b**3 - 5*b**2 + 12*b - 8. Let m(a) = -a**3 + 5*a**2 - 13*a + 9. Let z = -16 + 11. Let o(j) = z*n(j) - 4*m(j). Factor o(t).
-(t - 2)**2*(t - 1)
Let y(s) be the third derivative of -1/70*s**5 + 0 - 2/21*s**3 + 0*s + 1/735*s**7 - 1/420*s**6 + 3*s**2 + 5/84*s**4. Factor y(c).
2*(c - 1)**3*(c + 2)/7
Let m(z) be the first derivative of z**4/4 - 2*z**3 + 11*z**2/2 - 6*z + 11. Factor m(b).
(b - 3)*(b - 2)*(b - 1)
Let 56*x**4 - 57*x**4 - x**3 + 3*x**2 + 4*x**3 - 5*x**2 = 0. Calculate x.
0, 1, 2
Let a(m) = m**2 + 10*m + 4. Let s be a(-10). Suppose 2*t + 0*t = s. Determine c so that -2/3*c + 0 + 2/3*c**t + 2/3*c**3 - 2/3*c**4 = 0.
-1, 0, 1
Let g(s) be the first derivative of 3/2*s**4 - 1 + 0*s**2 - 4/3*s**3 + 0*s - 2/5*s**5. Let g(m) = 0. What is m?
0, 1, 2
Let d(p) be the third derivative of -1/336*p**8 + 0 + 0*p**4 + 0*p**3 + 2*p**2 + 1/120*p**6 + 0*p - 1/60*p**5 + 1/210*p**7. Determine m so that d(m) = 0.
-1, 0, 1
Let w(i) be the first derivative of i**4/26 - 4*i**3/39 - 4. Factor w(j).
2*j**2*(j - 2)/13
Let u = 6 + -7. Let c = u + 3. Factor s**3 - 7 + 7 + 0*s - c*s**4 - s + 2*s**2.
-s*(s - 1)*(s + 1)*(2*s - 1)
Let b(u) = -10*u**4 + 6*u**3 + 26*u**2 - 33*u + 8. Let o(c) = -9*c**4 + 7*c**3 + 26*c**2 - 34*c + 8. Let r(a) = -2*b(a) + 3*o(a). Suppose r(m) = 0. What is m?
-2, 2/7, 1, 2
Factor -2/11*t**2 - 4/11*t + 0.
-2*t*(t + 2)/11
Let a(x) = x**2 - 4*x - 1. Let s be a(5). Let i = s + -4. Let i - j**2 + 1 + 0 = 0. What is j?
-1, 1
Let p(d) be the first derivative of d**4/10 + 4*d**3/3 + 17*d**2/5 + 16*d/5 + 17. Solve p(r) = 0.
-8, -1
Suppose 0 = 4*v - 12, -3*p + p + v = -1. Find z such that 7*z**2 + z**5 + 0*z**2 - z**4 - p*z**2 - 4*z**2 - z**3 = 0.
-1, 0, 1
Let y(v) be the first derivative of -v**6/24 - v**5/20 + v**4/16 + v**3/12 + 3. Find a such that y(a) = 0.
-1, 0, 1
Determine b, given that 1/6*b**5 + 0 + 1/6*b + 0*b**2 - 1/3*b**3 + 0*b**4 = 0.
-1, 0, 1
Let d = -11 + 16. Let x(a) = -2*a**2 + 3*a - 5. Let g(v) = v**2 - 2*v + 4. Let n(i) = d*g(i) + 4*x(i). Let n(m) = 0. What is m?
0, 2/3
Let r(m) be the third derivative of m**6/450 + 2*m**5/75 + 2*m**4/15 - 4*m**3/3 - 2*m**2. Let z(d) be the first derivative of r(d). Solve z(a) = 0 for a.
-2
Let j(p) = -p**2 + 2*p + 3. Let a be j(3). Factor 11*c**2 - 8*c**2 + a - 3.
3*(c - 1)*(c + 1)
Let m(r) = r**2 - 5*r + 7. Let y be m(4). Factor 1/2*f**2 - 1/2 - 1/2*f + 1/2*f**y.
(f - 1)*(f + 1)**2/2
Let q(j) be the first derivative of j**6/10 + 3*j**5/25 - 3*j**4/20 - j**3/5 + 16. Factor q(l).
3*l**2*(l - 1)*(l + 1)**2/5
Let w(v) be the second derivative of v**6/1440 - v**5/240 + v**4/96 + v**3/2 - 2*v. Let n(f) be the second derivative of w(f). Factor n(j).
(j - 1)**2/4
Let w(u) be the third derivative of u**7/1155 + u**6/132 + 3*u**5/110 + 7*u**4/132 + 2*u**3/33 - 11*u**2. Suppose w(f) = 0. Calculate f.
