*(d - 2)*(d - 1)*(d + 1)/4
Let k(u) be the first derivative of -3 - 1/18*u**6 + 2/15*u**5 + 0*u**2 + 0*u**3 - 1/12*u**4 + 0*u. What is g in k(g) = 0?
0, 1
Let m = 2/2431 + 372/2431. Let 4/13*x**4 + 0 + 0*x**3 - 2/13*x + m*x**5 - 4/13*x**2 = 0. What is x?
-1, 0, 1
Let l(u) = -7*u**2 + 21*u - 33. Let b(t) = 8*t**2 - 20*t + 32. Let n(p) = -3*b(p) - 4*l(p). Solve n(h) = 0 for h.
3
Let n = -75 + 77. Factor -16/5 - 12/5*j**n + 2/5*j**3 + 24/5*j.
2*(j - 2)**3/5
Let y(l) = -3*l**4 - 4*l**3 - 3*l**2 - 2*l + 2. Let x(g) = -7*g**4 - 8*g**3 - 5*g**2 - 4*g + 5. Let d(c) = -2*x(c) + 5*y(c). Factor d(p).
-p*(p + 1)**2*(p + 2)
Let -12 + h**2 - 10*h**3 + 7*h**3 + 4*h + 11*h**2 - h**3 = 0. What is h?
-1, 1, 3
Let x(w) = -w**4 + w**3 + w**2 + w - 1. Let f(h) = 2*h**4 - 17*h**3 + 95*h**2 - 257*h + 257. Let y(m) = -f(m) - x(m). Suppose y(g) = 0. What is g?
4
Let b = -704 + 2819/4. Factor 15/4*c + 15/4*c**4 + 15/2*c**2 + 3/4 + 15/2*c**3 + b*c**5.
3*(c + 1)**5/4
Let k = -8 - -13. Let r(w) = 3*w**2 + w + 8. Let n(h) = -3*h**2 - 2*h - 7. Let p(q) = k*n(q) + 4*r(q). Factor p(c).
-3*(c + 1)**2
Let u be (4/14)/(4/8). Let p be ((-12)/(-56))/3*20. Factor u*y + 8/7*y**3 + p*y**2 + 0 + 2/7*y**4.
2*y*(y + 1)**2*(y + 2)/7
Suppose -4*v**3 + 4/3*v**4 + 24 + 20*v - 28/3*v**2 = 0. What is v?
-2, -1, 3
Suppose -25 = 4*u - 5*x + 16, -2*u + 5*x = 33. Let l be 15/(-20) - 5/u. Factor 1/2*o + l - 1/2*o**2 - 1/2*o**3.
-(o - 1)*(o + 1)**2/2
Let x = -1 - -6. Let t = -1 + x. Let -t*j + j**2 - 2*j**5 + 6*j**3 + 9*j**2 + 4*j - 2*j**4 + 4*j = 0. Calculate j.
-1, 0, 2
Let c(l) = l**3 + l**2 + l + 1. Let v(b) = -10*b**3 + 18*b**2 - 28*b + 4. Let a(k) = 4*c(k) + v(k). Let a(d) = 0. Calculate d.
2/3, 1, 2
Let f(t) be the third derivative of t**7/126 - t**5/36 - 20*t**2. Let f(p) = 0. What is p?
-1, 0, 1
Suppose 3*l**2 - 3*l**2 + 3*l**2 + 36 - l**2 - 38*l = 0. Calculate l.
1, 18
Let p(d) be the third derivative of 0*d + 0*d**4 + 3*d**2 + 1/360*d**5 + 0*d**3 + 1/720*d**6 + 0. Determine n, given that p(n) = 0.
-1, 0
Suppose 0*o - 2 = -2*o. Let t = o + -2. Let q(a) = -a**3 - a**2 + 1. Let j(p) = 23*p**3 + 27*p**2 + 4*p - 5. Let h(g) = t*j(g) - 5*q(g). Factor h(k).
-2*k*(k + 1)*(9*k + 2)
Let b be ((-4)/35)/((-6)/15). Factor b*l**2 + 0 - 4/7*l.
2*l*(l - 2)/7
Suppose -12 = -2*n - 0. Let i(h) be the first derivative of -1/5*h**5 + 2 - 1/6*h**n + 3/4*h**4 - h**2 + 1/3*h**3 + 0*h. Solve i(t) = 0.
-2, -1, 0, 1
Find w such that -1/5*w**2 + 0 + 2/5*w = 0.
0, 2
Suppose -5*u - 3*p = -37, -5*u + 25 = 5*p - 20. Factor 10/3*a**u + 0*a + 0 - 8*a**4 - 4/3*a**2 + 6*a**3.
2*a**2*(a - 1)**2*(5*a - 2)/3
Let m(c) be the second derivative of 0*c**3 + 0*c**2 - 9/140*c**5 + 1/70*c**6 + 0 + 1/14*c**4 - 5*c. Factor m(q).
