hat -1/3*n**3 - 1/3*n**2 + 1/3*n + b = 0.
-1, 1
Factor -6/5*c + 4/5 + 2/5*c**2.
2*(c - 2)*(c - 1)/5
Let u(b) be the first derivative of -b**7/210 + b**6/60 - b**5/60 - 5*b**2/2 - 2. Let i(p) be the second derivative of u(p). Determine d, given that i(d) = 0.
0, 1
Let o(h) be the second derivative of -h**5/30 + h**4/18 + 5*h**3/9 + h**2 + 7*h. Factor o(l).
-2*(l - 3)*(l + 1)**2/3
Suppose -2*k + 2 = k + 2*q, 2*k + 3*q + 2 = 0. Let i(a) be the first derivative of 0*a**k + 1/2*a**4 - 1 - 1/3*a**3 + 0*a - 1/5*a**5. Factor i(o).
-o**2*(o - 1)**2
Factor -3*t**2 + 12*t - 33*t**2 - 5801*t**3 + 5828*t**3.
3*t*(3*t - 2)**2
Let v(z) = 7*z**2 - 2*z + 2. Let x be v(2). Suppose x = 3*i - 4*s, -2*i + 4*s + 24 = -0*i. Let m**3 - 4*m**i + m**3 + 4*m**2 = 0. Calculate m.
0
Let h = -9/2 + 19/4. Factor 0 + 0*l**3 + 1/4*l - 1/2*l**2 + 1/2*l**4 - h*l**5.
-l*(l - 1)**3*(l + 1)/4
Let p = 13 - 22. Let c be 7 + p - (-5)/2. Factor -j + c*j**2 + 0.
j*(j - 2)/2
Let s(u) be the third derivative of -u**10/75600 - u**9/10080 - u**8/3360 - u**7/2520 - u**5/20 - u**2. Let o(k) be the third derivative of s(k). Factor o(i).
-2*i*(i + 1)**3
Let g(w) = 4*w**3 + 4*w**2 - 4*w - 3. Suppose 2*r - r - 4 = 0. Let p(z) = -z**4 + z**2 + 1. Let h(u) = r*p(u) - 4*g(u). Suppose h(v) = 0. What is v?
-2, -1, 1
Suppose -2*g = 2*a - 4, -4*g + 14 - 6 = -4*a. Determine t so that -g*t**3 + 0 - 2/3*t + 8/3*t**2 = 0.
0, 1/3, 1
Let l(n) = -n**2. Let j(a) = -a**2 + 5*a - 60. Let w(t) = -j(t) + 6*l(t). Suppose w(m) = 0. Calculate m.
-4, 3
Let c(a) be the first derivative of -16*a**5/25 - 8*a**4/5 - 4*a**3/3 - 2*a**2/5 - 1. What is b in c(b) = 0?
-1, -1/2, 0
Let x be ((-90)/8)/((-2)/8). Let m be 10/x - (-596)/18. Find p such that 40/3*p - m*p**2 - 16/9 + 250/9*p**3 = 0.
2/5
Let b(j) be the second derivative of j**7/7560 - j**4/4 + 3*j. Let h(v) be the third derivative of b(v). Solve h(l) = 0 for l.
0
Let x(g) be the first derivative of -g**4/8 - g**3/6 + 5*g**2/4 - 3*g/2 + 33. Factor x(s).
-(s - 1)**2*(s + 3)/2
Let m(s) = 2*s**2 - 3*s + 1. Let a be m(2). What is c in -c**2 + 3*c**a - 6*c**3 + 4*c**3 = 0?
0, 1
Let o(g) be the third derivative of -g**9/10584 - g**8/2940 - g**7/2940 - g**3/6 + g**2. Let f(j) be the first derivative of o(j). Solve f(a) = 0.
-1, 0
Let p = 22 - 15. Let w = -3 + p. Factor 9*l + 2*l**2 + 3 + 5 - w*l + 3*l.
2*(l + 2)**2
Let z(i) = 2*i**2 + 6*i - 16. Let u(w) = -w**2 - 7*w + 15. Let m(p) = -4*u(p) - 3*z(p). Factor m(b).
-2*(b - 3)*(b - 2)
Let h be (-1)/4 - 27/(-12). Find i such that -3*i**3 + 4*i**3 + 6*i**3 + 2*i**h = 0.
-2/7, 0
Let 2*g**2 + 10 + 5*g - 7*g**2 + 0*g**2 + 0*g = 0. What is g?
-1, 2
Let s(h) = h - 3. Let o(q) = -q + 7. Let p be o(0). Let j be s(p). Factor 0*m - 2/9*m**2 + 0 + 0*m**3 + 2/9*m**j.
