t v(y) be the second derivative of y**4/6 + 2*y**3/3 + y**2 + 29*y. Determine i so that v(i) = 0.
-1
Factor 5/3*p + 1/3*p**3 + 2/3 + 4/3*p**2.
(p + 1)**2*(p + 2)/3
Let j(d) be the third derivative of -d**5/60 - 5*d**2. Factor j(o).
-o**2
Let d = -4 - -9. Let w(a) be the first derivative of 4*a + d*a**2 - 2 - 14/3*a**3. Suppose w(r) = 0. What is r?
-2/7, 1
Suppose -5*k + 6 + 0 = -3*i, -k - 2*i - 4 = 0. Suppose -2*q + 15 = 3*q. Solve -9/2*p**3 + k + q*p**2 + 3/2*p**4 + 0*p = 0.
0, 1, 2
Let q(v) be the first derivative of v**4/42 + v**3/7 + 2*v**2/7 + 3*v + 2. Let p(r) be the first derivative of q(r). Factor p(u).
2*(u + 1)*(u + 2)/7
Determine t so that 2/5*t**2 - 2/5 - 2/5*t**3 + 2/5*t = 0.
-1, 1
Let j(h) be the first derivative of -4*h**3/3 + 6*h**2 - 8*h + 18. Determine n so that j(n) = 0.
1, 2
Suppose 3*w + 8 = 17. Suppose -4*o**3 - 9*o**4 + 7*o**w + 6*o**2 - 6*o**3 = 0. What is o?
-1, 0, 2/3
Let b be -1 + 2/((-3840)/(-1924)). Let w(q) be the third derivative of -1/120*q**5 + 0 + 2*q**2 + 0*q**3 - 1/96*q**4 + 0*q - b*q**6. Factor w(v).
-v*(v + 1)**2/4
Let b = 1289 - 12887/10. Suppose 0*l**2 + 1/10*l**3 + 1/5 - b*l = 0. What is l?
-2, 1
Let d(x) = x**2 - x - 1. Let s(f) = -f**2 + 15*f - 33. Let h(v) = d(v) - s(v). Suppose h(l) = 0. Calculate l.
4
Let m(f) = -f**3 - f**2 - f + 1. Let v(i) = -3*i**4 - i**3 + 5*i**2 - i - 2. Let b(t) = -m(t) + v(t). Determine w so that b(w) = 0.
-1, 1
Let s(w) = w + 1. Let k be s(2). Determine n so that -n**4 - 13*n**2 - 7*n**2 - 7*n**k + 23*n**3 - 3*n**4 + 8*n = 0.
0, 1, 2
Let v(n) be the first derivative of -2*n**3/3 + n**2 - 10. Factor v(y).
-2*y*(y - 1)
Find c such that -4/7*c**4 + 0 + 48/7*c + 4*c**3 - 64/7*c**2 = 0.
0, 2, 3
Let y be 420/147 + (-4)/14. Suppose 2/7*h**4 + 4/7 - 2*h - 10/7*h**3 + y*h**2 = 0. Calculate h.
1, 2
Let c(z) be the first derivative of z**6/180 - z**5/90 + z**2 + 1. Let s(b) be the second derivative of c(b). Solve s(k) = 0 for k.
0, 1
Factor 4*q**2 + q**4 - 23*q**3 + 11*q**3 + 3*q**4 + 4*q**2.
4*q**2*(q - 2)*(q - 1)
Let r(k) be the third derivative of k**5/240 + k**4/96 - 4*k**2. Factor r(q).
q*(q + 1)/4
Let s be (-24)/(-14)*(-126)/(-12). Suppose -19*p = -s*p. Suppose -6*u**2 - 10/3*u**3 + 14/3*u**5 + 6*u**4 + p - 4/3*u = 0. What is u?
-1, -2/7, 0, 1
Let r = 45 - 40. Find n such that -1/2*n**r + 3*n**2 - 2/3*n**4 + 1/3 + 11/6*n + 4/3*n**3 = 0.
-1, -1/3, 2
Let -8*h - 23*h**2 + 6 - 2 - 16*h**3 - 5*h**2 = 0. What is h?
-1, 1/4
Let a(y) be the third derivative of 5*y**8/112 - 11*y**7/35 + 23*y**6/40 - 3*y**5/10 - 16*y**2. Find f, given that a(f) = 0.
0, 2/5, 1, 3
Let z(p) be the first derivative of 3*p**5/5 + 9*p**4/4 - 6*p**2 + 5. Factor z(y).
3*y*(y - 1)*(y + 2)**2
Let n be 0/(4 + 2) + 4. Let w(h) be the second derivative of 0 - h + 4/5*h**2 + 0*h**3 - 1/30*h**n. Factor w(t).
