t l(n) be the first derivative of -2*n + 1 + 2/3*n**d - n**2 + 1/2*n**4. Factor l(i).
2*(i - 1)*(i + 1)**2
Let o(f) be the first derivative of -3*f**5 + 21*f**4/4 + 3*f**3 - 21*f**2/2 + 6*f + 23. Solve o(h) = 0 for h.
-1, 2/5, 1
Find g, given that -g**2 + 0*g + 0*g**3 + 1/2 + 1/2*g**4 = 0.
-1, 1
Suppose 0 = 3*x - 2*x - 1. Factor -3*w + w**4 - 5*w**3 - 2*w**4 + 3*w**3 + 2*w**2 + 4*w - x + w**5.
(w - 1)**3*(w + 1)**2
Let r(k) be the second derivative of -k**7/42 + k**5/10 - k**3/6 + 2*k. Solve r(b) = 0.
-1, 0, 1
Let l = 4 + -2. Let -3*w**2 - 2*w**3 + l*w - 2*w + 5*w**2 = 0. Calculate w.
0, 1
Factor 9 - 98*h + 0 + 4*h**2 + 92*h - 3*h**2.
(h - 3)**2
Let b(p) be the first derivative of -p**3/3 - 3*p**2/2 + 9*p - 3. Let w(o) = 2*o**2 + 4*o - 14. Let t(r) = -8*b(r) - 5*w(r). Factor t(s).
-2*(s - 1)**2
Suppose 0*k + 2*k = 2*b - 4, b + k = 2. Factor 2/3*p**3 - 2*p**b - 2/3 + 2*p.
2*(p - 1)**3/3
Factor -9/8*w**3 + 3/8*w**4 + 9/8*w - 3/4 + 3/8*w**2.
3*(w - 2)*(w - 1)**2*(w + 1)/8
Suppose -63*z**4 - 307*z**3 - 20*z**3 - 53*z**5 - 327*z**4 - 108*z + 468*z**2 - 22*z**5 = 0. Calculate z.
-3, 0, 2/5
Suppose 0 = -6*b - 5 + 17. Find t, given that 0 + 0*t + 1/4*t**3 + 1/4*t**b = 0.
-1, 0
What is g in 12/25*g + 14/25*g**2 + 0 + 2/25*g**3 = 0?
-6, -1, 0
Let j(d) be the first derivative of -d**6/21 - 2*d**5/5 - 9*d**4/7 - 44*d**3/21 - 13*d**2/7 - 6*d/7 + 20. Factor j(s).
-2*(s + 1)**4*(s + 3)/7
Let f(w) be the first derivative of w**4/12 - w**3/3 - w**2/6 + w - 7. Determine b, given that f(b) = 0.
-1, 1, 3
Let x(o) = 8*o**2 + 10*o + 2. Let v(a) = -8*a**2 - 4 - 3 - 10*a - 1 + 6. Let s(n) = -3*v(n) - 2*x(n). What is q in s(q) = 0?
-1, -1/4
Let t(w) be the third derivative of -2*w**7/525 + w**6/75 - w**5/75 - 5*w**2. What is c in t(c) = 0?
0, 1
Let h(q) be the first derivative of q**6/60 - q**5/40 - q**4/12 + 4*q + 6. Let r(b) be the first derivative of h(b). Suppose r(u) = 0. What is u?
-1, 0, 2
Let o(x) = x**3 + x**2 - x - 3. Let q be o(0). Let b = -3 - q. Factor -1/2*u**2 + 3/4*u**4 + 0 + 1/4*u**3 + b*u.
u**2*(u + 1)*(3*u - 2)/4
Let l(v) be the third derivative of v**7/70 + v**6/20 - 3*v**5/20 - v**4/2 + 2*v**3 + 21*v**2. Factor l(c).
3*(c - 1)**2*(c + 2)**2
Let g(k) be the third derivative of -4/315*k**7 + 0*k**4 - 6*k**2 + 7/360*k**6 + 0*k + 1/336*k**8 + 0 - 1/90*k**5 + 0*k**3. Factor g(x).
x**2*(x - 1)**2*(3*x - 2)/3
Let l(v) = 23*v**3 + 98*v**2 + 105*v + 23. Let h(k) = 15*k**3 + 65*k**2 + 70*k + 15. Let m(g) = -7*h(g) + 5*l(g). Let m(q) = 0. What is q?
-2, -1, -1/2
Let j(x) = -3*x**2 - x - 4. Let b(v) = 7*v**2 + 3*v + 9. Let m(k) = 4*b(k) + 9*j(k). Solve m(n) = 0.
-3, 0
Let a(g) be the second derivative of -g**5/60 + g**4/12 - g**3/6 + 3*g**2/2 - 2*g. Let k(p) be the first derivative of a(p). Suppose k(o) = 0. Calculate o.
