i(r).
-2*(r - 1)**2*(r + 12)/5
Let x(w) be the third derivative of -w**5/210 - w**4/21 - w**3/7 + 19*w**2. Factor x(b).
-2*(b + 1)*(b + 3)/7
Let c be (-306)/8*206/927 + 10. Factor 0*u + 0 - 15/2*u**4 - 6*u**2 + 12*u**3 + c*u**5.
3*u**2*(u - 2)**2*(u - 1)/2
Let l(p) = 4*p**4 - 18*p**3 - 69*p**2 + 30*p + 11. Let f(x) = x**4 - 4*x**3 - 13*x**2 + 6*x + 2. Let s(a) = -11*f(a) + 2*l(a). Factor s(y).
-y*(y - 3)*(y + 1)*(3*y - 2)
Let m(i) = 2*i + 15. Let j be m(-6). Suppose -5*z**j - 3*z**2 + 0*z**2 + 2*z**3 + 6*z + 0*z**3 = 0. What is z?
-2, 0, 1
Let i(g) be the first derivative of -1/2*g**4 + 6/11*g**3 + 2/11*g**2 + 6 + 0*g. Factor i(b).
-2*b*(b - 1)*(11*b + 2)/11
Let z(a) be the second derivative of -a**4/48 + 15*a**3/4 - 2025*a**2/8 - 22*a. Suppose z(g) = 0. Calculate g.
45
Let f(o) be the second derivative of o**7/42 - o**6/10 - o**5/20 + o**4/4 - 54*o + 1. Let f(u) = 0. Calculate u.
-1, 0, 1, 3
Find s such that -27*s**2 + 15*s**4 + 17 - 9*s**3 - 3*s**5 - 5 - 12 = 0.
-1, 0, 3
Suppose 5*n**2 + 3/5*n**3 + 6/5*n - 16/5 = 0. Calculate n.
-8, -1, 2/3
Factor -46*i + 28*i - i**3 + 20*i + i**2.
-i*(i - 2)*(i + 1)
Determine r, given that 3*r**3 - 6 - 7*r**3 + 42*r - 2*r**4 + 8*r**2 - 38*r = 0.
-3, -1, 1
Let a(s) = -3*s**3 - 2*s**2 + 7*s - 7. Let j(i) = 2*i**3 + i**2 - 5*i + 5. Let c(l) = -5*a(l) - 7*j(l). Factor c(x).
x**2*(x + 3)
Let v(s) be the third derivative of -s**7/525 - s**6/900 - 4*s**3/3 + 28*s**2. Let q(z) be the first derivative of v(z). Factor q(b).
-2*b**2*(4*b + 1)/5
Let l(y) be the third derivative of 0*y + 1/180*y**6 - 1/18*y**4 + 0 - 1/630*y**7 + 1/60*y**5 - 2/9*y**3 - 13*y**2. What is b in l(b) = 0?
-1, 2
Let v(s) be the third derivative of 0 + 1/630*s**7 + 19*s**2 + 0*s + 1/72*s**6 + 0*s**3 + 1/18*s**4 + 2/45*s**5. Solve v(z) = 0 for z.
-2, -1, 0
Suppose c - 7 = -h, -2*h - 16 = -2*c - 2*c. Let m(a) = 12*a + 15. Let i(d) = d**2 + 12*d + 14. Let g(n) = h*m(n) - 3*i(n). Factor g(u).
-3*(u + 2)**2
Suppose -g + 13/5*g**2 - 6/5 - 2/5*g**3 = 0. What is g?
-1/2, 1, 6
Let x(w) be the second derivative of -w**7/6 - 47*w**6/30 - 21*w**5/10 + 32*w**4/3 - 16*w**3/3 - 421*w. Solve x(i) = 0 for i.
-4, 0, 2/7, 1
Let h(c) be the second derivative of 0*c**2 + 0 - 4/21*c**3 + 1/42*c**4 - 4*c. Suppose h(x) = 0. Calculate x.
0, 4
Let i(w) be the third derivative of w**7/42 - w**6/4 - w**5 + 35*w**4/3 + 80*w**3 + 2*w**2 + 392*w. Factor i(c).
5*(c - 6)*(c - 4)*(c + 2)**2
Suppose -c - 6 = -4*c. Factor 0*b**c + 20 - 4*b**2 - b**2.
-5*(b - 2)*(b + 2)
Let t(l) be the second derivative of -l**6/10 + l**4/4 + 244*l. Factor t(f).
-3*f**2*(f - 1)*(f + 1)
Suppose -12/13 + 2/13*j**2 - 10/13*j = 0. Calculate j.
-1, 6
Factor -376/3 + 128*q - 34*q**2 + 2/3*q**3.
