Let w(c) = c**3 - 8*c**2 + 7*c + 1. Let p be w(7). Let s(q) = p*r(q) - 5*a(q). Factor s(x).
3*x*(x + 1)
Let x(o) be the second derivative of o**6/120 + o**5/80 + 3*o. Factor x(s).
s**3*(s + 1)/4
Determine x, given that -4/7*x**2 + 0*x + 2/7*x**4 + 2/7 + 0*x**3 = 0.
-1, 1
Let c(l) be the third derivative of 0 - 1/240*l**6 + 0*l**4 + 0*l**5 + 0*l**3 + 0*l + 2*l**2. Factor c(n).
-n**3/2
Suppose -4*z - 4*w + 24 = 0, -4*z + w - 6*w = -23. Suppose -2*f - z = -k, 4*k - f - 2 - 12 = 0. Find o such that -5/4*o**2 + 1/2*o**k + 1/2*o + 0 = 0.
0, 1/2, 2
Let o(d) be the third derivative of -d**5/140 + d**4/14 - 3*d**3/14 - 25*d**2. What is a in o(a) = 0?
1, 3
Let a(y) = 3*y**2 + 8*y. Let x be a(4). Find d such that -10 + 15 + 41*d**2 + 36*d**4 + 107*d**2 - x*d - 120*d**3 + 11 = 0.
2/3, 1
Let q(u) be the second derivative of 1/10*u**5 + 0 + u**2 - u + u**3 + 1/2*u**4. Suppose q(p) = 0. Calculate p.
-1
Let s(m) be the second derivative of m**6/120 - m**5/20 + m**4/8 - m**3/6 - 3*m**2 - 3*m. Let t(d) be the first derivative of s(d). Find b such that t(b) = 0.
1
Factor 2/9*s**2 + 2/9*s - 4/9.
2*(s - 1)*(s + 2)/9
What is g in -3*g**5 + 6*g**5 + 9*g**4 + 12*g**5 + 12*g**4 + 6*g**3 = 0?
-1, -2/5, 0
Factor 1/4*n**2 - 1/4 + 0*n.
(n - 1)*(n + 1)/4
Let x(n) = -n**2 + 9*n + 2. Let f(s) = -3 - 4*s**2 + 18*s + 8 + 3*s**2. Let k(d) = 4*f(d) - 7*x(d). Factor k(j).
3*(j + 1)*(j + 2)
Let q = 12 - 9. Let d be (3*2/6)/q. Solve 1/3*a + 0 + d*a**2 = 0.
-1, 0
Suppose -5*c = -c - 8. Suppose -c*r - 1 = -3*f - r, -f + r - 3 = 0. Factor 1/4*v - 1/4*v**f + 1/4 - 1/4*v**3.
-(v - 1)*(v + 1)**2/4
Let s(t) be the second derivative of t**10/10080 - t**8/2240 + t**4/3 + t. Let d(f) be the third derivative of s(f). Factor d(a).
3*a**3*(a - 1)*(a + 1)
Suppose 116*p - 3 = 115*p. Let 1/4*a**2 + 0 - 1/2*a + 1/4*a**p = 0. What is a?
-2, 0, 1
Let f(h) be the third derivative of -3*h**5/100 - 7*h**4/40 - h**3/5 + 2*h**2. Solve f(y) = 0 for y.
-2, -1/3
Let g(o) = -o**2 + o - 2. Let k(d) = -d**2 + 3*d - 1. Let z be k(3). Let u(s) = s**2 + s + 1. Let l(c) = z*g(c) - 2*u(c). Factor l(w).
-w*(w + 3)
Let c(f) be the second derivative of 7*f**4/18 + 5*f**3/9 - 2*f**2/3 + 12*f. Suppose c(x) = 0. What is x?
-1, 2/7
Let d(f) be the first derivative of 10*f**3/3 + 5*f**2/2 + 12. Solve d(v) = 0 for v.
-1/2, 0
Let r = 0 + -5. Let j = r + 2. Let m(b) = -b**3 + 2*b**2 - 2*b - 2. Let o(w) = w**3 - w**2 + w + 1. Let z(s) = j*o(s) - 2*m(s). Factor z(f).
-(f - 1)*(f + 1)**2
Let u(n) = -n**3 + 11*n**2 - 9*n - 8. Let m be u(10). Factor -6 - 6*a - 3/2*a**m.
-3*(a + 2)**2/2
Let j(g) be the second derivative of g**5/60 - g**4/18 + 23*g. Find p, given that j(p) = 0.
0, 2
Let t(r) be the second derivative of r**4/12 - 5*r**3/6 - 2*r**2 + r. Let x be t(6). Factor -x*l**5 + 6*l**4 + 14*l**3 - 2 + 16*l**2 + 4 + 3*l**5 + 9*l.
