t d(q) = -3*c(q) + 10*h(q). Factor d(x).
-5*(x - 3)*(x - 1)**2*(x + 1)
Let j = 393/3208 - -1/401. Factor 0 + 1/8*u - j*u**3 + 1/4*u**4 - 1/4*u**2.
u*(u - 1)*(u + 1)*(2*u - 1)/8
Let b(i) be the first derivative of -1 + 1/42*i**4 + 0*i**3 - 1/7*i**2 + i. Let l(m) be the first derivative of b(m). Factor l(c).
2*(c - 1)*(c + 1)/7
Let t(j) be the second derivative of 0*j**2 + 1/3*j**4 + 2/3*j**3 - 67/20*j**5 - 13/3*j**6 - 5*j - 3/2*j**7 + 0. Determine k, given that t(k) = 0.
-1, -2/7, 0, 2/9
Factor 27/5*i + 3 + 12/5*i**2.
3*(i + 1)*(4*i + 5)/5
Let i(n) be the third derivative of n**8/168 - n**6/60 - 3*n**2. Suppose i(x) = 0. Calculate x.
-1, 0, 1
Let m = 9 - 9. Let q = 5 + m. Find z, given that z - 3*z**2 - z**q + 4*z**5 + 9*z**3 - z - 9*z**4 = 0.
0, 1
Let x(j) be the third derivative of 0 + 1/210*j**5 - 4*j**2 + 1/84*j**4 + 0*j + 0*j**3. Factor x(g).
2*g*(g + 1)/7
Let a(x) be the second derivative of x**5/30 - x**4/12 + 2*x**2 + x. Let u(k) be the first derivative of a(k). Factor u(i).
2*i*(i - 1)
Let h(q) = 1. Let x(f) = -f**2 - 4*f**2 + 4*f + 12 + 9*f**2 - 4. Let o(d) = -8*h(d) + x(d). Factor o(c).
4*c*(c + 1)
Let r(f) = 76*f**3 - 77*f**2 + 16*f + 3. Let n(q) = -75*q**3 + 78*q**2 - 15*q - 4. Let h(w) = 5*n(w) + 6*r(w). Factor h(c).
(3*c - 1)**2*(9*c - 2)
Let g = -24 - -28. Let m(v) be the first derivative of -2/35*v**5 + 1/7*v**g + 0*v**2 + 0*v - 2/21*v**3 - 2. Solve m(t) = 0 for t.
0, 1
Determine l, given that -14*l + 5*l + 5*l + 20*l**2 = 0.
0, 1/5
Let r(q) be the first derivative of -1/4*q**2 + 1/2*q**3 + 0*q + 5/8*q**4 - 1/3*q**6 - 9 - 3/10*q**5. Determine d so that r(d) = 0.
-1, 0, 1/4, 1
Suppose 4/9*r + 0 - 2/9*r**2 = 0. What is r?
0, 2
Suppose -15*s = -0*s. Factor 1/3*w**4 + 0*w + 0*w**3 + s + 0*w**2.
w**4/3
Suppose 4*d = -2*p - 2, -p + 9 + 0 = -3*d. Let 21/2*k**4 + 9/2*k**5 + 0 + 8*k**p + 2*k**2 + 0*k = 0. What is k?
-1, -2/3, 0
Let b(x) = -x**2 - x + 14. Let m be b(0). Suppose 5*o = 1 + m. Factor q**2 - q**o + 2 - 4 + q + 1.
-(q - 1)**2*(q + 1)
Suppose 20/3*l - 5 - 5/3*l**2 = 0. What is l?
1, 3
Let t = 4 + 1. Suppose 4*a - 18 = -t*l, -a = -4*l + a + 4. Determine f so that -44*f**3 + f**l - f**2 + f**4 + 43*f**3 = 0.
0, 1
Let l be ((-1032)/(-56))/3 - (-6)/(-1). Factor -l*g**2 - 1/7*g**3 + 1/7*g + 0 + 1/7*g**4.
g*(g - 1)**2*(g + 1)/7
Let s(j) be the third derivative of -j**6/360 + j**5/60 - 4*j**3/3 + 8*j**2. Let l(m) be the first derivative of s(m). Solve l(r) = 0.
0, 2
Let s = 52/21 - 8/7. Find t, given that -s*t**2 - 2/3*t**3 - 2/3*t + 0 = 0.
-1, 0
Let y(r) be the second derivative of -r**7/336 - r**6/120 + r**5/80 + r**4/24 - r**3/48 - r**2/8 - 10*r. Solve y(b) = 0 for b.
-2, -1, 1
Let q = -5 - -7. Suppose 3*j - 5*o = 21, -3*j - 4*o = o + 9. Let -3*w**j + w**2 + w**q = 0. What is w?
