e of 3*h**4/28 - 9*h**2/14 + 6*h/7 + 5. Factor x(f).
3*(f - 1)**2*(f + 2)/7
Solve -13/4*r + 3/4 + r**2 = 0 for r.
1/4, 3
Let y(w) be the third derivative of -w**8/112 + w**7/35 + w**6/20 - 2*w**5/5 + 7*w**4/8 - w**3 + w**2. Factor y(z).
-3*(z - 1)**4*(z + 2)
Let c(t) = t**3 - t - 1. Let h(r) = r**5 - 12*r**3 + 11*r + 11. Let a(o) = 44*c(o) + 4*h(o). Factor a(n).
4*n**3*(n - 1)*(n + 1)
Let j(q) be the first derivative of 0*q - 5 + 0*q**2 + 1/12*q**3 - 1/20*q**5 + 1/16*q**4 - 1/24*q**6. Let j(v) = 0. What is v?
-1, 0, 1
Let 4*b**4 - 2*b**3 - 2*b**3 + 2*b**3 + 0*b**5 + 2*b**5 - 4*b**2 = 0. What is b?
-2, -1, 0, 1
Let o(c) be the second derivative of 0*c**3 + 1/24*c**4 + 0*c**2 + c + 0. Let o(f) = 0. What is f?
0
Let r = 12 - 9. Let c(i) be the second derivative of i - 1/18*i**4 + 2/9*i**r + 0 - 1/3*i**2. Solve c(u) = 0.
1
Let k be 0 + -6 - (-1 - 1). Let n be (0 + k)/(4/(-2)). Factor 2/3 + 1/3*u**n - u.
(u - 2)*(u - 1)/3
Factor 6/7*a**2 + 4/7 + 2*a.
2*(a + 2)*(3*a + 1)/7
Let r = 643/414 - 5/46. Let t(w) be the third derivative of -w**2 - 7/20*w**6 + 0*w + 8/9*w**3 - r*w**4 + 17/15*w**5 + 0. Determine s, given that t(s) = 0.
2/7, 2/3
Let r(n) be the third derivative of -1/420*n**6 - 1/1470*n**7 + 0*n + 1/2352*n**8 - 1/42*n**3 + 6*n**2 + 1/168*n**4 + 1/210*n**5 + 0. Factor r(j).
(j - 1)**3*(j + 1)**2/7
Let k be 67/5 + 9/15. Suppose -2*a**3 + 6*a - 2*a**4 - 4 - 4*a**3 - 8*a**4 + k*a**2 = 0. What is a?
-1, 2/5, 1
Let a(s) be the second derivative of -1/72*s**4 + 0*s**2 + 2*s + 1/1080*s**6 - 1/3*s**3 + 0 + 0*s**5. Let w(h) be the second derivative of a(h). Factor w(o).
(o - 1)*(o + 1)/3
Let k(w) = w**4 - 11*w + 11. Let t(n) = -3*n + 1. Let d(s) = s + 1. Let c(u) = d(u) + t(u). Let l(g) = -11*c(g) + 2*k(g). Factor l(h).
2*h**4
Suppose 57 = 3*x + 3*s, s + 81 = -0*x + 4*x. Let i be 18/20 - 8/x. Factor 3/2*l**4 + 0*l + 0 - i*l**3 - l**2.
l**2*(l - 1)*(3*l + 2)/2
Let s(c) be the second derivative of 48*c**2 + 81/5*c**6 - 27/14*c**7 - 54*c**5 + 92*c**4 - 88*c**3 - 3*c + 0. Factor s(t).
-3*(t - 2)**2*(3*t - 2)**3
Let z = -3 - -5. Let r(p) be the first derivative of -1/12*p**4 + 0*p - 1/6*p**z - 2 - 2/9*p**3. Determine n so that r(n) = 0.
-1, 0
Let v(f) be the third derivative of 1/40*f**6 - 1/20*f**5 - 8*f**2 + 0*f + 1/2*f**3 + 0 - 1/8*f**4. Suppose v(j) = 0. What is j?
-1, 1
Factor -8/9*d - 8/9*d**3 - 4/3*d**2 - 2/9*d**4 - 2/9.
-2*(d + 1)**4/9
Let h be (-4)/6 - 5/(-3). Let d be -1 - (-3*h)/3. Determine k, given that 5*k**2 - 2*k + d*k**2 - 4*k**2 = 0.
0, 2
Let v(s) = -4*s**2 - 12*s + 10. Let t(g) = 4*g**2 - 2*g - 1. Let k be t(-1). Let c(h) = 3*h**2 + 11*h - 9. Let r(q) = k*v(q) + 6*c(q). Factor r(u).
-2*(u - 2)*(u - 1)
Find y such that -4/5*y**2 - 8/5*y**3 + 0*y**4 + 4/5 + 2/5*y**5 + 6/5*y = 0.
