et c(r) be the third derivative of 1/60*r**5 - 1/6*r**3 + 0*r + 2*r**2 + 0 + 0*r**4. Factor c(s).
(s - 1)*(s + 1)
Let i(r) be the third derivative of r**5/300 + r**4/40 - 2*r**3/15 + 7*r**2. Factor i(y).
(y - 1)*(y + 4)/5
Let t(a) = -4*a**3 - 3*a**2 + 12*a - 8. Let m(s) = -12*s**3 - 8*s**2 + 36*s - 24. Let l(h) = -3*m(h) + 8*t(h). Factor l(i).
4*(i - 1)**2*(i + 2)
Let i be 428/28 - (-6)/(-21). Let g = 18 - i. Find x such that 0*x + 1/4 + 0*x**g + 1/4*x**4 - 1/2*x**2 = 0.
-1, 1
Let b be 81/(-5)*16/(-6). Let w = b - 43. Factor 0 - 2/5*f + w*f**2.
f*(f - 2)/5
Let c = -2478239/480 + 5163. Let p(f) be the third derivative of -1/240*f**5 - 2*f**2 + 0*f**4 - c*f**6 + 0*f**3 + 0*f + 0. Find s such that p(s) = 0.
-1, 0
Let z(m) = -4*m**4 + m**3 + 3*m**2 + 5. Let x(w) = 2*w**4 - w**3 - w**2 - 3. Let o(i) = -5*x(i) - 3*z(i). Let o(u) = 0. What is u?
-2, 0, 1
Let t(x) = -7*x**2 - x + 10. Let b(r) = r**2 + r. Let p(k) = -2*k**2 + 4*k + 9. Let q(u) = -4*b(u) + p(u). Let w(v) = 4*q(v) - 3*t(v). Factor w(f).
-3*(f - 2)*(f + 1)
Let c(x) be the third derivative of -x**6/480 - 3*x**5/160 - x**4/16 - x**3/6 - 4*x**2. Let z(n) be the first derivative of c(n). Factor z(o).
-3*(o + 1)*(o + 2)/4
Let p(q) = 7*q + 38. Let v be p(-5). Factor 2/9*k**v + 2/9 - 2/9*k - 2/9*k**2.
2*(k - 1)**2*(k + 1)/9
Let y be 11 - 3/(-3)*-1. Suppose -j - y = -6*j. Factor 1 + 1/2*i**j + 3/2*i.
(i + 1)*(i + 2)/2
Let s = 20/13 - 194/143. Factor -s*q**2 + 2/11*q**4 + 0 - 2/11*q + 2/11*q**3.
2*q*(q - 1)*(q + 1)**2/11
Let q = -3 - -7. Factor 0 + 4*w**3 + 0*w**q + 2 - 2*w**4 - 4*w.
-2*(w - 1)**3*(w + 1)
Let o(z) be the second derivative of z**4/72 + z**3/36 - 76*z. Factor o(h).
h*(h + 1)/6
Let d(a) be the third derivative of a**8/504 - a**6/45 + a**5/45 + a**4/12 - 2*a**3/9 + 13*a**2. Find x, given that d(x) = 0.
-2, -1, 1
Let w be 0/1 + (0 - -2). Let d be w/(-7) - 27/(-21). Determine c so that -2*c**4 - 1 + 2*c**2 + d = 0.
-1, 0, 1
Suppose 0 = -10*u - 4*u. Let d(y) be the third derivative of 0*y**4 + u*y**3 + 2*y**2 + 0*y**5 - 1/180*y**6 + 0*y + 0. Suppose d(o) = 0. Calculate o.
0
Let s = -23 - -23. Let o(y) be the first derivative of -1/16*y**4 + s*y**3 + 0*y + 1/20*y**5 + 1 + 0*y**2. Factor o(x).
x**3*(x - 1)/4
Let c = -207 + 210. Factor -1/3*m**4 + 2/3 + m**2 - 1/3*m**c + 5/3*m.
-(m - 2)*(m + 1)**3/3
Factor -8/13*h - 10/13*h**3 + 0 - 2/13*h**4 - 16/13*h**2.
-2*h*(h + 1)*(h + 2)**2/13
Factor 4*g**2 + 9*g + g**2 - 2*g**2 + 6.
3*(g + 1)*(g + 2)
Let l be -1 + (34/10 - 2). Suppose l*h + 2/5*h**2 - 4/5 = 0. Calculate h.
-2, 1
Let o(m) be the third derivative of m**7/350 - m**6/75 + m**5/75 + 11*m**2. Find f such that o(f) = 0.
0, 2/3, 2
Let d = 1 + 4. Let w(x) be the first derivative of -14/3*x**6 - 7*x**4 - x**3 + 0*x + 57/5*x**d + x**2 - 2. Solve w(l) = 0 for l.
