
-1, 0, 1
Let s be 6 + -6 + (-2)/(-160). Let y(b) be the second derivative of 0 - 1/2*b**3 - b**2 - 1/8*b**4 - 3*b - s*b**5. Factor y(a).
-(a + 2)**3/4
Let a be -1 - (-6 - -3) - 2. Find c such that -3*c**3 + 2*c**2 + 3*c**4 - 7*c**2 + 2*c**2 + a*c**2 + 3*c**5 = 0.
-1, 0, 1
Let a(q) be the first derivative of -q**7/2940 + q**6/1260 + q**5/420 - q**4/84 - 5*q**3/3 + 2. Let i(z) be the third derivative of a(z). Solve i(u) = 0.
-1, 1
Let v(u) be the second derivative of u**4/12 - 2*u**3/3 + 2*u**2 + 2*u. Factor v(y).
(y - 2)**2
Let d(a) be the third derivative of a**8/1344 + a**7/210 + a**6/96 + a**5/120 - 10*a**2. Determine o so that d(o) = 0.
-2, -1, 0
Let z(x) be the first derivative of x**5/210 - x**2/2 - 1. Let n(r) be the second derivative of z(r). What is d in n(d) = 0?
0
Let k(n) be the first derivative of -1 + 0*n + 0*n**4 + 1/27*n**6 + 4/45*n**5 - 1/9*n**2 - 4/27*n**3. Solve k(t) = 0 for t.
-1, 0, 1
Let j(p) be the third derivative of p**5/15 + 5*p**4/6 + 4*p**3 - 18*p**2. Solve j(v) = 0.
-3, -2
Let m(z) be the first derivative of 7*z**6/1800 + 19*z**5/600 - z**4/20 + 2*z**3 + 2. Let h(u) be the third derivative of m(u). Find s such that h(s) = 0.
-3, 2/7
Suppose -v + 8 = -4*z, 2*v - 9*z - 13 = -4*z. Suppose 0 = i - 0*i - v. Find d, given that 0*d - 3*d - 2*d**5 + 5*d + 4*d**4 - i*d**2 = 0.
-1, 0, 1
Let m be (-454)/9*(-3)/2. Let o = m + -75. Factor o*x**2 - 2/3*x - 2/3*x**4 + 0 + 2/3*x**3.
-2*x*(x - 1)**2*(x + 1)/3
Let j be 5 + (8/(-6))/((-10)/(-36)). Suppose -1/5*l + 1/5*l**2 - 1/5 + j*l**3 = 0. Calculate l.
-1, 1
Let w = 12 - 10. Let c be (1/5)/(w/6). Factor -1/5*g**4 - 3/5*g**3 - c*g**2 + 0 - 1/5*g.
-g*(g + 1)**3/5
Let x(l) = 10*l**5 - 8*l**3 - 2*l. Let h(y) = -y**5 + y**3 - y**2 + y. Let v be 14/(-12) + (-2)/(-12). Let n(d) = v*x(d) - 2*h(d). Solve n(i) = 0.
-1/2, 0, 1
Let d(o) = o**3 + o**2 + 1. Let p be ((-6)/9)/(2/(-3)). Let g(w) = -8*w**5 + 10*w**4 - 16*w**2 + 2*w - 6. Let c(a) = p*g(a) + 6*d(a). Solve c(v) = 0 for v.
-1, 0, 1/4, 1
Suppose 10 = 2*w + 2. Let 5*z**4 + 3*z**w + 0*z**2 + 10*z**2 - 2*z - 16*z**3 = 0. Calculate z.
0, 1/2, 1
Factor -1/2 - 1/2*b**2 - b**3 - 1/4*b**5 + 5/4*b + b**4.
-(b - 2)*(b - 1)**3*(b + 1)/4
Let t = 11 + -7. Suppose 4*f - 10 = -3*g + 5, 4*f + t*g - 16 = 0. Determine y, given that -80/3*y**f - 2/3 - 22*y**2 - 20/3*y - 32/3*y**4 = 0.
-1, -1/4
Let q(g) = -7*g**3 - 6*g**2 - 12*g - 8. Let m(k) = k + 10. Let n be m(-9). Let z(t) = t**3. Let l(i) = n*q(i) + 6*z(i). Determine x, given that l(x) = 0.
-2
Let o = -1305 - -39143/30. Let v = 1/10 - o. Determine w so that 0 + 0*w - v*w**2 = 0.
0
Determine c so that -4/3*c - 2 + 2/3*c**2 = 0.
-1, 3
Let v(b) = -b + 5. Let o be v(0). Let m(x) = -x**3 + 5*x**2 + 2. Let w be m(o). Factor -6*s**2 + 2*s**5 + 7*s**2 - w*s - 4*s**4 + 3*s**2.