2*m**2*(m - 1)*(m + 1)/9
Let x(d) = 11*d**2 - 4*d - 1. Let k be x(-3). Let n be (2 - -1) + k/(-50). Factor 6/5*s - n + 4/5*s**2.
2*(s + 2)*(2*s - 1)/5
Let j(a) = a - 5. Let d be j(5). Suppose d = 3*w + w - 8. Determine p, given that 2/3*p**w - 4/3 + 2/3*p = 0.
-2, 1
Let x(j) be the second derivative of -j**7/21 + 2*j**6/9 - j**5/3 + 5*j**3/9 - 2*j**2/3 + 5*j. Let x(b) = 0. Calculate b.
-2/3, 1
Let p be (8/14)/(2/7). Factor -1/3*m + 0 - 2/3*m**p.
-m*(2*m + 1)/3
Let j(m) = -m**2 - 1. Let w(p) = -8*p**2 - 2*p - 3. Let l(y) = 3*j(y) - w(y). Let t be l(2). Factor -3*i - 7*i - 10*i**3 - 8*i - 4 - t*i**2.
-2*(i + 1)**2*(5*i + 2)
Let g(r) = -2*r**4 - 12*r**3 - 16*r**2 - 8*r + 2. Let w(d) = -2*d**4 - 13*d**3 - 16*d**2 - 8*d + 3. Let z(x) = 3*g(x) - 2*w(x). Factor z(i).
-2*i*(i + 1)*(i + 2)**2
Suppose 3 = 4*v + 7. Let t(u) = -147*u**5 - 379*u**4 - 327*u**3 - 108*u**2 - 11*u. Let i(z) = -z**4 + z. Let d(x) = v*t(x) + i(x). Find j such that d(j) = 0.
-1, -2/7, 0
Suppose g = -2 + 4. Factor 3*y - g*y - y**2 - y.
-y**2
Let q(h) be the third derivative of -h**6/30 + h**5/5 + 2*h**4/3 - 9*h**2. Factor q(s).
-4*s*(s - 4)*(s + 1)
Let a be 3/(2 + (-415)/2). Let s = a + 558/685. Factor 2/5*b**2 + s + 6/5*b.
2*(b + 1)*(b + 2)/5
Let u = -123 + 131. Let i(r) be the first derivative of 4*r**2 + u*r + 3 + 2/3*r**3. Factor i(g).
2*(g + 2)**2
Let p be (-1)/2*-4 + -3 + 3. Factor 2*t**3 - 4/3 + 2/3*t**4 + 2/3*t**p - 2*t.
2*(t - 1)*(t + 1)**2*(t + 2)/3
Let u(l) be the first derivative of 12*l**5/5 + 11*l**4/2 - 40*l**3/3 + 3*l**2 + 12. Determine z, given that u(z) = 0.
-3, 0, 1/6, 1
Suppose 2*q - 2 = 2. Solve -u**3 - 3*u**3 + 4*u**3 - 2*u**4 + q*u**2 = 0.
-1, 0, 1
Let n be (16/12)/((-8)/(-18)). Solve n*v**2 + 1 + 1 - 5 = 0.
-1, 1
Let y = 325/3 - 107. Factor -2/3*q**2 + 0 + y*q.
-2*q*(q - 2)/3
Let v be 102/(-4)*2/(-3). Let w = v + -12. Factor -6*o**4 + o**2 + 7*o**2 - 4*o**3 + 4*o**w + 0 - 2.
2*(o - 1)**3*(o + 1)*(2*o + 1)
Let f(s) be the second derivative of s**4/28 + 5*s**3/42 - s**2/7 - s. Find g, given that f(g) = 0.
-2, 1/3
Let f(b) = b**3 - 6*b**2 + 5*b + 4. Let k be f(5). Factor -4*g - 7*g**2 + 3*g**2 + k*g**3 - g - 5*g**3 - 2.
-(g + 1)**2*(g + 2)
What is a in 2/3*a**2 + 2*a**4 - 2*a**3 + 0*a + 0 - 2/3*a**5 = 0?
0, 1
Let o(u) be the second derivative of -2*u + 0*u**5 + 0*u**3 + 0 - 1/98*u**7 + 1/7*u**4 - 3/70*u**6 + 0*u**2. Find n such that o(n) = 0.
-2, 0, 1
Factor -2/3 - 10/3*y - 25/6*y**2.
-(5*y + 2)**2/6
Solve 19*i**4 + i + i**3 - 20*i**4 + 0*i**2 + 3*i**2 + 2 - 6*i = 0 for i.
-2, 1
Let a be 15/(-42)*108/(-20). Let c = a + -10/7. Solve d + 1/2 + c*d**2 = 0 for d.
-1
Let h(p) be the second derivative of 4*p - 1/12*p**5 - 1/2*p**3 - 1/3*p**4 - 1/3*p**2 + 0. Let h(l) = 0. Calculate l.