-2, -1
Let c(u) be the first derivative of 2*u**5/25 - 8*u**3/15 + 38. Suppose c(s) = 0. Calculate s.
-2, 0, 2
Let l(p) be the third derivative of p**10/75600 + p**9/10080 + p**8/5040 - p**5/30 - 3*p**2. Let w(k) be the third derivative of l(k). Factor w(h).
2*h**2*(h + 1)*(h + 2)
Let s(w) be the third derivative of 2*w**7/105 + w**6/15 - w**5/15 - w**4/3 + 9*w**2. Factor s(c).
4*c*(c - 1)*(c + 1)*(c + 2)
Let a(i) be the second derivative of i**4/114 - 10*i**3/57 + 9*i**2/19 + 2*i + 14. Solve a(m) = 0 for m.
1, 9
Let a(d) = -3*d + 3. Let s be a(-10). Suppose -p - 5*r = -28, 14 = -3*p - 2*r + s. Solve -9/2*g**p - 3*g**2 - 2*g**4 - 1/2*g + 0 = 0.
-1, -1/4, 0
Let z(v) = v**3 + 26*v**2 - 27*v + 3. Let q be z(-27). Suppose 0 - 6/5*o**q + 6/5*o**5 + 2/5*o**4 - 2/5*o**2 + 0*o = 0. What is o?
-1, -1/3, 0, 1
Let s(j) be the second derivative of j**6/6 - 5*j**4/12 + 10*j. Factor s(q).
5*q**2*(q - 1)*(q + 1)
Let n = -1/7 + 13/42. Let v(z) be the first derivative of -1/4*z**4 + n*z**3 + 0*z + 1/4*z**2 - 2. Factor v(c).
-c*(c - 1)*(2*c + 1)/2
Let h(v) be the third derivative of -v**5/150 - 2*v**4/15 - 16*v**3/15 - 6*v**2. Find g such that h(g) = 0.
-4
Let o be (-2)/((-1)/(-2)*-1). Factor -i**2 + i**5 - 6*i**4 - i**4 + 3*i**3 + 4*i**o.
i**2*(i - 1)**3
Let w = -137 - -141. Let 3/4*n**w + 0*n - 3/4*n**3 + 0 + 0*n**2 = 0. What is n?
0, 1
Let v = 11 - 7. Find f such that 4*f + v + 0*f**3 + 2*f - 2*f**3 = 0.
-1, 2
Let w(h) = h**3 - h**2 + h. Let y = 3 - -4. Let a = -6 + y. Let z(x) = 3*x**3 + 2*x**2 - 11*x + 2. Let q(m) = a*z(m) + 4*w(m). Factor q(v).
(v - 1)*(v + 1)*(7*v - 2)
Suppose -3*a - a = -3*o - 10, a = -2*o + 8. Factor -3*r + a*r + 3*r**2 - 3*r - 3*r**3 + r + r**4.
r*(r - 1)**3
Let s(a) = -a**5 + 45*a**4 - 27*a**3 - 26*a**2 - 8*a - 17. Let n(m) = 15*m**4 - 9*m**3 - 9*m**2 - 3*m - 6. Let y(v) = 17*n(v) - 6*s(v). Factor y(j).
3*j*(j - 1)**3*(2*j + 1)
Let k = -111 + 111. Let -2/11*d**2 + 0 + k*d = 0. What is d?
0
Suppose -5*p = -0*x + 4*x + 31, -19 = 2*x - p. Let q(g) = 10*g**2 + 18*g. Let u(t) = -19*t**2 - 36*t + 1. Let w(i) = x*q(i) - 4*u(i). Solve w(o) = 0.
-1, -2/7
Let f(k) be the first derivative of -35/9*k**6 - 8/9*k**3 + 0*k**2 - 14/3*k**4 - 2 + 0*k - 118/15*k**5. What is m in f(m) = 0?
-1, -2/5, -2/7, 0
Let a(o) = 63*o - 1. Let d be a(-2). Let k = d + 637/5. Solve k*i - 4/5*i**2 - 2/5*i**3 + 4/5 = 0.
-2, -1, 1
Solve 5*l + 172*l**4 - l**5 - 162*l**4 - 4*l**5 - 10*l**2 = 0 for l.
-1, 0, 1
Let n(p) be the third derivative of -p**6/1020 + p**5/170 - p**4/102 - 3*p**2 + 5. Factor n(y).
-2*y*(y - 2)*(y - 1)/17
Let m(a) be the third derivative of a**8/448 + a**7/70 + a**6/32 + a**5/40 + 4*a**2. Let m(x) = 0. Calculate x.