2*(q - 47)*(q - 2)**2/3
Let v(p) be the first derivative of -24/7*p**3 - 4/35*p**5 - 7 - p**4 - 40/7*p**2 - 32/7*p. Factor v(b).
-4*(b + 1)*(b + 2)**3/7
Let m(n) = -n + 16. Let u be m(-11). Let t = 32 - u. Factor -3 - 6 + t*a**2 - 6 + 10*a.
5*(a - 1)*(a + 3)
Let s be (-8 - 0)/((-8)/(-12)*-3). Let -5*w**2 + 2*w + 3*w**2 + 0*w**2 + s*w**2 = 0. Calculate w.
-1, 0
Let k(x) be the first derivative of -5*x**3/3 - 20*x**2 - 60*x + 36. Factor k(j).
-5*(j + 2)*(j + 6)
Suppose 0 = 21*q + 47*q. Determine g so that -4/3*g**3 + q*g + 0 - 4/3*g**2 - 1/3*g**4 = 0.
-2, 0
Factor -31/4*m + 8*m**2 - 1/4*m**3 + 0.
-m*(m - 31)*(m - 1)/4
Let z(g) = 5*g**2 + 6*g + 4. Let n(l) = -l**2. Let f(d) = 4*n(d) + z(d). Let x(o) = -10*o**2 - 65*o - 45. Let k(a) = -45*f(a) - 4*x(a). Factor k(p).
-5*p*(p + 2)
Let h = -1855 + 1857. Let i(k) be the first derivative of 0*k**h + 1/12*k**3 - k + 9. What is p in i(p) = 0?
-2, 2
Factor -4 - 9/2*f - 1/2*f**2.
-(f + 1)*(f + 8)/2
Suppose 10*j - 6*j - 80 = 0. Let y = -18 + j. Factor -7*s**y + 3 + 1 + 8*s + 11*s**2.
4*(s + 1)**2
Let n(i) be the first derivative of i**5/8 + 25*i**4/24 + 5*i**3/3 + 40*i - 17. Let x(r) be the first derivative of n(r). Factor x(s).
5*s*(s + 1)*(s + 4)/2
Let s(q) be the third derivative of q**8/1008 + 4*q**7/315 + 7*q**6/120 + 11*q**5/90 + q**4/9 + 5*q**2 - 8. Find z such that s(z) = 0.
-4, -2, -1, 0
Let y(o) be the second derivative of o**6/120 + o**5/16 + 7*o**4/48 + o**3/8 - 201*o. Determine r so that y(r) = 0.
-3, -1, 0
Let 6*j - j**2 - 6*j + 4*j**2 = 0. Calculate j.
0
Let j be 14/(((-65)/(-39))/(5/6)). Let i(h) be the third derivative of j*h**2 + 2/15*h**4 + 16/15*h**3 + 0*h + 1/150*h**5 + 0. Factor i(p).
2*(p + 4)**2/5
Factor 1/6*j**4 + 0 + 5/6*j**2 - 2/3*j**3 - 1/3*j.
j*(j - 2)*(j - 1)**2/6
Let z(s) = s**2 + 7*s - 8. Let i be z(-8). Let w be 4 + (-288)/30 + 6. Solve 0*l**2 - 1/5*l**5 + 0*l + i - w*l**4 - 1/5*l**3 = 0 for l.
-1, 0
Let x be 9/(22/(-8) - -2). Let g = -9 - x. Solve 3 - g + 2*p**2 - 4*p**2 = 0.
0
Let m(c) = c**4 + 31*c**3 - 19*c**2 - 40*c + 9. Let b(q) = -q**4 - 16*q**3 + 9*q**2 + 20*q - 4. Let v(i) = -9*b(i) - 4*m(i). Factor v(f).
5*f*(f - 1)*(f + 1)*(f + 4)
Let v(i) be the second derivative of -i**7/10080 - i**6/576 - i**5/120 + 3*i**4/2 + 11*i. Let f(k) be the third derivative of v(k). Factor f(m).
-(m + 1)*(m + 4)/4
Let p(z) be the second derivative of 19/10*z**5 + 0 + 16*z + 8/3*z**3 - 4/15*z**6 + 4*z**2 - 9/2*z**4. Solve p(v) = 0.
-1/4, 1, 2
Let n(a) = -3*a - 5. Let m be n(-4). Let -m*t + 10*t**3 + 3*t - 4*t**2 - 6*t**3 + 1 + 3 = 0. Calculate t.
-1, 1
Let y(a) = -13*a - 180. Let i be y(-14). Let f be 6/(-4)*(-4)/3. Solve 0*w**f - 12*w**i + 3 + 3*w**2 + 6*w = 0 for w.
-1/3, 1
Let w be (1 - 2/1)*1. Let b(j) = -j. Let t(g) = 5*g**4 - 10*g**2 + 6*g + 5. Let p(o) = w*t(o) - 6*b(o). Factor p(l).