-1/4, 0, 2/7, 1
Let f(p) be the first derivative of 3*p - 2 + 1/20*p**5 - 1/6*p**3 + 0*p**4 + 0*p**2. Let v(i) be the first derivative of f(i). Factor v(w).
w*(w - 1)*(w + 1)
Let v(p) be the third derivative of p**8/252 - 2*p**7/315 - p**6/45 + 2*p**5/45 + p**4/18 - 2*p**3/9 + 25*p**2. Factor v(x).
4*(x - 1)**3*(x + 1)**2/3
Let a = -5 + 10. Suppose -23 = -5*o - 2*g, -2 = -a*o + 3*g + 1. Solve -d**2 + 7*d**2 + d**o + 3*d + 2*d**3 = 0 for d.
-1, 0
Let g(i) = i**2 - i. Let n(p) = 6*p**2 - 7*p + 1. Let w(l) = 35*g(l) - 5*n(l). Suppose w(k) = 0. What is k?
-1, 1
Let y(a) = 7*a**3 + 4*a**2 + 5*a + 8. Let b(j) = j**3 + j**2 + j + 1. Let l = -5 - -4. Let u(z) = l*y(z) + 6*b(z). Let u(c) = 0. What is c?
-1, 1, 2
Let y(r) be the first derivative of r**4 - 4*r**3/3 - 2*r**2 + 4*r - 24. Factor y(o).
4*(o - 1)**2*(o + 1)
Let 4*p**5 + 5*p**3 - 11*p**3 - 2*p**3 + p**4 - 5*p**4 = 0. What is p?
-1, 0, 2
Let w(x) be the first derivative of -1/3*x**6 - 3/2*x**4 + 0*x + 8/5*x**5 - 8/3*x**3 + 2 + 4*x**2. Find a, given that w(a) = 0.
-1, 0, 1, 2
Let i(k) be the first derivative of -k**5/20 - k**4/8 + k**3/12 + k**2/4 + 8. Factor i(o).
-o*(o - 1)*(o + 1)*(o + 2)/4
Let b(n) = 6*n**4 - 3*n**3 + 3*n**2 + 3*n. Let r(f) = 3*f**4 - f**3 + f**2 + f. Let d(a) = -4*b(a) + 9*r(a). Let d(x) = 0. What is x?
-1, 0, 1
Suppose 0 = 5*j - 3*j - 6. Let u(z) be the first derivative of 2/5*z**5 + 0*z**4 + 0*z**2 - 4/3*z**j + 2*z + 2. Find d such that u(d) = 0.
-1, 1
Let f(o) be the second derivative of 0*o**4 + 0 + 1/30*o**5 - o**2 + 1/60*o**6 + o + 0*o**3. Let d(k) be the first derivative of f(k). Factor d(q).
2*q**2*(q + 1)
Let x(w) be the first derivative of -w**7/5460 + w**6/780 - w**5/390 + w**3 - 1. Let o(b) be the third derivative of x(b). Let o(r) = 0. What is r?
0, 1, 2
Suppose -4*q**3 - 7*q**3 - 2*q**2 + 12*q**4 - 10*q**2 + 15*q**3 - 4*q**5 = 0. Calculate q.
-1, 0, 1, 3
Let g(b) be the second derivative of -b**5/10 - b**4/3 - b**3/3 + 14*b. Determine j, given that g(j) = 0.
-1, 0
Let n(k) be the third derivative of 1/120*k**6 + 3*k**2 + 0*k - 1/12*k**4 - 1/60*k**5 + 0*k**3 + 0. Factor n(j).
j*(j - 2)*(j + 1)
Let y(a) = a**3 + 4*a**2 - 4. Let r be y(-4). Let l be (1 + 0)/((-2)/r). Let -10*p**3 + p**3 + 7*p**4 + 14*p - 5*p - l - 5*p**2 = 0. What is p?
-1, 2/7, 1
Let c be -3*(39/(-27) + 0). Suppose -4/3 - 2*a**3 - c*a**2 - 4*a - 1/3*a**4 = 0. Calculate a.
-2, -1
Let b be (1 - 21/18)/(3/(-48)). Factor b + 162*m**2 + 36*m + 243*m**3.
(9*m + 2)**3/3
Suppose 5 = 5*g - 0. Suppose -3*v - g = -7. Factor 12*l**2 + v*l + 6*l + 1 + 4*l**2.
(4*l + 1)**2
Let 4/7 - 8/7*h**2 + 4/7*h**4 + 0*h + 0*h**3 = 0. Calculate h.
-1, 1
Let l(u) be the second derivative of -2/27*u**3 - 1/54*u**4 - 1/9*u**2 + 0 - 3*u. Factor l(w).
