et a(q) be the first derivative of q**6/60 + q**5/10 - 4*q**3/3 - q**2/2 - 7. Let t(l) be the second derivative of a(l). Factor t(n).
2*(n - 1)*(n + 2)**2
Let g = 18085/3 + -6028. Factor 0 + 0*y**4 + 2/3*y**2 + 0*y + g*y**5 - y**3.
y**2*(y - 1)**2*(y + 2)/3
Let z(j) be the first derivative of -j**4/30 - 692*j**3/45 - 29929*j**2/15 + 161. Factor z(c).
-2*c*(c + 173)**2/15
Suppose 161 = 3*c + 5*n, 3*n = -3*c + n + 158. Suppose -1 - 9*f - 67*f**3 - 27*f**2 + 4 + c*f**3 = 0. What is f?
-1, 1/5
Factor 16*h**3 + 1749*h**2 - 16*h**3 - 1749*h**2 + 3*h**5 - 87*h**4.
3*h**4*(h - 29)
Let p(g) be the third derivative of 2/3*g**3 + 0 - 1/8*g**4 + 0*g + 21*g**2 - 1/60*g**5. Find s, given that p(s) = 0.
-4, 1
Let k = -7509/10 - -751. Find h, given that -1/10*h + k*h**2 + 0 = 0.
0, 1
Let x be 2/4 - (-9)/2. Let d = -15132/35 - -2166/5. Factor d*g**3 - 3/7*g**4 - 3/7*g**x + 0*g + 0 + 0*g**2.
-3*g**3*(g - 1)*(g + 2)/7
Let t(m) = -2 - 13 + 14*m**2 - 9*m - 15*m**2. Let c be t(-6). Find s, given that -c*s - 5*s**2 - s**3 + 4*s**3 + s**4 - s**5 + 5*s = 0.
-2, 0, 1
Factor -164*s - s**4 + 86*s - 3*s**4 - 29*s**2 + 21*s**3 + 84*s.
-s*(s - 3)*(s - 2)*(4*s - 1)
Suppose 5*d + 0*d = 10. Let f(k) = -k + 2. Let t be f(-1). Determine s so that -3*s + s**3 + 5*s**d + 14*s**2 - 10*s**3 - t - 4*s**2 = 0.
-1/3, 1
Factor 42*x + 6/5*x**2 + 396/5.
6*(x + 2)*(x + 33)/5
Let n(m) = m**4 + m**3 + m**2 - m - 1. Let k(i) = i**3 - 5*i**3 + 6 + 6*i - 931*i**2 + 925*i**2 - 8*i**4. Let r(j) = k(j) + 6*n(j). Solve r(s) = 0.
0, 1
Let w(i) = i**3 + i**2 - i. Let p(u) be the third derivative of -u**6/40 - u**5/10 - u**4/8 - u**3 + 8*u**2. Let d(c) = p(c) + 6*w(c). Solve d(y) = 0.
-1, 2
Let v be (3/(-2))/(3/(-6)). Suppose -5*f**4 + 5*f**v - 19*f + 19*f = 0. What is f?
0, 1
Let r be 10/8*2/5. Suppose 12*p - 2 = 10*p, -5*u - 2*p = -22. Solve r*g**2 + u*g + 8 = 0 for g.
-4
Let -65*p**2 + 9*p - 50*p**3 + 0*p - p + 212*p**3 - 7*p**2 = 0. Calculate p.
0, 2/9
Let o(v) be the second derivative of -v**5/10 + v**4/3 + 41*v**3/3 - 42*v**2 - 108*v. Suppose o(d) = 0. Calculate d.
-6, 1, 7
Suppose 2*q = -13*n + 11*n + 6, 0 = -2*n + 4*q + 12. Determine r so that 8/3*r**3 + 4/3*r + 0 + 10/3*r**2 + 2/3*r**n = 0.
-2, -1, 0
Let o be 935/561*(-11 + 15)*(-6)/(-20). Factor 0 + 20/9*b + 4/9*b**o.
4*b*(b + 5)/9
Let c(b) be the second derivative of b**5/70 + 2*b**4/21 - 5*b**3/21 + 2*b + 22. Factor c(z).
2*z*(z - 1)*(z + 5)/7
Let w(p) be the first derivative of 2/5*p**2 - 1/5*p**3 - 7/20*p**4 + 0*p + 20. Solve w(r) = 0 for r.
-1, 0, 4/7
Let i be (-120)/32*(11/(-10) + 1). Find y such that -i + 3/8*y**2 - 3/8*y**3 + 3/8*y = 0.
-1, 1
Suppose 0 = 2*v - 5*v - 9*v. Let i(u) be the first derivative of -u**3 + 9/2*u**2 + v*u - 4. Factor i(x).