(l + 1)**4*(l + 2)
Let c(n) = 7*n**2 - 7*n + 4. Let f(m) = -13*m**2 + 13*m - 7. Let l = -30 - -19. Let k(y) = l*c(y) - 6*f(y). Let k(j) = 0. Calculate j.
-1, 2
Suppose 2 = 3*i - 2*q, 3*i - i + 17 = 5*q. Suppose -5*o + 42 = 4*g, i*g + 4*o - 32 = g. What is n in -4*n**4 - 8*n - n**2 + g*n + 0*n**2 + 5*n**3 = 0?
0, 1/4, 1
Let h = 3 + -15. Let b = h - -12. Determine f so that -3/5*f**3 - 3/5*f - 6/5*f**2 + b = 0.
-1, 0
Suppose 13*o = 10*o. Solve o + 3/4*w**5 + 3/2*w + 27/4*w**3 + 21/4*w**2 + 15/4*w**4 = 0 for w.
-2, -1, 0
Suppose b - 4 + 2 = 0. Suppose -6*c + c - i + 59 = 0, b*c - 6 = 4*i. Suppose -9*u**2 + c - 8 - 7 + 12*u = 0. Calculate u.
2/3
Let j(m) be the second derivative of -1/110*m**5 + 0*m**2 + 0 + m + 1/66*m**4 + 1/231*m**7 + 0*m**3 - 1/165*m**6. Factor j(p).
2*p**2*(p - 1)**2*(p + 1)/11
Let c = 3 + 3. Suppose 2*b - 2*m - 2 + 4 = 0, -1 = -2*b + m. Factor 4 - c*r - 2 + 2*r + 2*r**b.
2*(r - 1)**2
Let v(s) = -s**3 - s - 1. Let m(z) = 3*z**3 - 4*z**2 + 7*z. Suppose 2*c + 2*r = 3*r + 1, 23 = c - 5*r. Let h(l) = c*v(l) - m(l). Factor h(g).
-(g - 2)*(g - 1)**2
Factor -2/3*t**3 + 0 + 4/3*t**2 + 0*t.
-2*t**2*(t - 2)/3
Let p(k) be the first derivative of 2*k**3/3 - 8*k**2/5 - 8*k/5 - 13. Factor p(w).
2*(w - 2)*(5*w + 2)/5
Factor 2/3*z + 0 - 4/3*z**2 + 2/3*z**3.
2*z*(z - 1)**2/3
Let z be -1 - -8 - (8 - 10). Solve z*a**2 - 4*a**2 - a**2 - 2*a - 2*a**3 = 0.
0, 1
Let o(n) be the third derivative of -n**5/15 - 2*n**4/3 + 10*n**3/3 + 9*n**2. Solve o(d) = 0.
-5, 1
Let c(z) be the third derivative of 7*z**6/60 - 37*z**5/30 - 8*z**4/3 + 4*z**3 + 40*z**2. What is g in c(g) = 0?
-1, 2/7, 6
Suppose 0 = 4*z - 12 + 52. Let b(t) = t**2 + 10*t + 3. Let f be b(z). Factor 3*o**3 + 20*o + 3*o**4 - f*o**2 - 3*o**5 - 20*o.
-3*o**2*(o - 1)**2*(o + 1)
Let t be (-3 - 255)/(0 + -2). Let m = t - 383/3. What is w in 2/3*w**3 + 0*w + 0 + 2/3*w**5 + 0*w**2 - m*w**4 = 0?
0, 1
Suppose 0 = 2*d - 0 + 2. Let y(b) = b**2 + b - 1. Let t(j) = 26*j**2 - 22*j + 8. Let i(m) = d*t(m) - 6*y(m). Factor i(r).
-2*(4*r - 1)**2
Let o(t) be the second derivative of t**4/132 - t**3/33 - t. Find k such that o(k) = 0.
0, 2
Let r(d) = -d**3 + 5*d**2 + d - 21. Let i be r(3). Factor 0*z**2 + i - 2/7*z**5 + 0*z**4 + 0*z + 2/7*z**3.
-2*z**3*(z - 1)*(z + 1)/7
Let z(h) be the first derivative of -2*h**5/65 + h**4/26 + 2*h**3/39 - h**2/13 + 2. Factor z(f).
-2*f*(f - 1)**2*(f + 1)/13
Factor -3/2*p + 0 + 1/2*p**2.
p*(p - 3)/2
Let v(k) be the second derivative of k**5/70 - k**4/14 + 2*k**3/21 + 27*k. Solve v(n) = 0 for n.
0, 1, 2
Let l(x) be the second derivative of x**5/35 - x**4/7 + 4*x**3/21 + 4*x. Let l(r) = 0. Calculate r.