1
Suppose -5*x + 5*o - 6 + 1 = 0, 3*x = 5*o - 5. Let p(u) be the second derivative of 0*u**4 - 1/60*u**5 - 2*u + 0*u**2 + x*u**3 + 0. Find q, given that p(q) = 0.
0
Let d be (-10)/(-6)*(-6)/(-25). Let d - 4/5*l**3 + 0*l**2 - 2/5*l**4 + 4/5*l = 0. What is l?
-1, 1
Let z(w) be the first derivative of -w**4/20 + 2*w**3/15 - w**2/10 + 19. Determine c, given that z(c) = 0.
0, 1
Let u(z) be the first derivative of -z**4/12 - 4*z**3/9 - 5*z**2/6 - 2*z/3 - 1. Find p such that u(p) = 0.
-2, -1
Let z be ((-4)/(-198))/(1/(-6)). Let v = z - -556/231. Determine d so that 0*d - 2/7 - v*d**3 + 6/7*d**4 + 12/7*d**2 = 0.
-1/3, 1
Suppose -5*h - 10 = 2*g - 0, -15 = -h + 3*g. Let c(a) be the second derivative of -1/42*a**4 + h - 1/7*a**2 - 2/21*a**3 - 2*a. Factor c(q).
-2*(q + 1)**2/7
Let j(f) be the first derivative of 35*f**6/6 + 19*f**5 + 75*f**4/4 + 5*f**3/3 - 5*f**2 + 20. Find z, given that j(z) = 0.
-1, 0, 2/7
Factor -2*k**3 + 3*k**3 + 5*k**2 - 3964*k - 8 + 3966*k.
(k - 1)*(k + 2)*(k + 4)
Determine d, given that -3/2*d**4 + 0 + 0*d + 3/2*d**2 + 0*d**3 = 0.
-1, 0, 1
Factor 1/2*v**2 + 0 + 1/4*v**3 + 0*v - 1/4*v**4.
-v**2*(v - 2)*(v + 1)/4
Let r = -6/1165 - -133/16776. Let q(b) be the third derivative of -2*b**2 + 0*b - 1/72*b**4 + 1/180*b**5 + r*b**6 + 0*b**3 + 0 - 1/630*b**7. Factor q(f).
-f*(f - 1)**2*(f + 1)/3
Let q(d) = d. Let z(i) = 6*i**3 - 2*i**2 + 3*i**2 + 0*i**2 - i. Let j be z(1). Let k(m) = m**2 + 7*m. Let h(f) = j*q(f) - k(f). Factor h(o).
-o*(o + 1)
Let q(t) be the second derivative of t**7/7 - 4*t**6/15 - 7*t**5/10 + 2*t**4/3 + 4*t**3/3 + 19*t. Let q(h) = 0. What is h?
-1, -2/3, 0, 1, 2
Let w(x) = x**3 - x**2 - 2*x - 2. Let g be w(3). Let o = -6 + g. Factor 0*t**2 + 4 + 2 - o - 2*t**2.
-2*(t - 1)*(t + 1)
Let w be 7 + 2 + (-4)/1. Let c(a) be the first derivative of 0*a + 3/2*a**4 - 8/5*a**w + 2/3*a**3 + 0*a**2 + 2. Factor c(h).
-2*h**2*(h - 1)*(4*h + 1)
Let m(h) be the second derivative of -h**5/10 + h**4/3 + 4*h**3/3 - 8*h**2 - 19*h. Factor m(n).
-2*(n - 2)**2*(n + 2)
Let s be 10/45 - (-32)/180. Let -2/5 + s*k**2 + 0*k = 0. What is k?
-1, 1
Let m(d) be the third derivative of -d**3 + 0*d**7 + 1/10*d**6 - 3/8*d**4 + d**2 + 0 - 1/112*d**8 + 1/10*d**5 + 0*d. Suppose m(z) = 0. What is z?
-1, 1, 2
Let j(x) be the first derivative of x**7/42 - x**6/15 + x**4/6 - x**3/6 - x - 3. Let f(v) be the first derivative of j(v). Find z, given that f(z) = 0.
-1, 0, 1
Let m(o) be the first derivative of -5*o**4/4 - 5*o**3/3 + 5*o**2/2 + 5*o + 40. Suppose m(d) = 0. Calculate d.
-1, 1
Let o(p) = 9*p**3 - 33*p**2 - 9*p + 33. Let v(u) = u**3 - 4*u**2 - u + 4. Let q(n) = -4*o(n) + 33*v(n). Factor q(x).
-3*x*(x - 1)*(x + 1)
Let n = 1/33 + 7/11. Factor -2/3*o**2 + 2/3*o**5 - n*o**3 + 0 + 0*o + 2/3*o**4.