-1, 1, 2
Let q = -56 - -58. Let y(d) be the first derivative of -1/5*d**5 + 0*d**4 - 1/12*d**6 + 1/4*d**q + 1/3*d**3 + 0*d - 3. Let y(g) = 0. Calculate g.
-1, 0, 1
Let y(m) be the first derivative of 0*m**2 + 0*m**3 - 1/21*m**6 + 1/14*m**4 - 4 + 0*m + 0*m**5. Factor y(o).
-2*o**3*(o - 1)*(o + 1)/7
Let a(u) be the first derivative of -u**8/1176 + u**6/420 + 11*u**2/2 + 9. Let l(w) be the second derivative of a(w). Factor l(q).
-2*q**3*(q - 1)*(q + 1)/7
Let p(j) be the second derivative of j**7/231 + 4*j**6/165 + j**5/55 - 2*j**4/33 - j**3/11 - 18*j. Suppose p(d) = 0. Calculate d.
-3, -1, 0, 1
Let a = 3/6529 - -45448/554965. Let i = a + 2/17. Determine u, given that i*u**3 + 2/5 + u + 4/5*u**2 = 0.
-2, -1
Factor 2*a + 0 + 1/2*a**2.
a*(a + 4)/2
Let q(a) be the second derivative of a**6/30 - a**5/20 - a**4/3 + 2*a**3/3 + 66*a. Find y, given that q(y) = 0.
-2, 0, 1, 2
Factor 0*d - 1/3*d**2 + 0.
-d**2/3
Let m(i) = i**2 - 1. Let a(p) = 4*p**2 - p - 5. Let c(q) = -a(q) + 5*m(q). Factor c(w).
w*(w + 1)
Let c(l) = -4*l**2 - 2*l. Let o(t) = t**2 - t + 1. Let p(s) = c(s) + 6*o(s). Factor p(r).
2*(r - 3)*(r - 1)
Let q be 1/(-6) + -8*2/(-96). Factor 1/3 + 1/3*w**4 + q*w**3 - 2/3*w**2 + 0*w.
(w - 1)**2*(w + 1)**2/3
Let k be -11*2/(-72) + 2/(-8). Let f(y) be the first derivative of -2 + 1/6*y**2 - 2/9*y**3 - k*y**6 + 0*y + 2/15*y**5 + 0*y**4. Solve f(b) = 0 for b.
-1, 0, 1
Let m(d) = -d**3 + 7*d**2 - 7*d + 8. Let l be m(6). Suppose -6 = 3*v - 5*q, 4*v = l*q - 5*q + 21. Factor -2*s + s**3 - 2*s**2 - 4*s**3 + v*s.
-s*(s + 1)*(3*s - 1)
Suppose 26*j + 15 + 4*j**2 + 46*j - 24*j + 5*j**2 = 0. What is j?
-5, -1/3
Let h(s) be the second derivative of 3*s - 1/36*s**4 - 1/18*s**3 + 0 + 1/6*s**2 + 1/60*s**5. Factor h(j).
(j - 1)**2*(j + 1)/3
Let z be ((-8)/56)/(0 - (-12)/(-21)). Let i(w) be the first derivative of -2*w + 3/2*w**2 + 0*w**3 - z*w**4 - 2. Factor i(n).
-(n - 1)**2*(n + 2)
Let m(g) be the third derivative of g**7/840 - g**5/120 + g**3/6 - 2*g**2. Let i(j) be the first derivative of m(j). Factor i(s).
s*(s - 1)*(s + 1)
What is d in 0 + 0*d - 9/2*d**3 - 6*d**2 + 3/2*d**4 = 0?
-1, 0, 4
Let k(w) be the third derivative of -w**5/20 + 3*w**4/8 + 2*w**3 - 13*w**2. Suppose k(c) = 0. Calculate c.
-1, 4
Let r(c) = c + 0 - c**2 + 3 - 2. Let p be (0 - 1)*-1*-1. Let q(y) = -y**2 + 3*y + 2. Let o(s) = p*q(s) + 2*r(s). Let o(x) = 0. Calculate x.
-1, 0
Let j(x) = -2*x**3 - 2*x. Let u(v) = -2*v**3 - 3*v. Let l(i) = 5*j(i) - 4*u(i). Suppose l(s) = 0. Calculate s.
-1, 0, 1
Suppose 12/7 - 34/7*u + 10/7*u**2 = 0. What is u?
2/5, 3
Let w = -40 + 42. Factor -2/3*r**5 - 16/3*r - 2/3*r**4 + 8/3 + 10/3*r**3 + 2/3*r**w.