-3*x*(x - 3)
Suppose -3*d + 52 = -k, d + 0*k - 12 = -k. Let f be (1*(-4 - d/(-6)))/(-3). Factor 0*l**3 + f*l**2 - 2/9*l + 0 - 4/9*l**4 + 2/9*l**5.
2*l*(l - 1)**3*(l + 1)/9
Let c(t) be the third derivative of t**5/420 + t**4/12 + 4*t**3/7 - 150*t**2. Factor c(h).
(h + 2)*(h + 12)/7
Suppose 3*z - 25 + 1 = 0. Solve 12*m**4 + 40 - 46*m**2 + 52*m**2 + z*m**4 - 5*m**5 - 56*m**2 - 5*m**3 + 20*m = 0 for m.
-1, 2
Let l(y) be the first derivative of -120*y**2 + 144*y - 13 + 4/5*y**5 + 10*y**4 + 52/3*y**3. What is f in l(f) = 0?
-6, 1
Let a = -8 + 12. Suppose a*x + 8 = 2*d + 2*d, -4*d - 3*x + 8 = 0. Factor -4 - 2*r**3 + 42*r**2 + d - 40*r**2 + 2*r.
-2*(r - 1)**2*(r + 1)
Let m(b) be the third derivative of -b**5/270 - 5*b**4/108 + 2*b**3/9 - 82*b**2. Factor m(z).
-2*(z - 1)*(z + 6)/9
Let l = 1181/150 + -47/6. Let b(k) be the second derivative of 1/75*k**6 + 0 - l*k**5 + 0*k**2 + 6*k + 0*k**3 + 1/30*k**4. Factor b(n).
2*n**2*(n - 1)**2/5
Let p(g) be the first derivative of -3*g**5/5 + 15*g**4/4 - 6*g**3 - 6*g**2 + 24*g - 137. Factor p(m).
-3*(m - 2)**3*(m + 1)
Let r(b) be the first derivative of 8 + 1/51*b**6 + 8/85*b**5 + 5/34*b**4 + 4/51*b**3 + 0*b + 0*b**2. Factor r(v).
2*v**2*(v + 1)**2*(v + 2)/17
Factor -2646/5 - 888/5*s**2 + 9513/5*s + 21/5*s**3.
3*(s - 21)**2*(7*s - 2)/5
Let z(l) be the second derivative of -l**6/60 - l**5/40 + l**4/12 + 44*l. Suppose z(p) = 0. What is p?
-2, 0, 1
Let q = 15 + -13. Let 40 - 193*u**5 - 1205*u**3 + 8*u**2 - 130*u + 470*u + 68*u**5 + 700*u**4 + 422*u**q = 0. What is u?
-1/5, 2
Factor -22 - 22*c**2 + 32 + 38 - 20*c.
-2*(c + 2)*(11*c - 12)
Factor -16/5 - 14/5*f + 2/5*f**2.
2*(f - 8)*(f + 1)/5
Suppose 2*m + 6 = 0, 4*m = 3*g - 2*g + 8. Let n be (5/g)/((-1)/(-2))*0. Factor 3/2 + n*u - 3/2*u**2.
-3*(u - 1)*(u + 1)/2
Let i(g) be the first derivative of 2*g**6/3 - 68*g**5/5 + 80*g**4 - 256*g**3/3 - 352. Factor i(w).
4*w**2*(w - 8)**2*(w - 1)
Let s be (-2*(-24)/(-36))/(-4). Let p(r) be the first derivative of 1/9*r**3 + s*r**2 + 1 + 0*r. Factor p(a).
a*(a + 2)/3
Let j(t) be the third derivative of -7*t**6/10 + 4*t**5/3 + t**4/2 - 4*t**3/3 - 21*t**2 + 3. Factor j(i).
-4*(i - 1)*(3*i + 1)*(7*i - 2)
Let -4/5*z**2 - 36/5 - 1/5*z**3 + 41/5*z = 0. What is z?
-9, 1, 4
Let k(o) be the second derivative of o**6/120 + 3*o**5/40 + 2*o**3/3 - 9*o. Let r(m) be the second derivative of k(m). Factor r(s).
3*s*(s + 3)
Suppose 0*g = -2*h + 3*g + 26, 39 = 5*h - g. Suppose 3*t**5 - 10*t**2 + h*t**4 + 3 + 4*t**2 + 3*t - 4*t**4 + 0*t**5 - 6*t**3 = 0. What is t?
-1, 1
Let f(j) = 8*j**2 - 53*j + 24. Let t(q) = 5*q**2 - 35*q + 15. Let y(n) = -5*f(n) + 7*t(n). Factor y(z).
-5*(z - 3)*(z - 1)
Let c(r) be the first derivative of -2*r**3/45 + 154*r**2/15 - 11858*r/15 + 106. Suppose c(x) = 0. What is x?