-2, -1, 0
Let z(t) = -2*t**2 + 0*t**2 + t**2. Let y(u) = -30*u**2 - 10*u - 1. Let m(s) = -y(s) + 5*z(s). Factor m(v).
(5*v + 1)**2
Suppose -4*c + 8 = -3*o, -3*c + 2*o + 1 = -5. Find p, given that -10*p**3 - 5*p**c - 3*p**4 + p**3 - 3*p - 4*p**2 = 0.
-1, 0
Let g(v) = -v**5 - 4*v**4 + 2*v**3 - v**2 + 2*v - 1. Let u(h) = -2*h**5 - 7*h**4 + 4*h**3 - h**2 + 3*h - 2. Let p(i) = 5*g(i) - 3*u(i). Factor p(y).
(y - 1)**2*(y + 1)**3
Suppose 0 = -4*u + x + 6, -2 - 2 = -2*x. Determine j so that 7*j**3 - 8*j**5 + 4*j**u - 2*j**4 - 2 - j**3 + 10*j**3 - 8*j = 0.
-1, -1/4, 1
Let f(m) be the first derivative of m**6/120 - m**5/40 + 2*m**3/3 + 1. Let k(r) be the third derivative of f(r). Factor k(x).
3*x*(x - 1)
Let b(q) be the third derivative of -q**5/12 + q**4/6 - q**3/2 + 6*q**2. Let c(w) = -11*w**2 + 8*w - 6. Let m(s) = -9*b(s) + 4*c(s). Factor m(z).
(z - 3)*(z - 1)
What is k in 0*k + 0*k**4 + 0*k**2 - 5/3*k**5 + 0*k**3 + 0 = 0?
0
Let i(o) = -7*o**4 - 9*o**3 + 19*o**2 + 3*o. Let m(a) = -36*a**4 - 44*a**3 + 96*a**2 + 16*a. Let x(g) = 16*i(g) - 3*m(g). Suppose x(s) = 0. What is s?
-4, 0, 1
Let a(q) be the first derivative of -98*q**6/45 + 7*q**5/5 + 8*q**4/3 + 8*q**3/9 - 7*q - 1. Let x(f) be the first derivative of a(f). Factor x(j).
-4*j*(j - 1)*(7*j + 2)**2/3
Let a(x) = -5*x - 8. Let f be a(-13). Let k = f - 227/4. Factor -1/4*b + 3/4*b**2 + 1/4*b**3 - 1/2 - k*b**4.
-(b - 2)*(b - 1)*(b + 1)**2/4
Let a(u) be the third derivative of -u**8/112 + 3*u**7/70 - 3*u**6/40 + u**5/20 - 2*u**2. Solve a(n) = 0.
0, 1
Let u(n) be the first derivative of -4*n**3 - 9*n**2/2 + 3*n - 2. Find v such that u(v) = 0.
-1, 1/4
Let c(d) be the third derivative of d**5/240 - d**4/32 + 14*d**2. Suppose c(y) = 0. What is y?
0, 3
Let i(u) = 4*u**2 + 36*u - 24. Let d(r) = -r**2 - 7*r + 5. Let o(f) = 24*d(f) + 5*i(f). Suppose o(z) = 0. Calculate z.
0, 3
Let h(v) be the first derivative of -2*v**3/3 + 8*v - 3. Solve h(l) = 0 for l.
-2, 2
Let j(h) = -h**2 - 9*h + 4. Let b be j(-9). Let -w**3 - 2*w**2 - w**2 + b*w**2 = 0. Calculate w.
0, 1
Determine t, given that 7/3*t**3 - 1/3*t**2 - 4/3 - 8/3*t + 1/3*t**5 + 5/3*t**4 = 0.
-2, -1, 1
Factor 0 + 0*f - 2/5*f**3 + 2/5*f**2.
-2*f**2*(f - 1)/5
Suppose 4*y - 5*y = -2. Factor -7*a - a**4 - 4*a**2 + 2 + 10*a - 4*a**3 + a**3 + 3*a**y.
-(a - 1)*(a + 1)**2*(a + 2)
Factor -1/4*q**4 - 1/2*q + q**2 + 1/2*q**3 - 3/4.
-(q - 3)*(q - 1)*(q + 1)**2/4
Let w(x) be the third derivative of -x**8/168 + 2*x**7/105 + x**6/20 - 2*x**5/15 - x**4/3 + 7*x**2. Suppose w(v) = 0. Calculate v.
-1, 0, 2
Let t(d) = d. Let c be t(4). Suppose -2*w + c + 0 = 0. Let k**4 + 2*k**3 - 3*k**w + 0*k**3 - 3*k**3 + 5*k - 2 = 0. What is k?
-2, 1
Let n(k) be the second derivative of -k**10/120960 - k**9/20160 - k**8/8960 - k**7/10080 - k**4/4 + 2*k. 