0
Let a = -2 + 6. Let p(y) = 3*y**4 + 1 - 4*y**3 + 2*y - 2*y**a + 2*y. Let r(j) = -2*j**4 + 9*j**3 - 9*j - 3. Let m(l) = 5*p(l) + 2*r(l). Factor m(x).
(x - 1)**3*(x + 1)
Factor -2/9*g**4 + 0*g**2 - 8/9*g + 0 + 2/3*g**3.
-2*g*(g - 2)**2*(g + 1)/9
Let l(o) = -o**2 - o. Let q be l(-1). Suppose -3*w + 8 + 1 = q. Find g, given that g**2 - 2*g - 3*g + g**2 + w*g = 0.
0, 1
Let t(o) = -5 + 2*o - 1 + 3 + o**2. Let i be -1 + -2 + 3 - -2. Let l(n) = -5*n**2 - 11*n + 16. Let v(j) = i*l(j) + 11*t(j). Solve v(w) = 0 for w.
-1, 1
Let j(c) be the second derivative of c**6/40 + 3*c**5/40 - c**4/4 - c**3/4 + 9*c**2/8 + 30*c. Suppose j(x) = 0. What is x?
-3, -1, 1
Let d(p) be the second derivative of p**7/720 + p**6/288 - p**5/120 - p**4/6 - 7*p. Let y(a) be the third derivative of d(a). Determine n, given that y(n) = 0.
-1, 2/7
Let p(z) be the third derivative of z**6/120 + z**5/20 - z**4/24 + z**3/2 + 3*z**2. Let l(t) = -2*t**2 - 2. Let r(v) = -3*l(v) - 2*p(v). Factor r(k).
-2*k*(k - 1)*(k + 1)
Let g(p) be the first derivative of 5*p**4/4 + 5*p**3/3 - 5*p**2/2 - 5*p - 25. Suppose g(z) = 0. What is z?
-1, 1
Suppose -4*j = 4*u - 8, -2 = -j + 4*u - 10. Factor 0*r**2 + 1/4*r**5 + 0 - 1/8*r**4 - 1/8*r**3 + j*r.
r**3*(r - 1)*(2*r + 1)/8
Suppose -8 = j - 3*c, 2*j = 5*j + 3*c - 24. Let k = j - 2. Factor -k*u - 1/2*u**2 - 2.
-(u + 2)**2/2
Let p = 12/17 + -43/85. Find b such that -2/5*b + p*b**2 + 1/5 = 0.
1
Suppose 5*l - 7 - 3 = 0. Suppose 3*x + l = 11. What is z in 4/3*z**2 + 0 + 2/3*z + 2/3*z**x = 0?
-1, 0
Let a(q) be the first derivative of q**6/480 - q**4/96 - 3*q**2/2 - 3. Let f(v) be the second derivative of a(v). Solve f(t) = 0.
-1, 0, 1
Let k + 0 + 1/2*k**3 + 3/2*k**2 = 0. What is k?
-2, -1, 0
Let q = -5 + 7. Find y such that 7*y + 3*y**q - 6*y**3 - 13*y**2 + 8 + y = 0.
-2, -2/3, 1
Let b(h) be the first derivative of -h**7/49 - 2*h**6/105 + 3*h**5/70 + h**4/21 - 5*h + 7. Let g(l) be the first derivative of b(l). Let g(d) = 0. Calculate d.
-1, -2/3, 0, 1
Suppose -4*h = g + h - 9, -h = -1. Let m(u) be the second derivative of 0 + 1/18*u**g + u - 1/3*u**2 + 0*u**3. Find w, given that m(w) = 0.
-1, 1
Let c(h) = h**3 - 5*h**2 + 6*h - 11. Let i(t) = 1. Let u(g) = c(g) + 5*i(g). Let k be u(4). What is w in 1/5 + 1/5*w**3 + 3/5*w**k + 3/5*w = 0?
-1
Suppose 4*p = -0*p + 20. Factor -6*a**4 + 6*a**2 + a**5 - 3*a + 5*a**5 - 3*a**p.
3*a*(a - 1)**3*(a + 1)
Let i(s) be the second derivative of s**6/75 - s**5/50 - s**4/10 + s**3/15 + 2*s**2/5 - 18*s. Factor i(o).
2*(o - 2)*(o - 1)*(o + 1)**2/5
Let a be (3 + 5)*1/2. Let m be (-2 + (-2)/a)*-2. Let -s**2 - 5 - s**3 + 3 - 3*s**2 - m*s = 0. Calculate s.
-2, -1
Let m(g) be the second derivative of 0*g**2 + 0 + 4/15*g**6 - 1/21*g**7 - 1/3*g**3 - 3*g + 2/3*g**4 - 3/5*g**5. Find l, given that m(l) = 0.