77
Let g(y) be the second derivative of -y**4/48 - y**3/24 - y - 135. Factor g(h).
-h*(h + 1)/4
Suppose 0 = w + w - x + 1, -w + 4*x - 4 = 0. Suppose 5*f - 30 = -w. Factor -f*j - 6*j**3 - 3*j**4 + 3*j**2 + 0*j + 12*j.
-3*j*(j - 1)*(j + 1)*(j + 2)
Let i(p) = -2 + 5*p + 68*p**2 - 9*p**3 - 73*p**2 + 10*p**3. Let l be i(4). Factor 2/15*o**3 - 2/15*o + 2/15*o**l - 2/15.
2*(o - 1)*(o + 1)**2/15
Let j(i) = -3*i**2 + 21*i + 26. Let v be j(8). Let k = -1 + 1. Determine y so that k*y**v + 2/5*y**4 + 4/5*y - 2/5 - 4/5*y**3 = 0.
-1, 1
Let v(k) = -21*k**3 - 23*k**2 + 101*k - 82. Let a(g) = -33*g**3 - 35*g**2 + 152*g - 124. Let y(t) = 5*a(t) - 8*v(t). Determine q so that y(q) = 0.
-6, 1, 2
Let p(n) be the first derivative of -n**6/4 - 3*n**5/5 + 3*n**4/8 + n**3 + 41. Suppose p(w) = 0. What is w?
-2, -1, 0, 1
Let l = 105 - 88. Factor t + 26*t**2 - l*t**2 + 0*t**3 + 5*t + 3*t**3.
3*t*(t + 1)*(t + 2)
Let y(b) = -10*b**2 + 36*b - 8. Let k(h) = h**2 + 5*h - 11. Let w be k(-6). Let l(x) = -11*x**2 + 36*x - 8. Let f(a) = w*y(a) + 6*l(a). Let f(u) = 0. What is u?
1/4, 2
Let b(d) be the first derivative of -d**4/7 + 32*d**3/7 + 50*d**2/7 + 226. Factor b(x).
-4*x*(x - 25)*(x + 1)/7
Let k(j) be the third derivative of -j**7/945 - 11*j**6/180 - 197*j**5/270 - 133*j**4/36 - 26*j**3/3 + 2*j**2 - 389. Determine w, given that k(w) = 0.
-26, -3, -1
Let q(f) = -13*f**3 + 76*f**2 + 150*f - 150. Let r(y) = 25*y**3 - 152*y**2 - 302*y + 302. Let w(u) = 7*q(u) + 3*r(u). Factor w(z).
-4*(z - 6)*(z + 2)*(4*z - 3)
What is r in 118*r - 13*r**2 + 2*r - 13*r**2 - 20 - 29*r**2 = 0?
2/11, 2
Let n(g) be the first derivative of g**5/50 + g**4/15 + g**3/15 - 12*g + 13. Let x(q) be the first derivative of n(q). Determine i, given that x(i) = 0.
-1, 0
Factor 7347*o + 61590 - 2271 + 3*o**4 + 11623*o**2 - 9049*o**2 + 144*o**3 + 12933*o.
3*(o + 9)*(o + 13)**3
Let f(l) be the first derivative of -l**6/9 + 16*l**5/15 - 23*l**4/6 + 56*l**3/9 - 4*l**2 + 99. Determine w so that f(w) = 0.
0, 1, 2, 3
Let f(c) be the first derivative of -3*c**4/4 - 6*c**3 - 27*c**2/2 - 12*c + 20. Factor f(q).
-3*(q + 1)**2*(q + 4)
Factor 68*n**3 + 4*n**4 - 16*n + 22*n**4 + 15*n**4 + 19*n**4 - 112*n**2.
4*n*(n - 1)*(n + 2)*(15*n + 2)
Let c(b) be the second derivative of 17*b + 1/60*b**6 + 1/8*b**2 - 5/48*b**3 - 1/8*b**4 - 1/160*b**5 + 0. Determine w so that c(w) = 0.
-1, 1/4, 2
Let d(n) be the second derivative of -n**5/20 - n**4/12 + 7*n**3/2 + 45*n**2/2 - 187*n. Determine t, given that d(t) = 0.
-3, 5
Let b(w) = -24*w**2 + 42*w - 7. Let p(q) = -12*q**2 + 21*q - 3. Let l(s) = -s + 4. Let k be l(-7). Let a(o) = k*p(o) - 6*b(o). Factor a(h).
3*(h - 1)*(4*h - 3)
Let o(y) = 4*y**5 - 19*y**4 + 15*y**3 + y**2 - y. Let z(r) = r**5 - r**4 + r**2 - r. Let u(n) = o(n) - z(n). Factor u(i)