-1, -2/5
Let g(s) = -27*s**2 + 32*s - 8. Let w(n) = 27*n**2 - 33*n + 9. Let d(a) = 3*g(a) + 4*w(a). Suppose d(v) = 0. What is v?
2/3
Let l be (-1)/(((-520)/16)/13). Determine o, given that -l*o**2 + 0 + 0*o = 0.
0
Suppose -j + 2*s + 1 = -10, -j = -4*s - 7. Suppose -p - 3 = -2*f - 2*p, 0 = -5*p + j. Find l, given that 4/3*l + 14/3*l**2 + f - 8/3*l**3 = 0.
-1/4, 0, 2
Let y(m) be the first derivative of -2*m**6/21 - 3. Suppose y(i) = 0. Calculate i.
0
Find y, given that 2/7*y**4 + 0*y + 0*y**2 + 0*y**3 - 2/7*y**5 + 0 = 0.
0, 1
Factor -1/4 - 3/8*s - 1/8*s**2.
-(s + 1)*(s + 2)/8
Let y(n) be the third derivative of n**5/12 - 5*n**3/6 + 6*n**2. Find h, given that y(h) = 0.
-1, 1
Let j(h) be the second derivative of -h**7/70 + h**6/30 + h**5/60 - h**4/12 - h**2 - 2*h. Let w(c) be the first derivative of j(c). Solve w(i) = 0.
-2/3, 0, 1
Let b be -6*1/(3/(-4)). Find c such that -b*c - 3*c**2 + 2*c - 6*c**2 - 3*c**3 = 0.
-2, -1, 0
Let v(p) be the second derivative of p**7/273 - 4*p**6/195 + 3*p**5/65 - 2*p**4/39 + p**3/39 - 6*p. What is j in v(j) = 0?
0, 1
Let m = -16 + 20. Let q(z) be the second derivative of 1/105*z**6 + 5/42*z**m + 0*z**2 + 2/35*z**5 + 0 + 2/21*z**3 - z. Solve q(w) = 0.
-2, -1, 0
Let d(o) = o**2 - 1. Let t(h) = h**2 - 4*h - 6. Let n(z) = z**2 - 7*z + 4. Let a be n(6). Let k(r) = a*d(r) + t(r). Suppose k(y) = 0. What is y?
-2
Let c be 1309/1836 + 4/(-6). Let s(j) be the third derivative of 0*j - 2/135*j**5 + 0 + j**2 + c*j**4 + 1/540*j**6 - 2/27*j**3. Factor s(r).
2*(r - 2)*(r - 1)**2/9
Let v(f) be the first derivative of f**6/18 - f**4/6 + f**2/6 - 12. Factor v(q).
q*(q - 1)**2*(q + 1)**2/3
Let g be ((-63)/(-35))/((-1)/(-5)). Suppose 0 = i + 5*u - 14, g = 5*u - 1. Factor -1/2*m**i + 1/2*m**2 + 0 + 0*m**3 + 0*m.
-m**2*(m - 1)*(m + 1)/2
Let g(b) be the third derivative of -b**6/60 - b**5/20 + b**3/6 - 40*b**2. What is s in g(s) = 0?
-1, 1/2
Let g(v) be the second derivative of -5/3*v**3 + 2*v**2 + 0 + 2/3*v**4 - 1/10*v**5 - 2*v. What is k in g(k) = 0?
1, 2
Let j(q) be the first derivative of q**6/21 - 2*q**4/7 - 4*q**3/21 + 3*q**2/7 + 4*q/7 + 34. Factor j(x).
2*(x - 2)*(x - 1)*(x + 1)**3/7
Let s(m) be the second derivative of m**6/2160 + m**5/240 + m**4/72 + 4*m**3/3 - 6*m. Let v(b) be the second derivative of s(b). Solve v(r) = 0 for r.
-2, -1
Let q(h) = 16*h + 450. Let b be q(-28). Factor 0*a**b + 1/4*a**3 - 1/4*a + 0.
a*(a - 1)*(a + 1)/4
Let d be (-4)/(-1*8/6). Let l(r) be the second derivative of -1/3*r**d - 1/6*r**4 + 0*r**2 + 0 - 2*r. Find q, given that l(q) = 0.
-1, 0
Let s(o) = 2*o**2 - 2. Let z be s(2). Let q(f) be the third derivative of 0 - 1/180*f**z - 1/72*f**4 + 2*f**2 + 0*f**3 + 0*f - 1/60*f**5. Factor q(g).
-g*(g + 1)*(2*g + 1)/3
Suppose 6*o - 5*o + 2*o**3 - 3*o + 0*o = 0. What is o?
-1, 0, 1
