(k - 1)*(k + 1)*(k + 2)
Suppose -3*z + 28 = z. Let g = -7 + z. Factor 1/3*k**2 + g*k + 0.
k**2/3
Let f(g) be the second derivative of -2*g + 3*g**2 - 27/20*g**5 + 1/2*g**4 + 9/2*g**3 + 0 - 2/5*g**6. Let f(j) = 0. Calculate j.
-2, -1, -1/4, 1
Let g(d) be the first derivative of -4*d**3/3 - 2*d**2 + 8*d - 1. Let g(z) = 0. Calculate z.
-2, 1
Factor 4/5*l**2 - 152/5*l + 1444/5.
4*(l - 19)**2/5
Let d be (0 + -2 - 2) + 2. Let g be 1 + 6/d + 4. Suppose 2/3*r**g + 2/3*r - 4/3 = 0. Calculate r.
-2, 1
Factor 0 + 2/3*a + 2/3*a**2 - 2/3*a**3 - 2/3*a**4.
-2*a*(a - 1)*(a + 1)**2/3
Let z(h) = -5*h**4 + h**3 + 22*h**2 - 16*h - 40. Let d(r) = 10*r**4 - r**3 - 42*r**2 + 31*r + 80. Let v(k) = -4*d(k) - 9*z(k). Find s such that v(s) = 0.
-2, -1, 2
Let x(k) = 3*k**3 - k**2 + k + 1. Let o(z) be the second derivative of 0*z**2 - 2*z + 0*z**3 + 0 - 1/20*z**5 + 0*z**4. Let t(l) = 4*o(l) + x(l). Factor t(y).
-(y - 1)*(y + 1)**2
Suppose -4 = -v - 6, s = v + 5. Suppose -m**2 + 5/4*m - 1/2 + 1/4*m**s = 0. What is m?
1, 2
Let m be (-21)/27 + (-2)/9. Let t = 1 + m. Let u - 2*u**3 + t*u**3 + u = 0. Calculate u.
-1, 0, 1
Let k(t) be the second derivative of 4*t**7/63 - 2*t**6/9 + 11*t**5/40 - 5*t**4/36 + t**3/36 - 9*t. Suppose k(v) = 0. What is v?
0, 1/4, 1
Let j(a) = -a + 7. Let b be j(4). Factor -9*f**4 + 9*f + 18*f**2 - 29*f**2 + 17*f**2 - 6*f**b - 3*f**5 + 3.
-3*(f - 1)*(f + 1)**4
Let 0 - 2/3*g + 2/3*g**2 = 0. What is g?
0, 1
Let j = 22 + -52. Let o be ((-4)/j + 0)*3. Factor 0*f - 2/5*f**2 + 0 + o*f**5 - 2/5*f**3 + 2/5*f**4.
2*f**2*(f - 1)*(f + 1)**2/5
Let r(z) be the second derivative of 2/33*z**3 + 0 + 1/66*z**4 + 2*z + 1/11*z**2. Solve r(j) = 0 for j.
-1
Let l be 23/15 - 1 - (-118)/177. Determine y so that -l*y - 3/5*y**2 - 3/5 = 0.
-1
Let a(q) be the second derivative of q**4/132 - 2*q**3/11 + 18*q**2/11 + 21*q. Suppose a(m) = 0. Calculate m.
6
Let b = 127 + -633/5. Find p, given that 2*p**4 + 8/5*p**5 + 0 - 6/5*p**3 - 2*p**2 - b*p = 0.
-1, -1/4, 0, 1
Let f be 26/8 + 9/12. Factor 9/2*x**3 + 5/2*x**2 + 7/2*x**f + x**5 + 0 + 1/2*x.
x*(x + 1)**3*(2*x + 1)/2
Let q(b) be the first derivative of -3*b**4/14 + 110*b**3/21 - 261*b**2/7 + 162*b/7 - 48. Determine j, given that q(j) = 0.
1/3, 9
Let m(q) be the first derivative of q**3/12 + q**2/4 - 3*q/4 + 4. Suppose m(s) = 0. Calculate s.
-3, 1
Let w(k) = -k**3 + 4*k**2 + 3. Let y be w(4). Find g, given that 20*g + 9*g + y*g + 16 + 12*g**2 = 0.
-2, -2/3
Let w = -985 + 88651/90. Let x(k) be the third derivative of 0*k**3 - 1/180*k**6 + 0*k**4 - w*k**5 - 3*k**2 + 0*k + 0. Factor x(b).
-2*b**2*(b + 1)/3
Let z be (-4)/1 + (9 - 2). Let q(y) be the first derivative of -4 - 3/20*y**5 - 3/8*y**2 - 9/16*y**4 + 0*y - 3/4*y**z. Suppose q(r) = 0. What is r?
-1, 0
Let b(x) = x**3 + x**2 + x. Let l(z) = z**4 + 2*z**3 - 2*z**2 + 2*z. Let m(k) = 2*b(k) - l(k). Factor m(s).