-2*(r - 1)**3*(r + 2)**2/3
Let n = 1 - 1. Let l = 2 + n. Factor 4*x**l - 3*x**2 + 0*x**2 - x.
x*(x - 1)
Suppose n - 2 = 4*q, 2*n + 2*n = -3*q + 27. Let -n*i**4 + 2*i**5 + 0*i**4 - 2*i**3 - 3*i**2 + 4*i**4 + 5*i**2 = 0. What is i?
-1, 0, 1
Let g be 4/(-12)*0 - -2. Let k be g/(-4) + 10/20. Factor -3/2*z**3 + 1/2*z**2 + k + z.
-z*(z - 1)*(3*z + 2)/2
Let y be 8/(-2)*48/(-6). Factor 9*k**4 - k**5 - 2*k + 56*k**2 + 14 - 46*k - y*k**3 + 2.
-(k - 2)**4*(k - 1)
Suppose -14*y - 15*y = 0. Factor 0 + y*l - 1/4*l**2.
-l**2/4
Let b(q) be the second derivative of -q**7/14 + 3*q**5/10 - q**3/2 + 2*q. What is w in b(w) = 0?
-1, 0, 1
Solve -18/7*n**2 - 54/7 + 2/7*n**3 + 54/7*n = 0.
3
Let t(m) = -2*m - 12. Let k be t(-8). Let z(f) be the third derivative of 0*f**3 + 0*f + 1/72*f**k - 2*f**2 - 1/180*f**5 + 0. Solve z(c) = 0 for c.
0, 1
Let v be 4/((-1)/6*-3). Let z(q) = -q**3 + 7*q**2 + 8*q. Let m be z(v). Factor m*u**2 + 0*u**2 - u**3 - 2*u**3 + 3*u**4.
3*u**3*(u - 1)
Let o(q) = q**3 + 7*q**2 + 8*q - 5. Let w be o(-5). Let a(l) be the second derivative of 1/2*l**4 - l**3 + l - 1/10*l**w + l**2 + 0. Factor a(p).
-2*(p - 1)**3
Let a(m) be the first derivative of -2 + 2/3*m**4 - 3*m + 0*m**2 + 1/15*m**6 + 4/9*m**3 + 11/30*m**5. Let f(i) be the first derivative of a(i). Solve f(p) = 0.
-2, -1, -2/3, 0
Factor 0 - 9/4*q + 1/4*q**2.
q*(q - 9)/4
Let q(f) be the second derivative of f**9/7560 - f**7/630 + f**5/60 - 3*f**4/4 - 2*f. Let j(i) be the third derivative of q(i). Factor j(r).
2*(r - 1)**2*(r + 1)**2
Let q(p) be the third derivative of p**7/3780 - p**6/270 + p**5/45 + p**4/6 + 2*p**2. Let o(d) be the second derivative of q(d). Factor o(r).
2*(r - 2)**2/3
Let x(n) be the second derivative of 5*n**7/168 - n**6/12 - n**5/16 + 5*n**4/24 + 6*n. Determine f so that x(f) = 0.
-1, 0, 1, 2
Suppose 0 = -0*w - 2*w - 26. Let o = w - -18. Suppose -v + 8*v**o - 2*v**4 + v = 0. Calculate v.
0, 1/4
Suppose 0 = -3*o - k + 4, 0*o + 3*k = 4*o + 12. Let s = 0 - o. Factor x**2 - 3*x + 2*x + s*x.
x*(x - 1)
Let v be (-7)/(63/66)*-3. Suppose 7 = -5*x + v. Factor -8*y**x - 22/3*y**2 - 2/9 - 20/9*y.
-2*(3*y + 1)**2*(4*y + 1)/9
Suppose -7*u + 2*u - 5*f - 20 = 0, 4 = -u - 5*f. Let z be 2/u + 10/12. Factor z - 2/3*h**2 - 1/3*h + 1/3*h**4 - 1/3*h**5 + 2/3*h**3.
-(h - 1)**3*(h + 1)**2/3
Let z(x) = -x**3 + 3*x**2 + x - 6. Let y be z(2). Factor 2/7*w**2 - 2/7*w + y.
2*w*(w - 1)/7
Let f(m) be the third derivative of -m**8/5880 - m**7/1470 + m**5/210 + m**4/84 - m**3/6 - 2*m**2. Let o(x) be the first derivative of f(x). Factor o(l).
-2*(l - 1)*(l + 1)**3/7
Let s(v) be the second derivative of v**5/110 - 2*v**4/11 + 16*v**3/11 - 64*v**2/11 + 3*v. Factor s(j).
2*(j - 4)**3/11
Let -1/5*x**5 + 2*x**2 + 6/5*x**4 + 0 - 3/5*x - 12/5*x**3 = 0. Calculate x.
0, 1, 3
Let w(f) = -13*f**3 - 17*f**2 + 5*f. Let q(j) = -3*j**3 - 4*j**2 + j. Let m(x) = -9*q(