0, 1
Suppose -m - 4 + 1 = -a, 4*a = 20. Factor -14*z**3 + 10*z**2 - 2*z - 3*z**2 + z + 0*z**m + 8*z**4.
z*(z - 1)*(2*z - 1)*(4*z - 1)
Let b(h) be the second derivative of 0*h**4 - 2*h - 1/300*h**5 + 1/30*h**3 + 0 + h**2. Let v(m) be the first derivative of b(m). Solve v(n) = 0.
-1, 1
Let c(f) be the first derivative of -f**7/350 + 3*f**5/100 - f**4/20 - f**2/2 + 8. Let k(j) be the second derivative of c(j). Factor k(a).
-3*a*(a - 1)**2*(a + 2)/5
Suppose c + 15 = 2*p, -2*c - 4*p + 10 = -0*p. Let n(h) = h**3 + 6*h**2 + 5*h + 2. Let s be n(c). Factor -3*m**2 - 2*m - m**2 + s*m**5 + 0*m**4 + 4*m**4.
2*m*(m - 1)*(m + 1)**3
Let k(v) = v**2 + 4*v + 9. Let a(m) = -45 + m**2 - 7*m**2 + m**2 - 19*m. Let n(w) = 6*a(w) + 33*k(w). Factor n(r).
3*(r + 3)**2
Let a(c) be the second derivative of c**7/42 - c**6/10 + c**5/10 + c**4/6 - c**3/2 + c**2/2 - 16*c. Factor a(r).
(r - 1)**4*(r + 1)
Suppose t - 3 = -9. Let i = t + 9. Solve -6*z**3 + 3*z + 6*z**4 + 6*z**2 - i*z - 4*z**2 - 2*z**5 = 0.
0, 1
Let m be (-1)/(-3) - 2/6. Let v(k) = k**3 - k + 2. Let j be v(m). Suppose n**2 - n**4 + j*n**2 + n**3 - 3*n**2 = 0. Calculate n.
0, 1
Let y(c) be the first derivative of -c**5/40 + c**4/24 + c**3/12 - c**2/4 - 4*c + 1. Let f(d) be the first derivative of y(d). Factor f(p).
-(p - 1)**2*(p + 1)/2
Let g(u) be the second derivative of 0*u**3 + 0 - 6*u + 1/6*u**4 + 1/10*u**5 + 0*u**2. Let g(d) = 0. What is d?
-1, 0
Let s(c) be the first derivative of c**4/8 - c**3/6 - c**2/2 - 4. Factor s(l).
l*(l - 2)*(l + 1)/2
Let v(d) be the first derivative of -4/15*d**3 + 0*d**4 - 1/5*d**2 + 4/25*d**5 + 1/15*d**6 + 1 + 0*d. Factor v(b).
2*b*(b - 1)*(b + 1)**3/5
Let v(y) = y**3 - y**2 + 1. Let z(d) be the second derivative of d**7/14 - 7*d**5/20 + d**4/12 + d**3/2 - d**2/2 - 9*d. Let i(g) = v(g) + z(g). Factor i(n).
3*n*(n - 1)**2*(n + 1)**2
Suppose 0 = -3*v - 12, -p - v + 6 = -6*p. Let s be -3 + (35/p)/(-5). Find g, given that -1/4*g + 1/4*g**4 - 1/4*g**5 - 1/2*g**2 + 1/4 + s*g**3 = 0.
-1, 1
Solve -23/6*i - 2/3 + i**2 = 0 for i.
-1/6, 4
Let d(b) be the second derivative of 0 - 1/20*b**5 + 0*b**2 - 1/12*b**4 + 1/42*b**7 + 0*b**3 + 9*b + 1/30*b**6. Factor d(i).
i**2*(i - 1)*(i + 1)**2
Let t(z) be the third derivative of -1/6*z**4 + 0*z + 0 + 2*z**2 - 1/3*z**3 + 1/180*z**6 + 1/60*z**5. Let y(p) be the first derivative of t(p). Factor y(v).
2*(v - 1)*(v + 2)
Let a = 13 - -9. What is y in 18*y**3 + 2*y**2 + 2*y**2 - a*y**4 - 6*y**2 + 8*y**5 - 2*y = 0?
-1/4, 0, 1
Factor 14*r + 3*r**2 + r**2 - 6*r + 4.
4*(r + 1)**2
Let c(m) be the first derivative of m**3/6 - 7*m**2/4 - 4*m + 30. Find f, given that c(f) = 0.
-1, 8
Let b = -2 + 2. Let c = 82 - 80. Solve -2/5*f + 6/5*f**c + b + 2/5*f**4 - 6/5*f**3