-s**2*(s - 2)*(s + 2)
Let p(m) be the second derivative of m**7/4200 + m**6/1200 - m**4/3 - m. Let r(q) be the third derivative of p(q). What is s in r(s) = 0?
-1, 0
Find t such that 2/11*t + 2/11*t**2 - 12/11 = 0.
-3, 2
Let o(s) = -s**3 + 3*s**2 + 4*s. Let r be o(4). Suppose r = -2*d - 0*i + 2*i - 8, 0 = -i + 4. Solve 0*n**3 + 0*n + 2/5*n**2 - 2/5*n**4 + d = 0 for n.
-1, 0, 1
Let m(h) = -4*h**2 + h - 1. Let k = -1 + 2. Let u(r) = -r**2 - 1. Let y(q) = -4*q**2 - 2. Let z(v) = k*u(v) - y(v). Let l(d) = -2*m(d) - 3*z(d). Factor l(a).
-(a + 1)**2
Let y = 559 - 398. Let h be y/35 + 6/(-10). Factor -3*m**3 + 0*m**2 - 3*m**2 - m**h + 19*m - 20*m.
-m*(m + 1)**3
Factor -24*v - 25*v**2 - 10*v - 4*v**2 - 12 - 6*v**3 + v**2.
-2*(v + 1)*(v + 3)*(3*v + 2)
Factor -45*k - 5*k**3 - 81/4 - 1/4*k**4 - 59/2*k**2.
-(k + 1)**2*(k + 9)**2/4
Let j(y) be the second derivative of -5*y**7/294 + y**6/105 - 2*y. Suppose j(n) = 0. What is n?
0, 2/5
Let n(d) be the first derivative of -3*d**5/20 + d**4/4 + 11*d**2/2 - 10. Let v(j) be the second derivative of n(j). Factor v(s).
-3*s*(3*s - 2)
Let -4*a - a**4 + 11/3*a**2 + 4/3 - 1/3*a**3 + 1/3*a**5 = 0. What is a?
-2, 1, 2
Factor -484 + 88*n - 7*n**2 + 0*n**2 + 3*n**2.
-4*(n - 11)**2
Let x(f) = -f**2 - 11*f - 8. Let a be x(-10). Suppose -2*s**a - s**2 + 2 + 1 + 0*s**2 = 0. Calculate s.
-1, 1
Let a = -645 - -647. Factor 2/5*j - 2*j**3 - 6/5*j**4 + 0 - 2/5*j**a.
-2*j*(j + 1)**2*(3*j - 1)/5
Let q(v) = -68*v**4 - 196*v**3 - 192*v**2 - 40*v. Let o(x) = 23*x**4 + 65*x**3 + 64*x**2 + 13*x. Let l(n) = -8*o(n) - 3*q(n). Factor l(r).
4*r*(r + 1)*(r + 2)*(5*r + 2)
Let y(h) = -h**3 - 8*h**2 - h. Suppose 34 - 2 = -4*w. Let i be y(w). Factor -4*u**3 + 2*u**4 + 0*u**4 + i*u**3.
2*u**3*(u + 2)
Let z be (-10 + 12)/(1 - 3). Let i(k) = -3*k**4 - 3*k**3 - 3*k**2 - 3*k + 3. Let t(h) = -h**3 + h - 1. Let l(a) = z*i(a) - 3*t(a). Let l(v) = 0. Calculate v.
-1, 0
Let d = 2 - 7. Let g(b) = 4*b**2 - 2*b. Let y(k) = -k**2. Let w(p) = d*y(p) - g(p). Factor w(a).
a*(a + 2)
Let r(n) be the second derivative of n**4/36 + n**3/6 + n**2/3 + 2*n - 39. Factor r(f).
(f + 1)*(f + 2)/3
Let m(i) = -i. Let q(y) be the first derivative of 2*y**3/3 + y**2/2 + 2*y + 2. Let c(f) = 5*m(f) + q(f). Factor c(s).
2*(s - 1)**2
Factor -2/7 - 4/7*l - 2/7*l**2.
-2*(l + 1)**2/7
Suppose 3*n = n + 6. Suppose -n*x = 4*u + 10, -3*x + 30 = -5*u + 4. Determine d so that -2/9*d**3 - 2/9*d - 4/9*d**x + 0 = 0.
-1, 0
Suppose -y - 2*b = 2, -2*b - 14 = -3*y + 2*b. Let i = -2 - -2. Factor 0 + 2/9*s**y + i*s.
2*s**2/9
Let n(j) = -j**3 + 0*j**4 + 3*j + j**2 + 5 - 5*j**2 + 9*j**4 - 7*j. Let h(s) = -14*s**4 + 2*s**3 + 6*s**2 + 6*s - 8. Let z(k) = 5*h(k) + 8*n(k). Factor z(b).