2*o**2*(o - 1)*(o + 1)**2/3
Let p = -196 - -201. What is w in 1/4*w**p + 0*w**4 + 0*w + 0 + 0*w**2 - 1/4*w**3 = 0?
-1, 0, 1
Suppose o - 12 = -o. Let i = -1 + o. Factor -s**i - s**5 + 2*s**2 + 3*s**5 + s - s**4 - 2*s**3 - 1.
(s - 1)**3*(s + 1)**2
Let t(s) be the first derivative of -35*s**6/4 - 141*s**5/5 - 39*s**4/2 - 4*s**3 - 2. Suppose t(j) = 0. What is j?
-2, -2/5, -2/7, 0
Factor -1/8*u**4 - 3/4*u**2 + 1/2*u**3 + 1/2*u - 1/8.
-(u - 1)**4/8
Let 3/2*v**2 - 21/2*v + 15 = 0. What is v?
2, 5
Let j = 688 - 2062/3. Factor 0*q - j*q**3 - 2/3*q**2 + 0.
-2*q**2*(q + 1)/3
Let n be (-9)/(-24)*(-12)/(-3). Let r = n + -1. Determine l, given that r + 1/4*l**2 - 3/4*l = 0.
1, 2
Let u = 342 + -342. Solve -2/9*n**3 - 2/9*n**2 + u*n + 0 + 2/9*n**4 + 2/9*n**5 = 0 for n.
-1, 0, 1
Let w(c) be the third derivative of 0 + 2*c**2 + 1/300*c**6 + 0*c - 1/60*c**4 + 0*c**3 + 0*c**5. Factor w(y).
2*y*(y - 1)*(y + 1)/5
Solve 22/13*l - 12/13*l**2 + 2/13*l**3 - 12/13 = 0 for l.
1, 2, 3
Suppose 2*o + 0*o = 24. Let -10*g**2 + 16*g**2 - 3*g**2 - o*g + 12 = 0. What is g?
2
Factor -5/2*w + 0 - 5/2*w**2.
-5*w*(w + 1)/2
Factor 2/3*m**2 - 2*m + 0.
2*m*(m - 3)/3
Suppose -5*z + 1 = -3*a, 5*a - 2*a - 1 = 4*z. Let w(f) be the second derivative of 3/20*f**5 + z*f + 0 - 1/2*f**2 + 1/12*f**4 - 1/2*f**3. Factor w(l).
(l - 1)*(l + 1)*(3*l + 1)
Suppose -h - 5*l = -18, -4*l = 2*h - h - 15. Factor 5*u**3 + 4*u**4 + 4*u**5 - 7*u**2 + 3*u**2 - 9*u**h + 0*u**4.
4*u**2*(u - 1)*(u + 1)**2
Let w(a) = -a**3 + 6*a**2 - 6*a + 8. Let k be w(5). Factor -1/2*m**2 + 1/4*m**k - 1/4*m + 1/2.
(m - 2)*(m - 1)*(m + 1)/4
Let f = 221 + -219. Let v(s) be the second derivative of -2/3*s**3 + 0 - 3*s**2 + f*s - 1/18*s**4. Suppose v(g) = 0. What is g?
-3
Let m be (-1 + 1)/((-4)/2). Let i(u) be the third derivative of 0*u + 0 + m*u**4 + 1/60*u**5 + 4*u**2 + 0*u**3. Let i(w) = 0. Calculate w.
0
Let z = -1139 + 7975/7. Let 2/7*j**5 + 4/7*j**4 + z*j**3 + 0 + 0*j + 0*j**2 = 0. Calculate j.
-1, 0
Let y = -2/215 - -131/215. Let r(x) be the first derivative of -y*x**5 - 1 - 5/3*x**3 - 7/4*x**4 + 0*x - 1/2*x**2. Factor r(t).
-t*(t + 1)**2*(3*t + 1)
Let w(y) be the second derivative of -7*y**5/60 + 10*y**4/9 - 17*y**3/6 - 3*y**2 + 5*y. Factor w(l).
-(l - 3)**2*(7*l + 2)/3
Let i(y) be the third derivative of y**6/40 + y**5/4 + 7*y**4/8 + 3*y**3/2 + y**2. Factor i(h).
3*(h + 1)**2*(h + 3)
Let l(b) be the second derivative of b**5/60 - 5*b**4/6 + 50*b**3/3 - 500*b**2/3 - 41*b. Factor l(j).
(j - 10)**3/3
Let p(h) = h**3 + 4*h**2 + 2*h - 1. Let o be p(-3). Factor -2/5*n**3 + 0 + 0*n**o + 0*n + 2/5*n**4.
2*n**3*(n - 1)/5
Let u(d) be the second derivative of d**6/60 - d**5/160 - d**4/6 + d**3/12 + 28*d. Factor u(t).
t*(t - 2)*(t + 2)*(4*t - 1)/8
Let k(o)