.
-2*w*(w - 3)/3
Let r(h) be the second derivative of -1/5*h**2 + 0*h**3 + 0 + 2*h + 1/30*h**4. Factor r(v).
2*(v - 1)*(v + 1)/5
Let a(k) be the third derivative of k**8/840 - k**6/300 - 3*k**2. Factor a(q).
2*q**3*(q - 1)*(q + 1)/5
Let c be (-6)/4 + 56/16. Let 2*t - c*t**2 + 2/3*t**3 - 2/3 = 0. Calculate t.
1
Let w(h) = -h**5 + 5*h**3 - 2 - 1 + 8 + h - 3*h**2 + 3*h**4. Let r(n) = -n**5 + 4*n**4 + 6*n**3 - 4*n**2 + n + 6. Let t(x) = 5*r(x) - 6*w(x). Factor t(k).
k*(k - 1)*(k + 1)**3
Let l(h) be the second derivative of -h**4/12 + 5*h**3/12 - h**2/2 - 10*h. Find t, given that l(t) = 0.
1/2, 2
Let p(t) be the first derivative of -2*t**3/21 + 16*t**2/7 - 128*t/7 + 18. Factor p(q).
-2*(q - 8)**2/7
Let r(h) = 2*h**2 - 5*h - 23. Let t be r(5). Find s, given that -3/4 - 1/4*s**t - s = 0.
-3, -1
Let c(v) be the second derivative of -3*v + 2/21*v**4 - 3/49*v**7 + 0 + 0*v**2 - 4/35*v**6 - 1/21*v**3 + 1/35*v**5. Suppose c(t) = 0. What is t?
-1, 0, 1/3
Let j(o) be the first derivative of 0*o + 2/5*o**5 - 1/3*o**2 + 5 + 2/9*o**3 + 5/6*o**4. Factor j(k).
2*k*(k + 1)**2*(3*k - 1)/3
Let 2855*k**2 - 210 - 1090*k**2 + 214 + 220*k + 1260*k**2 = 0. What is k?
-2/55
Let n(v) be the second derivative of -1/60*v**5 - 2*v + 0*v**3 + 1/12*v**4 - 2/3*v**2 + 0. Solve n(t) = 0.
-1, 2
Suppose -12*k + 37*k**2 - 3 - 5 - 41*k**2 = 0. Calculate k.
-2, -1
Let b be 10/(-4) + 1/((-1)/(-3)). Solve 0 + b*r - 3/2*r**2 - 1/2*r**4 + 3/2*r**3 = 0.
0, 1
Let i = 8429/1179 - 5/131. What is p in -32/9*p - 32/9*p**2 - 2/9*p**5 + 16/9*p**3 + 4/9*p**4 + i = 0?
-2, 2
Let n = -1 - -4. Suppose -n*a - 6 = -6*a. Suppose -3*f**5 + 4*f**4 - 3*f**a + 3*f**4 - 5*f**3 + 8*f**2 - 4*f**2 = 0. Calculate f.
0, 1/3, 1
Let k = -1231/13 + 95. What is w in -k + 6/13*w - 6/13*w**3 + 2/13*w**2 + 2/13*w**4 = 0?
-1, 1, 2
Let c = 2 - -2. Let w = -2 + 4. Factor -6*f**w + 1 - 3 - c*f + 4*f**2.
-2*(f + 1)**2
Let v(d) be the second derivative of 3*d**5/20 + d**4/2 - d**3/2 - 3*d**2 - 2*d. Factor v(r).
3*(r - 1)*(r + 1)*(r + 2)
Let t(l) be the third derivative of l**7/2520 + l**6/360 - l**5/120 - l**4/72 + 5*l**3/72 + 21*l**2. Find r such that t(r) = 0.
-5, -1, 1
Let z(f) be the first derivative of -f**5/80 + f**4/16 - 5*f**2/2 - 5. Let t(k) be the second derivative of z(k). Find g such that t(g) = 0.
0, 2
Let 0*r - 6/7*r**2 + 2/7*r**3 + 8/7 = 0. What is r?
-1, 2
Let d(y) = 20*y**2 - 26*y + 24. Let a(n) = n**2 - n + 1. Let g(l) = -36*a(l) + 2*d(l). Factor g(t).
4*(t - 3)*(t - 1)
Let v(y) be the first derivative of y**3/18 - y**2/6 + y/6 + 22. What is o in v(o) = 0?
1
Let f(i) be the first derivative of 8*i**3 - i**4 - 4*i**3 - 18*i**2 + 6 + 4*i**3. Factor f(u).
-4*u*(u - 3)**2
Determine r so that 2/9*r**4 - 4/9*r**3 - 4/9*r**2 + 2/9 + 2/9*r**5 + 2/9*r = 0.