2*s*(s - 1)**3*(s + 1)
Factor 26/15*v**3 + 8/15*v + 0 + 2/15*v**5 - 4/5*v**4 - 8/5*v**2.
2*v*(v - 2)**2*(v - 1)**2/15
Let h = 4/5421 + 1035395/21684. Let j = -47 + h. Find v such that -j*v**4 + 0*v**3 + 3/2*v**2 + 0*v - 3/4 = 0.
-1, 1
Let i(r) be the third derivative of r**7/1785 - r**5/170 + r**4/102 + 4*r**2. Factor i(f).
2*f*(f - 1)**2*(f + 2)/17
Let y(m) = -m**2 + 7*m - 3. Suppose -k + 3*k = 12. Let r be y(k). Factor -2*t**2 - 2*t + 0*t**3 + t**4 + t**4 + 2*t**r.
2*t*(t - 1)*(t + 1)**2
Let f(c) = 3*c**3 - 4*c**2 + c. Let a(i) = i**2 - i. Suppose -5*r + 3*w = -29, 0*r - w = 2*r - 5. Let p(o) = r*a(o) + f(o). Find t, given that p(t) = 0.
-1, 0, 1
What is a in -157 + 157 + 3*a - 4*a + a**2 = 0?
0, 1
Let j(z) = z**3 + 11*z**2 - 12*z. Let b be j(-12). Factor k + k**2 + k + b*k + 4 - 3*k**2.
-2*(k - 2)*(k + 1)
Let y(i) = i - 12 + 12 - i**2. Let w be y(1). What is u in 0 - 1/3*u**3 + w*u - 1/3*u**4 + 0*u**2 = 0?
-1, 0
Suppose -2*n = 2*q, 2*n + q - 12 = -2*n. Let u be n/4 - 1/3. Factor -2/3*k + 0 - u*k**2.
-2*k*(k + 1)/3
Let f(i) be the third derivative of i**6/120 + i**5/40 - i**3 + i**2. Let t(w) be the first derivative of f(w). Let t(d) = 0. Calculate d.
-1, 0
Let o(c) = -30*c**2 + 69*c - 81. Let d(g) = 3*g**2 - 7*g + 8. Let l(j) = 21*d(j) + 2*o(j). Factor l(q).
3*(q - 2)*(q - 1)
Let n(h) be the second derivative of -h**9/30240 - h**8/13440 + h**7/5040 + h**6/1440 + h**4/12 - 7*h. Let v(l) be the third derivative of n(l). Factor v(x).
-x*(x - 1)*(x + 1)**2/2
Let i(l) = l**3 + 3*l**2 - 10*l. Let d be i(-5). Factor 2/7*n**2 - 2/7*n + d.
2*n*(n - 1)/7
Let g(r) be the first derivative of -3*r**4/20 + r**3/5 + 8. Suppose g(u) = 0. What is u?
0, 1
Determine q so that -1/7*q**4 + 0 + 0*q**2 + 1/7*q**3 + 0*q = 0.
0, 1
Suppose 3*s + 8 = s, -2*y - 28 = 3*s. Let a be y - -9 - 2/4. Factor 0*b**4 + 1/4*b + 0 + 1/4*b**5 - a*b**3 + 0*b**2.
b*(b - 1)**2*(b + 1)**2/4
Suppose -6*z + 4 = -14. Let v(g) be the third derivative of 0 + 1/240*g**5 + 1/480*g**6 + 0*g + 0*g**z - g**2 - 1/96*g**4 - 1/840*g**7. Solve v(c) = 0.
-1, 0, 1
Suppose -5*w + 0*p = 3*p - 16, 4*p - 8 = 0. Let j(x) be the first derivative of 0*x**w + 0*x + 2/5*x**5 + 0*x**3 - 1/2*x**4 - 3. Solve j(k) = 0 for k.
0, 1
Let h(x) be the second derivative of -x**5/80 - x**4/12 - x**3/6 + 5*x. Factor h(t).
-t*(t + 2)**2/4
Let f be -8 - (-2 - -1)*2. Let r be 3/(-2)*16/f. Solve -7*i - i**3 + 0*i**2 - i - r - 7*i**2 + 2*i**2 = 0 for i.
-2, -1
Suppose -19 = -3*k - 10. Let m(n) be the third derivative of 0*n + 0*n**4 + 1/20*n**5 - n**2 - 2/3*n**k + 0 + 1/120*n**6. What is w in m(w) = 0?
-2, 1
Let b(g) be the first derivative of 322/15*g**3 + 8/5*g + 5 + 44/5*g**2 + 98/5*g**4. Factor b(o).
2*(4*o + 1)*(7*o + 2)**2/5
Let j = 49 - 97/2. Factor -2 - j*x**2 + 2*x.
