) = r**2 + 10. Let t be u(0). Suppose 3*q = -12, -3*q - 4 = -o + t. Factor f + f**2 + 0*f**2 - 2*f**o.
-f*(f - 1)
Let y(h) be the third derivative of 0 + 0*h + 1/6*h**3 - 1/12*h**4 + 3*h**2 + 1/60*h**5. Determine d, given that y(d) = 0.
1
Let 2/9 + 2/9*d**2 + 4/9*d = 0. Calculate d.
-1
Suppose 0 = -0*a + 4*a - 36. Let d be (-1)/3*-1*a. Suppose -d + 4*q - q**2 - 3 + 2 = 0. Calculate q.
2
Find n such that 5/4*n - 1/4*n**3 - 1/2 + 1/4*n**4 - 3/4*n**2 = 0.
-2, 1
Let z be (2/36)/((-1)/(-4)). Suppose -2*t = 2*g - 8, 2*g + 0*g = 2*t. Solve -4/9*f + 2/9 + z*f**t = 0 for f.
1
Suppose 3*n = 7*n - 12. Let z(c) = c - 4. Let l be z(6). Factor -l*g**2 + g**3 + g**n + g - g**3.
g*(g - 1)**2
Let s(v) be the second derivative of -1/12*v**3 + 0 + 1/40*v**5 + 0*v**2 + v + 0*v**4. Suppose s(d) = 0. Calculate d.
-1, 0, 1
Let o = 124 + -122. Let m(c) be the first derivative of 3/8*c**o + 1/4*c**3 - 4 - 3/2*c. Suppose m(v) = 0. What is v?
-2, 1
Suppose -2*v = -v. Solve 5 - 3 - x - x**2 + v*x = 0.
-2, 1
Let n(a) = -9*a**4 + 46*a**3 - 116*a**2 + 80*a. Let t(w) = -6*w**4 + 31*w**3 - 77*w**2 + 53*w. Let p(f) = -5*n(f) + 8*t(f). Factor p(l).
-3*l*(l - 2)**3
Suppose 0 = -5*u - 4*t - 38, 3*u + t = 3 - 23. Let m be (-9)/u*4 - 1. Factor 2 - 18*y + 2 + 8*y**3 - y**5 - 24*y**4 + 20*y**2 - y**m + 12*y**5.
2*(y - 1)**3*(y + 1)*(5*y - 2)
Factor 4*y + 6*y**2 - 33*y**4 + 4*y**3 - 4*y**3 + 31*y**4.
-2*y*(y - 2)*(y + 1)**2
Let 0*k + 1/4*k**2 + 0 = 0. Calculate k.
0
Let w be (1 - (2 + 3)) + 4. Let c(k) be the third derivative of w*k + 0*k**3 + 1/24*k**4 - 1/120*k**6 + 0*k**5 + 0 + k**2. Factor c(a).
-a*(a - 1)*(a + 1)
Let r(k) = k**2 - 6*k + 7. Let m be 115/25 - 2/(-5). Let d be r(m). Factor -2*v**5 + 4*v**d + 4*v**4 - v**5 + 5*v**3 - 2*v**2 + 4*v**5.
v**2*(v + 1)**2*(v + 2)
What is j in 0 + 4/5*j + 6/5*j**2 + 2/5*j**3 = 0?
-2, -1, 0
Let h be ((-176)/77)/((-2)/7). Factor -3*w + 26*w**2 - 13*w**3 + 0*w - h*w**2 - 14*w**3 + 12*w**4.
3*w*(w - 1)**2*(4*w - 1)
Let r(z) be the third derivative of -z**7/420 - z**6/120 + z**4/24 + z**3/12 - 4*z**2. Determine x so that r(x) = 0.
-1, 1
Factor -2/7*x**4 + 0*x + 0 - 2/7*x**3 + 4/7*x**2.
-2*x**2*(x - 1)*(x + 2)/7
Suppose 2/3*s**2 + 8/3 - 8/3*s = 0. What is s?
2
Let z = 288 + -285. Factor 1/3*t**z + 2/3*t**2 - 2/3 - 1/3*t.
(t - 1)*(t + 1)*(t + 2)/3
Let j(z) be the third derivative of -z**8/60480 + z**7/7560 - z**6/2160 - z**5/20 - 2*z**2. Let u(c) be the third derivative of j(c). Solve u(g) = 0.
1
Let d(r) be the third derivative of r**5/30 - r**4/2 + 5*r**3/3 - 25*r**2. Find x, given that d(x) = 0.