-1, 1
Let k(u) = 4*u**2 + 20*u - 10. Let h(f) be the third derivative of 3*f**2 + 1/60*f**5 + 1/6*f**4 - 1/3*f**3 + 0 + 0*f. Let a(w) = 14*h(w) - 3*k(w). Factor a(b).
2*(b - 1)**2
Let j = 10/27 + 8/27. Let -4/3*k**5 + 0 + 2*k**4 + j*k**3 - 2*k**2 + 2/3*k = 0. Calculate k.
-1, 0, 1/2, 1
Let r(y) be the second derivative of -y**4/24 - y**3/12 + 22*y. Factor r(c).
-c*(c + 1)/2
Determine j so that -32/3*j - 28/3*j**3 + 8/3 + 46/3*j**2 + 2*j**4 = 0.
2/3, 1, 2
Let f = 11 - 9. Let d be 10/2 + -3 + f. Factor 0 + 0*l**2 - 1/5*l**5 - 1/5*l + 2/5*l**3 + 0*l**d.
-l*(l - 1)**2*(l + 1)**2/5
Let l = -179 + 183. Let a(p) be the first derivative of 3*p + 3/5*p**5 + 3/2*p**2 + 1/2*p**6 + l - 3/2*p**4 - 2*p**3. Factor a(x).
3*(x - 1)**2*(x + 1)**3
Factor 2/13*n**3 + 0 + 2/13*n**4 + 0*n**2 + 0*n.
2*n**3*(n + 1)/13
Let 9*c**3 - 34*c + 15*c**4 - 10 - 5*c**2 + 16*c**3 + 9*c = 0. What is c?
-1, -2/3, 1
Let h(w) be the first derivative of w**2/2 + w + 4. Let u(p) = -p**2 + 4*p + 7. Let a(o) = 5*h(o) - u(o). Suppose a(x) = 0. What is x?
-2, 1
Let 4/5*s**3 - 19/5*s**2 + 4/5 - 4/5*s + 3*s**4 = 0. What is s?
-1, -2/3, 2/5, 1
Let f(y) be the third derivative of y**7/70 + 3*y**6/40 + 3*y**5/20 + y**4/8 - 16*y**2. Factor f(b).
3*b*(b + 1)**3
Let v be (-4 - (3 - 11))/1. Suppose -v*i - 5 = -17. Suppose -1 + k**2 + 1/2*k - 1/2*k**i = 0. What is k?
-1, 1, 2
Let a(r) be the first derivative of -2*r**3/9 + 7*r**2/3 - 20*r/3 + 17. Factor a(u).
-2*(u - 5)*(u - 2)/3
Suppose 1/7*t**2 + 4/7 - 4/7*t = 0. Calculate t.
2
Let k = -12 + 16. Factor 62*g**3 - 18 + 76*g + k*g**5 - 28*g**4 + 14*g**3 + 2 - 100*g**2 - 12*g.
4*(g - 2)**2*(g - 1)**3
Let 3 - h**2 - 2 - 40*h**3 + 39*h**3 + h = 0. What is h?
-1, 1
Suppose -4*y + 19 + 5 = 0. Let u = y + -4. Factor -6/7*x**3 + 0 - 2/7*x + 6/7*x**u + 2/7*x**4.
2*x*(x - 1)**3/7
Let c(d) be the first derivative of -3 - 1/48*d**4 + 0*d**5 + d + 1/120*d**6 + 0*d**3 + 0*d**2. Let o(x) be the first derivative of c(x). Factor o(f).
f**2*(f - 1)*(f + 1)/4
Let j(i) = -2*i**3 - 4*i**2 - 6*i + 8. Let d(s) = 3*s**3 + 4*s**2 + 7*s - 9. Let y(r) = 4*d(r) + 5*j(r). Factor y(p).
2*(p - 2)*(p - 1)*(p + 1)
Suppose 9*o - 2 - 25/4*o**3 - 15/2*o**2 = 0. What is o?
-2, 2/5
Let m be (0 - -2)/4*2. Factor -w**2 + m - w + 0 - 1.
-w*(w + 1)
Let a(y) be the first derivative of 0*y - 4/3*y**3 + 1/2*y**4 + y**2 - 1. Factor a(r).
2*r*(r - 1)**2
Let h(b) = b - 16. Let p be h(18). Let o(z) be the second derivative of 1/24*z**3 + 1/48*z**4 - z + 0 - 1/120*z**6 + 0*z**p - 1/80*z**5. Factor o(n).
-n*(n - 1)*(n + 1)**2/4
Let -4*t - 12/5*t**2 + 8/5 = 0. What is t?
-2, 1/3
Let f = 60 + 21. Let d be ((-2)/(-15))/(18/f). Find u, given that -2/5 + 12/5*u**2 - 7/5*u**3 - d*u = 0.