-2*(t - 2)*(t + 2)/5
Let k(i) be the second derivative of 0 + 0*i**2 + 0*i**4 - 3*i - 1/60*i**6 + 0*i**3 + 1/40*i**5. Let k(a) = 0. Calculate a.
0, 1
Let w be 2/(-8) - 36/(-16). Factor 3*k**5 - 7*k + 6*k**w - 10*k**4 + 3 + k**4 - 2*k + 6*k**3.
3*(k - 1)**4*(k + 1)
Let w(a) be the first derivative of -2*a**5/45 + 2*a**3/27 + 15. Solve w(z) = 0 for z.
-1, 0, 1
Let p(m) be the first derivative of -2*m**3/39 - m**2/13 + 4*m/13 - 3. Let p(z) = 0. Calculate z.
-2, 1
Let m(s) = 4*s**2 + 5 - s**2 + 7*s + 2*s**2. Let t(g) = -8*g + g**2 - 5 - 1 - 7*g**2. Let v(a) = 4*m(a) + 3*t(a). Factor v(f).
2*(f + 1)**2
Let w = 12 - 9. Factor 3*p**4 + 0*p**4 - 2*p**w + 2*p**2 + 2*p - 5*p**4.
-2*p*(p - 1)*(p + 1)**2
Suppose 0 = -3*h - 12, -7*h = 5*a - 2*h + 10. Suppose 9*m**a + 3*m**3 - 12 + 6 + 9*m + 9 = 0. Calculate m.
-1
Let z be (256/40 - 4)*10/14. Let -8/7*q**4 + 0 - 2/7*q - z*q**3 - 2/7*q**5 - 8/7*q**2 = 0. Calculate q.
-1, 0
Suppose 2 = 2*k - 5*f, 5*k = f + f + 26. Let r(d) = d. Let u(j) = 3*j**2 + 11*j + 2. Let h(w) = k*r(w) - u(w). Factor h(c).
-(c + 1)*(3*c + 2)
Let t(p) be the third derivative of 0 - 7/8*p**4 - 1/35*p**7 + 0*p + 2*p**2 + 1/112*p**8 - 1/20*p**6 + p**3 + 2/5*p**5. What is y in t(y) = 0?
-2, 1
Let w(b) be the second derivative of -b**8/2240 + b**7/840 - b**6/1440 - b**3/6 + 3*b. Let q(i) be the second derivative of w(i). Find d, given that q(d) = 0.
0, 1/3, 1
Let p(t) be the third derivative of t**5/20 + 5*t**4/8 + 3*t**2 + 3. Factor p(h).
3*h*(h + 5)
Let g(i) be the second derivative of -5*i**7/84 + 11*i**6/30 - 19*i**5/20 + 4*i**4/3 - 13*i**3/12 + i**2/2 + i. Suppose g(p) = 0. Calculate p.
2/5, 1
Suppose 4*c - 4 = -3*l, -5*l + l = -c + 1. Suppose l = k - 17 + 2. Determine m so that 6 + k*m**3 + m + 26*m + 36*m**2 + 0*m**2 = 0.
-1, -2/5
Suppose 2/3 - 2/3*l - 2/3*l**2 + 2/3*l**3 = 0. What is l?
-1, 1
Let h(o) be the first derivative of 0*o**2 + 1/27*o**3 - o + 4/135*o**6 - 7/90*o**5 + 1/27*o**4 - 3. Let l(y) be the first derivative of h(y). Factor l(f).
2*f*(f - 1)**2*(4*f + 1)/9
Let c(r) be the third derivative of -r**5/20 + r**4/2 + 5*r**3/2 + 5*r**2. Factor c(f).
-3*(f - 5)*(f + 1)
Let l(d) be the first derivative of -4*d**5 + 7*d**4 - 8*d**3/3 - 2. Factor l(k).
-4*k**2*(k - 1)*(5*k - 2)
Factor 2/7*z - 2/7*z**3 + 0*z**2 + 0.
-2*z*(z - 1)*(z + 1)/7
Suppose 4 + 16 = 4*i. Suppose 3*t - i - 1 = 0. Factor 3*v**t - v**2 + 2*v**3 + 2*v**4 - 2*v - 4*v**4.
-2*v*(v - 1)**2*(v + 1)
Let -2*s + 2*s + s**2 + s + 0*s**2 = 0. What is s?
-1, 0
Let h(g) be the first derivative of -1/2*g + 4 - 1/6*g**3 + 1/2*g**2. Factor h(m).
-(m - 1)**2/2
Suppose -3*l - 2*l + 45 = -5*o, 4*o + 20 = 0. Suppose 0 = 2*d + 8, -6*z = -4*z - 5*d - 24. Solve -l - 2*g + z*g**3 + 3*g**4 + 5 - 4*g**4 + 0 = 0.
