.
2*a**2*(a - 2)*(a + 1)/5
Let i(y) be the first derivative of -y**5/120 + y**4/12 - y**3/3 - y**2/2 - 3. Let c(g) be the second derivative of i(g). Factor c(z).
-(z - 2)**2/2
Factor -5*m**3 - 10*m**2 + 6 + 2*m + m**3 + 6*m + 0*m**3.
-2*(m - 1)*(m + 3)*(2*m + 1)
Let b = 871/336 + -18/7. Let p(w) be the second derivative of -w + 0 + 0*w**2 - 1/24*w**3 - b*w**4. Factor p(j).
-j*(j + 1)/4
Let o = 67/126 + -2/63. Let h be (-14)/(-8) + (-1)/(-4). Solve -3/2*w - 1/2 - o*w**3 - 3/2*w**h = 0.
-1
Let g(b) be the first derivative of 3*b**5/5 - 57*b**4/28 + 15*b**3/7 - 3*b**2/14 - 6*b/7 - 1. Factor g(h).
3*(h - 1)**3*(7*h + 2)/7
Let d be ((-110)/36)/(-11)*4. Let n(u) be the first derivative of -1 + 1/3*u**2 + d*u**3 + 1/2*u**4 - 2/3*u. Factor n(r).
2*(r + 1)**2*(3*r - 1)/3
Let g be 1/9 + 70/18. Let w(i) be the second derivative of 0 - 1/9*i**3 - 2*i + 0*i**2 - 1/45*i**6 + 1/30*i**5 + 1/18*i**g. Factor w(n).
-2*n*(n - 1)**2*(n + 1)/3
Let l(s) be the first derivative of -18/7*s - 2/21*s**3 - 3 + 6/7*s**2. Solve l(y) = 0 for y.
3
Let r(z) be the third derivative of -z**8/84 - 4*z**7/35 - 13*z**6/30 - 4*z**5/5 - 2*z**4/3 + 2*z**2. Factor r(c).
-4*c*(c + 1)**2*(c + 2)**2
Let s(f) be the second derivative of -f**6/120 + f**5/80 + 3*f**4/16 + 11*f**3/24 + f**2/2 + 22*f. Solve s(a) = 0 for a.
-1, 4
Let j(b) = 24*b**4 - 4*b**3 + 16*b**2 - 16*b - 20. Let a(w) = w**4 + w**2 - w - 1. Let h(c) = 20*a(c) - j(c). Factor h(p).
-4*p*(p - 1)**2*(p + 1)
Let j(y) be the third derivative of -y**8/21