-5*(l - 1)**2*(l + 1)**2
Let t(j) = 4*j**2 - 28*j - 76. Let b(p) = -p - 1. Let f(n) = -4*b(n) - t(n). Factor f(d).
-4*(d - 10)*(d + 2)
Let f(y) be the second derivative of -y**4 + 10*y**3 - 83*y**2/2 - 5*y. Let s(j) = -4*j**2 + 20*j - 28. Let h(w) = 4*f(w) - 11*s(w). Factor h(k).
-4*(k - 3)*(k - 2)
Suppose 14*u - 40 = 9*u. Solve -10 - u*d**2 - 11*d**2 + 33*d - 7*d**2 + 8*d**2 - 5*d**3 = 0 for d.
-5, 2/5, 1
Factor -104/7*k - 2/7*k**2 - 1352/7.
-2*(k + 26)**2/7
Let o(u) = u**3 + 3*u**2 - 5*u - 2. Let n be o(-3). Suppose -5*h - 3 = -n. Find v such that -v**3 - h*v**3 - 8*v**4 - 3*v**2 - v + 7*v**4 = 0.
-1, 0
Let g(z) be the second derivative of z**7/210 + 2*z**6/45 + z**5/6 + z**4/3 - 23*z**3/6 + 22*z. Let c(b) be the second derivative of g(b). Factor c(y).
4*(y + 1)**2*(y + 2)
Let f be 4/7 - (-226)/2373. Factor -2/3*l**3 + 2/9*l**2 - 4/9 + 2/9*l**4 + f*l.
2*(l - 2)*(l - 1)**2*(l + 1)/9
Let m(t) = -2*t**2 + 210*t - 2706. Let d(v) = v**2 - 211*v + 2707. Let b(u) = 2*d(u) + 3*m(u). Find c such that b(c) = 0.
26
Solve 2/7 + 13/7*p + 3*p**2 = 0.
-1/3, -2/7
Suppose -v + 37 = -2*a + 4*a, 4*v - 12 = 0. Suppose 21*o - a*o = 16. Suppose -2/3*i**o + 1/6*i**5 - 2/3*i**2 + 0 + 1/6*i + i**3 = 0. Calculate i.
0, 1
Factor 0 + 0*w - 4/7*w**4 + 12/7*w**3 - 8/7*w**2.
-4*w**2*(w - 2)*(w - 1)/7
Let l(f) be the third derivative of -f**6/1200 - f**5/600 + f**4/60 + f**3/15 - 6*f**2 + 27. Determine p, given that l(p) = 0.
-2, -1, 2
Let s(v) be the third derivative of v**8/168 - v**7/21 + 2*v**5/3 - 4*v**4/3 - 277*v**2. Let s(m) = 0. Calculate m.
-2, 0, 1, 2, 4
Let n(r) be the third derivative of r**6/60 + 2*r**5/5 - 13*r**4/12 + 329*r**2. Factor n(y).
2*y*(y - 1)*(y + 13)
Let h(i) be the third derivative of -i**8/112 - 11*i**7/70 - 43*i**6/40 - 73*i**5/20 - 7*i**4 - 8*i**3 - 4*i**2 + 37*i. Suppose h(k) = 0. Calculate k.
-4, -1
Let m(w) = 9*w**2 - 68*w + 585. Let b(y) = -4*y**2 + 34*y - 292. Let i(g) = -7*b(g) - 3*m(g). Factor i(x).
(x - 17)**2
Suppose 5*g - 8*g = -13*g. Let o(y) be the second derivative of -10*y + 0*y**5 + 0*y**2 + 0 + 0*y**3 - 1/75*y**6 + g*y**4 - 1/105*y**7. Factor o(j).
-2*j**4*(j + 1)/5
Let m(d) be the third derivative of -1/24*d**6 - 2/3*d**5 + 0*d**3 + 0 + 6*d**2 + 0*d - 10/3*d**4. Factor m(u).
-5*u*(u + 4)**2
Let a(y) be the third derivative of -1/2340*y**6 + 0*y - 1/156*y**4 + 1/390*y**5 - 1/3*y**3 + 0 - 5*y**2. Let j(q) be the first derivative of a(q). Factor j(p).
-2*(p - 1)**2/13
Let i(z) be the second derivative of z**4/18 + z**3/9 - 2*z**2/3 - 198*z. Factor i(g).
2*(g - 1)*(g + 2)/3
Let f = -23 - -27. Factor -f*j**2 + 20*j - 64 + 0*j**2 + 12*j.
-4*(j - 4)**2
Let q(h) be the first derivative of 20 + 2/3*h + 1/9*h**3 + 1/2*h**2. Find y, given that q(y) = 0.
-2, -1