3*q**2*(q - 2)*(q - 1)/7
Let k = -1 + 5. Let i(o) = o**3 + 13*o**2 - 65*o - 7. Let m be i(4). Determine f, given that 5/4*f**3 + 9/4*f**2 + 1/2*f - 7/4*f**m + 0 - 9/4*f**k = 0.
-1, -2/7, 0, 1
Let r(s) be the third derivative of 0*s**3 + s**2 + 0 - 1/1050*s**7 + 1/60*s**4 + 1/100*s**5 + 0*s + 0*s**6. Factor r(q).
-q*(q - 2)*(q + 1)**2/5
Let a(w) be the first derivative of 2*w + 1/3*w**3 - 2 + 3/2*w**2. Factor a(c).
(c + 1)*(c + 2)
Let b(z) be the third derivative of z**7/2100 - 7*z**6/1800 + z**5/150 + z**4/8 + z**2. Let w(i) be the second derivative of b(i). Let w(r) = 0. What is r?
1/3, 2
Let c(x) be the third derivative of -x**6/40 + x**5/20 + x**4/4 - 44*x**2. Let c(z) = 0. Calculate z.
-1, 0, 2
Let z(r) be the third derivative of 0 + 1/3*r**3 + 0*r + 0*r**4 - 1/30*r**5 - 5*r**2. Find h, given that z(h) = 0.
-1, 1
Let b(s) be the first derivative of -s**4/24 + s**3/12 + 3*s + 3. Let r(v) be the first derivative of b(v). Let r(x) = 0. Calculate x.
0, 1
Let w(t) be the third derivative of -t**7/630 + t**5/20 + t**4/18 - 2*t**3/3 + 4*t**2. Solve w(v) = 0.
-2, 1, 3
Let y(g) be the second derivative of -g**5/50 + g**3/5 + 2*g**2/5 - 40*g. Determine b so that y(b) = 0.
-1, 2
Let g(p) be the second derivative of -p**4/4 - 3*p**3 - 15*p**2/2 - 16*p. Let g(m) = 0. Calculate m.
-5, -1
Let k(p) = -p**2 - 9*p + 2. Let r be k(-9). Suppose 21 = r*s + s. Factor s*i - 22*i**3 + 2*i - 3*i**4 + 3 - 3*i + 16*i**3.
-3*(i - 1)*(i + 1)**3
Suppose 0 = -s + 5*q - 15, -5*s + 2*q = -0*q - 17. Factor 7*o**s - 4*o**3 - 6*o**5 + 3*o**3.
o**3*(o - 1)*(o + 1)
Let t be (-2)/21*(14/(-2) + 4). Suppose 0 + t*j - 2/7*j**3 + 0*j**2 = 0. What is j?
-1, 0, 1
Solve -18/7*r**4 - 32/7 + 64/7*r**3 + 96/7*r + 2/7*r**5 - 16*r**2 = 0.
1, 2
Let m(s) be the second derivative of -1/42*s**7 + 1/15*s**6 + 2*s + 0 + 0*s**5 + 0*s**2 + 1/6*s**3 - 1/6*s**4. Suppose m(j) = 0. What is j?
-1, 0, 1
Let r(b) = 2*b - 4. Let v be r(4). Determine o, given that 5*o**3 - 4*o**3 - 4 + 3*o**2 - 2*o**2 - v*o = 0.
-2, -1, 2
Solve -3/4*z**2 + 0 + 9/8*z**3 - 3/8*z**4 + 0*z = 0 for z.
0, 1, 2
Suppose 12 = -0*a + a + 2*j, 21 = 3*a + 3*j. Let t(y) be the first derivative of 1 - 7/9*y**3 + 1/3*y**a + 0*y. Determine p, given that t(p) = 0.
0, 2/7
Suppose z + 2 + 0 = -d, 6 = -3*z. Find u, given that -5/4*u**5 - 1/2*u**4 + d*u + 0 + 5/4*u**3 + 1/2*u**2 = 0.
-1, -2/5, 0, 1
Let g = -948346/8727 + 4/2909. Let p = g + 110. Factor 0 - 2/3*w**5 + 0*w**2 + 0*w**4 - 2/3*w + p*w**3.
-2*w*(w - 1)**2*(w + 1)**2/3
Let z be 105/28 - (-6)/(-8). Let o(p) be the first derivative of -3/2*p**2 - p - 2/3*p**z + 1. Factor o(w).
-(w + 1)*(2*w + 1)
Factor 0 - 4/11*r - 2/11*r**2 + 6/11*r**3.
2*r*(r - 1)*(3*r + 2)/11
Let v(d) = 7*d**3 + 5*d**2 + 5*d + 1. Let s(z) be the second derivative of -z**5 - 7*z**4/6 - 7*z**3/3 - 3*z**2/2 + z. Let l(w) = 6*s(w) + 17*v(w). Factor l(m).