-1, 1
Let l = -8/71 + 1618/497. Let x = 80/21 - l. Factor -x*y**3 + 0*y**2 + 2/3*y + 0.
-2*y*(y - 1)*(y + 1)/3
Let l(g) be the third derivative of -g**5/60 + 7*g**4/24 - g**3 - 2*g**2. Let j be l(4). Find b, given that 2*b**2 + 2*b + 6 - j = 0.
-1, 0
Let -9*x**2 + 7*x**2 - 4*x**2 - 27*x - 3*x**3 - 12*x**2 = 0. Calculate x.
-3, 0
Let o(w) be the second derivative of -w**4/12 - 2*w**3/3 - 2*w**2 - 5*w. Solve o(s) = 0.
-2
Let o be (4/18)/((-20)/(-30)). Factor 0*i + 0 + 0*i**3 - o*i**4 + 1/3*i**2.
-i**2*(i - 1)*(i + 1)/3
Let b(l) be the first derivative of l**6/540 - l**5/90 + l**4/36 - l**3 - 1. Let u(s) be the third derivative of b(s). Factor u(r).
2*(r - 1)**2/3
Let s = -6 - -8. Let o(j) be the first derivative of 3*j + j**3 - 5*j**s - 1 + j + j**3. Find x, given that o(x) = 0.
2/3, 1
Let r(q) be the third derivative of -q**8/84 - 4*q**7/105 + q**6/10 + 4*q**5/15 - 2*q**4/3 - 5*q**2. Solve r(j) = 0.
-2, 0, 1
Let r be 5 + -6 + 44/17. Let q = r + -19/119. Determine z so that -2/7 - q*z - 8/7*z**2 = 0.
-1, -1/4
Let t(u) be the first derivative of -4*u + 3*u**2 + 2/5*u**5 - 3/2*u**4 - 2 + 2/3*u**3. Find a, given that t(a) = 0.
-1, 1, 2
Let b(x) be the first derivative of x**3 + 3*x**2/2 - 6*x - 9. Determine t, given that b(t) = 0.
-2, 1
Let x = 193/2 - 96. Let h(y) be the first derivative of 2/15*y**5 - x*y**4 - 1/3*y**2 + 2 + 2/3*y**3 + 0*y. Factor h(t).
2*t*(t - 1)**3/3
Determine i, given that -61/2*i**2 - 42*i - 7*i**3 - 1/2*i**4 - 18 = 0.
-6, -1
Let m be -1 - 3/7*3/(-1). Factor 6/7*a**3 + 2/7*a + m*a**4 + 6/7*a**2 + 0.
2*a*(a + 1)**3/7
Let x(p) be the first derivative of p**5/5 + 7*p**4/6 + 23*p**3/9 + 8*p**2/3 + 4*p/3 + 3. Factor x(j).
(j + 1)**2*(j + 2)*(3*j + 2)/3
Let s(h) be the second derivative of -5*h**6/27 - h**5/3 - h**4/6 - 4*h. Suppose s(d) = 0. What is d?
-3/5, 0
Suppose -8*h + 4*h = -4. Let r(k) = -k**3 - k**2 + k + 1. Let b(o) = 16*o**3 + 4*o**2 - 12*o - 12. Let m(w) = h*b(w) + 12*r(w). Factor m(c).
4*c**2*(c - 2)
Let a(d) be the third derivative of -d**7/630 - d**6/60 - d**4/8 - d**2. Let p(u) be the second derivative of a(u). Suppose p(f) = 0. Calculate f.
-3, 0
Suppose -6/5*v**4 + 0*v**3 + 0 + 8/5*v**2 - 2/5*v**5 + 0*v = 0. Calculate v.
-2, 0, 1
Let d be (-214)/(-40) - 4/8. Let a = d - 23/5. What is i in 0 - 1/4*i**3 + a*i**4 - 1/4*i**2 + 1/4*i = 0?
-1, 0, 1
Let v(w) = -w**2 - 1. Let n(k) = -40 + 22 + 8 - 8*k**2. Let j(g) = n(g) - 10*v(g). Find t such that j(t) = 0.
0
Let s(a) be the first derivative of 1/10*a**5 - 2 - 3/8*a**4 + 3/4*a**2 - a + 1/6*a**3. Let s(q) = 0. What is q?
-1, 1, 2
Let q(y) = -3*y**2 + 2*y + 2. Let o be q(2). Let l be (-76)/(-84) - o/14. Factor 0*u + 2*u**3 + 0*u**4 - 2/3*u**5 + 0 + l*u**2.
-2*u**2*(u - 2)*