2*b*(b - 1)*(b + 1)**2
Let j(y) = -2*y - y + 7*y - 3*y. Let m be j(0). Factor -5*o + 27 - 13*o + 3*o**2 + m.
3*(o - 3)**2
Let n = -3/10 + 9/10. Solve n*j**3 + 63/5*j**4 - 12/5*j - 62/5*j**2 + 8/5 = 0 for j.
-2/3, 2/7, 1
Let d = -74 - -372/5. Let z(h) be the first derivative of d*h + 2 - 3/5*h**2 + 2/5*h**3 - 1/10*h**4. Let z(x) = 0. Calculate x.
1
Suppose -18 = 13*j - 18. Let h(g) be the third derivative of 0 - 3*g**2 - 1/600*g**6 + 1/100*g**5 + j*g - 1/1050*g**7 - 1/15*g**3 + 1/120*g**4. Factor h(x).
-(x - 1)**2*(x + 1)*(x + 2)/5
Let j be 12/16 + ((-15)/4)/(-3). Let 2/3 - 2/3*p**j - 7/3*p + 7/3*p**3 = 0. Calculate p.
-1, 2/7, 1
Let k(n) = -10*n**2 + 3*n - 5. Let s(q) = -11 + 5*q - 21*q**2 - 2*q + 7*q - 4*q. Let b(y) = 13*k(y) - 6*s(y). Let b(l) = 0. Calculate l.
-1/4, 1
Let u(f) be the second derivative of 0*f**3 - f + 0 + f**2 + 1/120*f**5 - 1/48*f**4. Let t(s) be the first derivative of u(s). Factor t(v).
v*(v - 1)/2
Determine h, given that 4/3*h**3 + 1/3*h**4 + 0 + 5/3*h**2 + 2/3*h = 0.
-2, -1, 0
Let m(t) be the third derivative of 1/15*t**3 - 2*t**2 + 2/75*t**5 + 0 + 1/12*t**4 + 0*t. Solve m(y) = 0 for y.
-1, -1/4
Let o be (-1)/((-1)/2) - 1. Suppose -2*i = 4*h - 20, h = i + 1 + o. Factor 2*d**2 + 8*d**4 - 3*d**i - d**2 + 6*d**3.
2*d**2*(d + 1)*(4*d - 1)
Determine w so that 3 - 8*w + 15*w**2 + 48*w + 9 - 3*w**2 - 48*w**3 - 16*w**4 = 0.
-3, -1/2, 1
Let j = -48 - -145/3. Suppose -2 + 2 = 3*y. Factor y + 2/3*c**2 - 1/3*c**3 - j*c.
-c*(c - 1)**2/3
Let q be (2/(-3))/(2/((-3)/3)). Factor 0 + 1/3*j - q*j**2.
-j*(j - 1)/3
Factor 0 + 1/5*k**3 + 2/5*k**4 - 8/5*k**2 - 4/5*k.
k*(k - 2)*(k + 2)*(2*k + 1)/5
Let 6/7 + 6/7*p**2 - 9/7*p**3 + 3*p = 0. What is p?
-1, -1/3, 2
Let g = -337/3 - -113. Solve -4/3 + 2/3*b**2 + g*b = 0.
-2, 1
Let s(d) be the second derivative of 0 + 0*d**3 - 1/270*d**5 - d**2 + 1/108*d**4 + 2*d. Let o(r) be the first derivative of s(r). Let o(t) = 0. Calculate t.
0, 1
Factor -42*f - 294 - 3/2*f**2.
-3*(f + 14)**2/2
Let d(u) = 24*u**5 - 57*u**3 - 33*u**2 - 33*u - 33. Let p(j) = -3*j**5 + 7*j**3 + 4*j**2 + 4*j + 4. Let x(o) = 4*d(o) + 33*p(o). Factor x(q).
-3*q**3*(q - 1)*(q + 1)
Suppose 4*r - 5*a = 23, -5*r - a + 13 = -2*a. Find d such that -2/7 + 0*d + 2/7*d**r = 0.
-1, 1
Determine v so that -20/3*v**2 + 5/3*v**3 + 0 - 25/3*v = 0.
-1, 0, 5
Let z(v) = 12*v**3 + 20*v**2 + 27*v - 7. Let s(r) = 11*r**3 + 20*r**2 + 26*r - 6. Let q(p) = -7*s(p) + 6*z(p). Factor q(x).
-5*x*(x + 2)**2
Let u(s) be the second derivative of -s**7/168 + s**6/24 - 9*s**5/80 + 7*s**4/48 - s**3/12 - 4*s. What is d in u(d) = 0?
0, 1, 2
Let l = -7/8 - -9/8. Determine r so that l*r + 1/4*r**2 - 1/2 = 0.
-2, 1
Let l(n) = -3*n**2. Let p(w) = 8*w. Let m(g) = -7*g. Let h(j) = -