-(m - 1)**2*(m + 1)
Suppose 2*a + 3*l = 9, a - 3*l = -0*l. Factor 16*u**5 + 6*u**3 + a - 27*u**4 + 4*u - 4*u**5 + 24*u**2 - 22*u.
3*(u - 1)**3*(u + 1)*(4*u - 1)
Let h(y) be the third derivative of -y**5/15 + 8*y**3/3 + 3*y**2. Factor h(s).
-4*(s - 2)*(s + 2)
Factor -15*x + 21/4 - 9/4*x**2.
-3*(x + 7)*(3*x - 1)/4
Let r(h) be the third derivative of 2/21*h**3 + 3*h**2 + 1/420*h**6 - 1/28*h**4 + 0 + 0*h + 0*h**5. Find b such that r(b) = 0.
-2, 1
Let h = 67/183 + -2/61. Factor -h*v**2 - 1/3 + 2/3*v.
-(v - 1)**2/3
Factor -10*i**2 - i**4 - 15*i**2 + i**3 + 25*i**2.
-i**3*(i - 1)
Let i(f) = -f**2 + 2*f - 3. Suppose -2*m - 1 = -5*v, -2*v - 2 - 4 = -4*m. Let t(h) = -h**2 + h - 1. Let n(p) = v*i(p) - 2*t(p). Factor n(x).
(x - 1)*(x + 1)
Factor 3/4*u**3 + 0*u + 0 + 3/2*u**2 - 3/4*u**4.
-3*u**2*(u - 2)*(u + 1)/4
Suppose 4/7*k**3 - 2/7*k - 2/7*k**2 + 0 = 0. What is k?
-1/2, 0, 1
Let r(a) = -10*a**3 + 25*a**2 - 50*a + 35. Let w(b) = -11*b**3 + 24*b**2 - 49*b + 36. Let v(d) = 6*r(d) - 5*w(d). Solve v(s) = 0 for s.
1, 2, 3
Let j(x) be the second derivative of -1/30*x**6 + 0 + 1/12*x**4 - 1/42*x**7 + 0*x**2 - 1/3*x**3 + 3*x + 3/20*x**5. Factor j(a).
-a*(a - 1)**2*(a + 1)*(a + 2)
Let x(v) = v**2 + 3*v + 2. Let a be x(-3). Suppose -2*h + 12 = -4*w + 3*h, a*w - 8 = -h. Suppose t**4 + 4*t + 0*t**2 - t**w - 3*t - t**3 = 0. Calculate t.
-1, 0, 1
Let j(x) be the first derivative of 2*x + 1/3*x**3 + 1/6*x**4 - 2*x**2 - 2. Let o(i) be the first derivative of j(i). Solve o(r) = 0.
-2, 1
Let f = 133 - 531/4. Let w(x) be the first derivative of -2/3*x**3 - 3 + 1/2*x**2 + f*x**4 + 0*x. Factor w(o).
o*(o - 1)**2
Let v(p) = -3 + 2*p**2 - 3*p + 9*p**3 + p**2 + 2*p - 2*p. Let g(q) = 26*q**3 + 8*q**2 - 9*q - 8. Let o(x) = -6*g(x) + 17*v(x). Factor o(c).
-3*(c - 1)**2*(c + 1)
Let j(k) be the third derivative of 1/36*k**4 + 1/90*k**5 + 0*k + 3*k**2 + 0*k**3 + 0. Factor j(g).
2*g*(g + 1)/3
Let m(j) be the first derivative of -2/27*j**3 - 1 + 0*j + 2/9*j**2. Factor m(w).
-2*w*(w - 2)/9
Let m be (-3)/(((-3)/1)/(-3)). Let w = 3 + m. Factor -2/5*n**2 + w*n + 0 - 2/5*n**3.
-2*n**2*(n + 1)/5
Suppose 0 = -y - 3*t + 6 + 8, -4*t = 2*y - 20. Factor -4*v + 2*v - v**2 + y*v**4 + 0*v**4 + 2*v**3 - v**2.
2*v*(v - 1)*(v + 1)**2
Suppose -4 = -3*t + l, -5*t - 4*l = -3*l - 20. Let d be (6/(-5))/(t/(-10)). Determine v, given that -2*v**4 + 6*v**3 - 4*v**d + 2*v - 6*v**2 + 4*v**4 = 0.
0, 1
Let h(t) be the third derivative of 0*t**7 + 1/300*t**6 + 0 + 0*t + 0*t**4 + 0*t**3 - t**2 - 1/840*t**8 + 0*t**5. Determine p so that h(p) = 0.
-1, 0, 1
Suppose -4 = f - 3*f. Determine a so that 6*a**3 + 3*a + 0*a**3 - a + f*a**2 - 2 - 8*a**3 = 0.
-1, 1
Let i(r) be the third derivative of r**7/63 + 5*r*