0, 1, 2
Let k + k**4 + 2 - 4 - k**3 + 2 - k**2 = 0. What is k?
-1, 0, 1
Factor -14/3*a**4 + 2/3*a**2 + 4/3*a**3 + 0*a + 0 + 8/3*a**5.
2*a**2*(a - 1)**2*(4*a + 1)/3
Suppose 3*x - 6*x + 10 = -4*j, 0 = 4*x - 4*j - 12. Factor -2/11*n**x - 8/11*n - 8/11.
-2*(n + 2)**2/11
Suppose 2*q + 2*u = 14, -3*q - q + 28 = 2*u. Let f = q - 20/3. Factor 1/6*c - 1/6*c**3 - 1/3*c**2 + f.
-(c - 1)*(c + 1)*(c + 2)/6
Let y(i) be the second derivative of 5*i**4/48 + i. Determine a so that y(a) = 0.
0
Let g = 8 - 4. Suppose -g*i + 1 = -19. Suppose h**4 + 4*h**i - 5*h**4 - 6*h**5 - 2*h**3 = 0. What is h?
-1, 0
Solve 0 + 2/7*o**2 + 4/7*o - 2/7*o**3 = 0.
-1, 0, 2
Let t be -12*3/((-27)/3). Let l be 1/(0 + (-2)/(-6)). Suppose -1/3*z**t + 1/3*z - z**2 + 0 + z**l = 0. What is z?
0, 1
Let v(d) be the third derivative of 0 + 4*d**2 + 0*d**3 + 1/40*d**5 + 1/80*d**6 + 0*d + 1/420*d**7 + 1/48*d**4. Find r such that v(r) = 0.
-1, 0
Let o(l) be the third derivative of 1/420*l**6 - l**2 - 1/42*l**4 + 1/210*l**5 + 0*l**3 + 0 + 0*l. Find v such that o(v) = 0.
-2, 0, 1
Let i = -29/10 + 7/2. Let j(s) be the first derivative of -s**3 + i*s**5 + 0*s + 4 - 3/2*s**2 + 3/4*s**4. Let j(u) = 0. What is u?
-1, 0, 1
Let z(s) be the third derivative of -s**8/1176 + s**7/735 + s**6/210 - s**5/105 - s**4/84 + s**3/21 - 7*s**2. Factor z(b).
-2*(b - 1)**3*(b + 1)**2/7
Let j(i) be the first derivative of i**7/2940 - i**6/1260 + i**3 - 1. Let s(k) be the third derivative of j(k). Factor s(y).
2*y**2*(y - 1)/7
Let z(k) = -2*k**2 + 10*k - 6. Let a(s) = -4*s**2 + 21*s - 11. Let x(c) = -2*a(c) + 5*z(c). Factor x(o).
-2*(o - 2)**2
Let z(t) = -183*t**2 + 117*t + 12. Let k(r) = 14*r**2 - 9*r - 1. Let a(q) = 27*k(q) + 2*z(q). Find j, given that a(j) = 0.
-1/4, 1
Let v(r) be the second derivative of -r**4/12 - r**3/6 - 5*r. Suppose v(f) = 0. Calculate f.
-1, 0
Let a(d) be the third derivative of -d**6/300 + d**5/150 + d**4/30 - 7*d**2. Factor a(r).
-2*r*(r - 2)*(r + 1)/5
Let z = 1608/11 - 146. Factor 0*o - z*o**2 + 0.
-2*o**2/11
Find y, given that -1/5*y + 0 - 1/5*y**2 = 0.
-1, 0
Let w(c) = -3*c**3 - c**2 + 1. Let l be ((-3)/3)/(3 + -2). Let t be w(l). What is a in 0 - 32/9*a**4 - 2/9*a - 16/3*a**t - 2*a**2 = 0?
-1, -1/4, 0
Suppose -1 + 0 = -2*f - 3*l, 0 = f + 2*l. Factor 1 - 2*v**4 - 1 + 4*v**5 + 2*v**f - 2*v**3 - 2*v**5.
2*v**2*(v - 1)**2*(v + 1)
Let f = 1/282 - -2251/1410. Factor 2/5*g**4 + 8/5 + f*g - 6/5*g**2 - 4/5*g**3.
2*(g - 2)**2*(g + 1)**2/5
Find n such that 0*n - 1/3*n**3 + 0 + 0*n**2 + 1/3*n**4 = 0.
0, 1
Let d(b) be the first derivative of b**6/60 - b**2 - 3. Let g(j) be the second derivative of d(j). Factor g(u).
2*u**3
Let o(i) be the second derivative of -i**4/42 + i**2/7 + 4*i. Factor o(q).
-2*(q - 1)*(q + 1)/7
Let z(b) be the third derivative of 0*b**4 + 0 + 1/180*b**5 + 1/360*b**6 + 3*b**2 +