-2*(w + 1)**2/9
Let w(l) = 5*l**2 - 20*l - 5. Let o(s) = -s. Let r(a) = -20*o(a) + w(a). Find k such that r(k) = 0.
-1, 1
Suppose -10*g + 11*g - 3 = 0. Suppose -8*q**2 - 2*q + 0*q**2 - 2*q - 4*q**g = 0. Calculate q.
-1, 0
Let m(c) be the first derivative of -5*c**4/4 + 10*c**3/3 - 5*c**2/2 - 3. Factor m(g).
-5*g*(g - 1)**2
Let w(j) be the first derivative of 2*j**5/35 + j**4/7 + 2*j**3/21 + 6. Let w(l) = 0. Calculate l.
-1, 0
Factor 3/2*x + 3/8*x**2 - 3/8*x**3 - 3/2.
-3*(x - 2)*(x - 1)*(x + 2)/8
Factor 0*y**2 + 0 + 1/4*y**4 + 0*y - 1/2*y**3.
y**3*(y - 2)/4
Factor 9*o - 68*o**2 - 60*o**2 + 125*o**2.
-3*o*(o - 3)
Let j be (-4)/22 + 168/198. Factor 0 - 1/3*b**2 - j*b.
-b*(b + 2)/3
Let d(g) be the third derivative of -g**7/105 - 2*g**6/75 - g**5/150 + g**4/30 + 3*g**2. Factor d(a).
-2*a*(a + 1)**2*(5*a - 2)/5
Let j(l) be the second derivative of -l**5/130 + 2*l**4/39 - 5*l**3/39 + 2*l**2/13 + 19*l. Factor j(c).
-2*(c - 2)*(c - 1)**2/13
Let a be (-4)/(-3)*(-3)/(-1). Suppose -2*s + 2 + a = 0. Suppose s*x**2 + 2*x - 7 + 3 - x**2 = 0. What is x?
-2, 1
Let t(q) be the third derivative of -q**5/12 - 5*q**4/8 - 5*q**3/3 + 3*q**2. Factor t(v).
-5*(v + 1)*(v + 2)
Let f be (5 + -14)*1/(-3). Let c(l) = -2*l**4 - 2*l**2 + 2*l + 2. Let h(i) = -i**5 - 2*i**4 - 3*i**2 + 3*i + 3. Let j(b) = f*c(b) - 2*h(b). Factor j(v).
2*v**4*(v - 1)
Let m(b) be the first derivative of b**6/27 - 4*b**5/45 + 4*b**3/27 - b**2/9 - 35. Factor m(u).
2*u*(u - 1)**3*(u + 1)/9
Let g = -14 - -18. Let c be 7/g - 3/(-12). Factor -4/5*m - 2/5 - 2/5*m**c.
-2*(m + 1)**2/5
Let p(k) be the second derivative of k**5/5 - k**4/3 - 2*k**3/3 + 2*k**2 - 3*k. Factor p(a).
4*(a - 1)**2*(a + 1)
Let k(j) be the first derivative of j**2 - 2/3*j + 1/6*j**4 - 2/3*j**3 + 6. Find p, given that k(p) = 0.
1
Let b be (-6 - -5)*0/3. Let h(l) be the second derivative of -1/40*l**5 + 0 + b*l**3 + 2*l + 0*l**2 + 1/48*l**4. Factor h(u).
-u**2*(2*u - 1)/4
Let c(g) be the second derivative of -7/50*g**5 + 1/75*g**6 + 3*g + 8/5*g**2 - 4/3*g**3 + 0 + 3/5*g**4. Factor c(y).
2*(y - 2)**3*(y - 1)/5
Let u = 4/13 - -40/39. What is j in -7*j**2 + 16/3*j + 3*j**3 - u = 0?
2/3, 1
Suppose 7*i = -209 + 223. Suppose 0 = 3*c + 2*c. Solve c + 2/7*t**i + 2/7*t = 0.
-1, 0
What is u in 3/2*u**2 + 0 + 3/4*u**3 + 3/4*u = 0?
-1, 0
Find q such that -4*q**3 + 8*q**2 - 2 + 0*q - 2*q**4 + 2*q**5 + 2*q - 4*q**2 = 0.
-1, 1
Factor 4*o**3 + 2*o**4 + 0*o + 8/3*o**2 + 0 + 1/3*o**5.
o**2*(o + 2)**3/3
Suppose 2*v + 14 - 44 = -4*a, 0 = 2*v + 3*a - 25. Let z be v*(-2)/(-20)*8. Factor z*y + 2*y + y**2 - 3*y - y.
y*(y + 2)
Let i = 4 - 6. Let k(r) = 2*r**4 - 4*r**2. Let g(h) = 2*h**4 - 4*h**2 - 1. Let b(j) = i*g(j) + 3*k(j). Determine n so that b(n) = 0.
-1, 1
Solve -13*s**2 + s**2