-2/7, 1
Suppose 0 = -18*h + 41 + 13. Determine t, given that -3/2*t**2 + 1/2*t**h + 0 + t = 0.
0, 1, 2
Let u = 3 - 0. Let n be (-4)/((-16)/12) - 1. Factor -2*l**3 - l - 6*l**2 + u*l + n*l**4 - 2 + 6.
2*(l - 2)*(l - 1)*(l + 1)**2
Let t(n) be the third derivative of -n**5/4 - 5*n**4/24 + 5*n**3/3 + 19*n**2. Factor t(a).
-5*(a + 1)*(3*a - 2)
Let g(j) be the third derivative of j**5/150 + j**4/20 + 2*j**3/15 - 3*j**2. Factor g(n).
2*(n + 1)*(n + 2)/5
Let c(s) be the second derivative of 0*s**2 - 1/27*s**3 + 0 - 1/54*s**4 + 3*s. Let c(t) = 0. Calculate t.
-1, 0
Let k(n) = -n**3 - 13*n**2 - 11*n + 14. Suppose -2*t + 43 + 3 = -4*m, -2*m + 2*t = 22. Let l be k(m). Factor 2/5*x**l + 4/5 - 6/5*x.
2*(x - 2)*(x - 1)/5
Factor -7*z**3 + 1 - 1/2*z**5 + 8*z**2 - 9/2*z + 3*z**4.
-(z - 2)*(z - 1)**4/2
Let w = 21 - 19. Let m(n) be the second derivative of 1/5*n**5 + 0 - 1/3*n**3 + n**w - 1/21*n**7 - 1/3*n**4 + 2*n + 1/15*n**6. Find b, given that m(b) = 0.
-1, 1
Let d(x) be the second derivative of x**6/45 + x**5/30 - x**4/18 - x**3/9 + x. Factor d(y).
2*y*(y - 1)*(y + 1)**2/3
Let o(b) be the first derivative of 5/12*b**3 + 11 - 2*b**2 + b + 25/16*b**4. Factor o(f).
(f + 1)*(5*f - 2)**2/4
Solve 78*c**2 - 6*c - 81*c**2 + 3 - 3 = 0 for c.
-2, 0
Let k be ((-5)/10*2 + 1)/2. Let v(n) be the third derivative of 0*n - 1/360*n**6 - n**2 + k*n**3 - 1/72*n**4 + 1/90*n**5 + 0. Solve v(w) = 0 for w.
0, 1
Suppose -j**3 - 3*j**3 + 9 + 15 + 15*j + 13*j = 0. Calculate j.
-2, -1, 3
Suppose -1/9*b**2 + 1/3*b + 4/9 = 0. Calculate b.
-1, 4
Let x(a) = 3*a**4 - 18*a**3 + 28*a**2 - 22*a + 5. Let b(w) = -65*w**4 + 395*w**3 - 615*w**2 + 485*w - 110. Let g(l) = 2*b(l) + 45*x(l). Factor g(k).
5*(k - 1)**4
Let p = -405 + 813/2. Let 3/2*z - p*z**2 + 0 = 0. Calculate z.
0, 1
Suppose 3*i**3 + 0*i**3 + 3*i**2 - 3*i**2 = 0. What is i?
0
Let v be (-4)/10*15/(-21). Suppose v*i**5 - 18/7*i**4 + 64/7*i**3 - 32/7 - 16*i**2 + 96/7*i = 0. Calculate i.
1, 2
Let y(r) be the third derivative of -r**7/1080 + r**6/240 - r**5/180 - r**4/24 - 4*r**2. Let s(w) be the second derivative of y(w). Factor s(q).
-(q - 1)*(7*q - 2)/3
Suppose 3 = 2*c + 1. Let o be (-33)/(-42) + c/(-2). Let 2/7*x**5 + 0 + 6/7*x**3 + o*x**2 + 0*x + 6/7*x**4 = 0. Calculate x.
-1, 0
Let v(x) be the second derivative of -x**8/1680 + x**6/360 - x**3/3 + 3*x. Let z(k) be the second derivative of v(k). Factor z(q).
-q**2*(q - 1)*(q + 1)
Solve -7/5*f + 2 + 1/5*f**2 = 0.
2, 5
Suppose 14 + 6 = 5*g. Suppose 2*t = 4*a - 32, 6*a - g*t = 2*a + 40. Factor -2 - a*c + 7/2*c**2.
(c - 2)*(7*c + 2)/2
Let w = -2/27 - -122/189. Let b(d) be the first derivative of 10/21*d**3 + w*d - 9/7*d**2 - 2/5*d**5 + 3 + 9/14*d**4. Determine q, given that b(q) = 0.
-1, 2/7, 1
Let a(o) be the first derivative of o**5/10 - o**4/3 + o**3/3 - 4*o + 4. Let q(l) be the fir