-(x - 2)**2/2
Let i(b) = b - 2. Let z be i(4). Let a = z + -4. Let m(f) = -f**2 - f - 5. Let v(p) = -2. Let s(x) = a*m(x) + 5*v(x). Suppose s(g) = 0. Calculate g.
-1, 0
Let h(f) be the first derivative of 2*f - 2/5*f**5 - f**4 + 0*f**3 + 2*f**2 - 3. Solve h(a) = 0.
-1, 1
Let 3/4 - 3/2*z**2 + 1/4*z - 1/2*z**3 + 1/4*z**5 + 3/4*z**4 = 0. Calculate z.
-3, -1, 1
Suppose -25*r + 6 = -24*r. Let l(h) be the third derivative of 1/105*h**7 - 1/30*h**5 + 0*h - 2*h**2 + 0 + 0*h**3 - 1/60*h**r + 1/12*h**4. Factor l(x).
2*x*(x - 1)**2*(x + 1)
Suppose 24 = 4*l + 4*s, 4 = -l - 2*s + 13. Find t, given that 1/3*t**4 - 2/3*t + 2/3*t**l + 0*t**2 - 1/3 = 0.
-1, 1
What is r in -1/5*r**3 + 1/5*r**2 - 1/5*r**4 + 0 + 1/5*r = 0?
-1, 0, 1
Suppose -6*z + 1147 = 1135. Factor 2/5*y**5 - 6/5*y**3 + 2/5*y**4 + 0 - 4/5*y - 2*y**z.
2*y*(y - 2)*(y + 1)**3/5
Suppose 9 - 21 = -4*s. Factor -2*p + p**3 + s*p**2 - 2*p + 5*p - p**2.
p*(p + 1)**2
Let r(g) be the first derivative of 3*g**5/4 - 21*g**4/16 + g**3/2 + 13. What is z in r(z) = 0?
0, 2/5, 1
Let a(w) be the first derivative of -6 - 16/5*w + 1/10*w**4 + 12/5*w**2 - 4/5*w**3. Solve a(v) = 0 for v.
2
Let y(w) be the third derivative of 0*w**3 + 0*w - 4*w**2 + 0 + 0*w**4 - 1/30*w**5. Factor y(j).
-2*j**2
Let g = 4 - -1. Factor -2 - 7 - 10*u - 3*u**2 + 3*u**3 - g*u.
3*(u - 3)*(u + 1)**2
Let d(j) be the second derivative of j**6/720 + 2*j**3/3 + 2*j. Let t(v) be the second derivative of d(v). Factor t(i).
i**2/2
Find n, given that -3/7*n + 3/7*n**3 + 18/7 - 18/7*n**2 = 0.
-1, 1, 6
Let k = -89 - -91. What is u in -7/2*u**3 + 9*u**k + 4 + 1/2*u**4 - 10*u = 0?
1, 2
Let d(c) be the first derivative of -5*c**5/2 + 55*c**4/16 + 20*c**3/3 - 55*c**2/8 - 15*c/2 - 32. Determine p, given that d(p) = 0.
-1, -2/5, 1, 3/2
Let v(d) be the third derivative of 1/24*d**4 - 1/30*d**5 + 0*d**3 + 1/120*d**6 - 3*d**2 + 0*d + 0. Determine t so that v(t) = 0.
0, 1
Let r be 28/7*2/4. Suppose 2 = 4*f + 3*v, r*v + 20 = 5*f - 3*v. Let 4*d + d**f - 3*d**2 + 0*d = 0. Calculate d.
0, 2
Let q(n) be the third derivative of n**7/2100 + n**6/200 + 11*n**5/600 + n**4/40 - 58*n**2. Factor q(r).
r*(r + 1)*(r + 2)*(r + 3)/10
Suppose t + 2*t = 15. Suppose t*c - m = 14, -5*m - 13 - 5 = c. Factor 3*d**c - 3*d**2 + 2*d**2 + 0*d**2.
2*d**2
Let w(s) = s**3 + 3*s**2 + s - 2. Let v be w(-2). Suppose -6*k = -k - 15. Let v*d**k + 0*d**3 - d**5 - d**3 + 2*d**4 = 0. What is d?
0, 1
Let x = -49/2 - -457/18. Factor 0 - 8/9*q**4 - x*q**2 - 2/9*q**5 - 2/9*q - 4/3*q**3.
-2*q*(q + 1)**4/9
Suppose -2*m + 13 = 3*s, 5*s = 2*m - 7*m + 20. Suppose s*a = a + 32. Suppose 5*w**4 - 2*w + 7*w**2 + a*w**3 + w**5 + w**3 + 4*w = 0. Calculate w.
-2, -1, 0
Let -26/7*h - 12/7 - 10/7*h**2 = 0. What is h?