1, 5
Let s = 4 - 4. Suppose s*q = q. Suppose 2*v**3 + v**2 + q*v**2 + 3*v**2 + 2*v = 0. Calculate v.
-1, 0
Let r be (-1 - -1)/(-2*1). Suppose -2*o = -2*l + 2, o + 3 = 2*l - r*o. Factor -3 - g**l - g**2 + 4*g + 1.
-2*(g - 1)**2
Let q(b) be the second derivative of -b**6/4 + 27*b**5/20 - 17*b**4/8 + 3*b**2 - 3*b. Find i, given that q(i) = 0.
-2/5, 1, 2
Solve 0*i + 1/11*i**5 - 7/11*i**2 - 1/11*i**3 + 4/11 + 3/11*i**4 = 0.
-2, -1, 1
Let l be 1/(-3) + 34/(-6). Let c be (l/4)/((-105)/20). Solve -4/7*y**5 + 4/7*y**3 + 0*y + 0 + c*y**2 - 2/7*y**4 = 0 for y.
-1, -1/2, 0, 1
Let d(n) be the second derivative of -n**6/60 + n**5/20 - n**3/6 + n**2/4 - 3*n. Solve d(s) = 0.
-1, 1
Suppose 52 = 2*k - 30. Factor -o**4 + 3*o**5 - 5*o**4 - k*o**3 - o**2 + 12*o + 32*o**3 + 13*o**2.
3*o*(o - 2)**2*(o + 1)**2
Let g be (-16)/(-4)*1/2. Suppose -1 = g*x - 4*y + 3*y, -3*x - y + 1 = 0. Let -1/3 + 1/3*o**2 + x*o = 0. Calculate o.
-1, 1
Let m(f) be the second derivative of f**4/12 + 2*f**3/3 + 2*f**2 + 5*f. Let m(p) = 0. What is p?
-2
Let a(y) = -y**5 - 15*y**3 - 5*y**2 - 10*y - 6. Let r(p) = -p**5 + p**4 - 16*p**3 - 4*p**2 - 11*p - 7. Let g(q) = 6*a(q) - 5*r(q). Factor g(m).
-(m + 1)**5
Suppose -8/3*t + 4/3*t**2 + 16/9 - 2/9*t**3 = 0. Calculate t.
2
Let r(y) = y**2 - 9*y + 23. Let z be r(4). Let a(j) be the second derivative of -j + 1/18*j**4 - 1/9*j**z + 0 - 2/3*j**2. Factor a(f).
2*(f - 2)*(f + 1)/3
Suppose 6 = -2*z + 4*z. What is h in -h**3 + h**z - 4*h**3 - 4*h**4 = 0?
-1, 0
Let a be (-2)/(-2) - 5/(-5). Let 2*z - 136*z**3 + 4*z**a + 108*z**3 - 5*z**2 = 0. Calculate z.
-2/7, 0, 1/4
Suppose 0 = 5*y - 0*y - 160. Suppose 2*h - 17 = -4*t + h, 4*h - y = -4*t. Solve -1 + 15*z + 12*z**2 + z**3 + 7 + 0*z**t + 2*z**3 = 0 for z.
-2, -1
Let d(s) be the second derivative of s**8/6720 - s**7/840 + s**6/360 + s**4/6 + 4*s. Let w(i) be the third derivative of d(i). Determine k, given that w(k) = 0.
0, 1, 2
Let c(f) be the first derivative of 0*f + 3 - 4/3*f**3 + 1/2*f**4 + 0*f**2. Suppose c(u) = 0. Calculate u.
0, 2
Let o(b) be the second derivative of -b**5/10 + b**4/2 + b**3/3 - 3*b**2 - 7*b. What is g in o(g) = 0?
-1, 1, 3
Let i(o) = o + 11. Let t be i(-7). Factor -2*a**2 - 4*a**3 - 4*a**t + a**4 + 0*a**3 + a**4.
-2*a**2*(a + 1)**2
Let t = 25 - 24. Let m(d) be the second derivative of 7*d**4/12 - 5*d**3/6 - d. Let y(w) = -1. Let c(u) = t*m(u) + 2*y(u). Factor c(v).
(v - 1)*(7*v + 2)
Let f be (24/(-9))/((-5)/15). Let b be (-2)/(-4)*f/1. Solve -7/2*y + 1/2*y**b + 9/2*y**2 + 1 - 5/2*y**3 = 0.
1, 2
Let n be ((-30)/(-20))/((-1)/(-2)). Let s be (-4)/(-12)*4/n. Factor s*b**2 + 2/9*b**5 - 4/9*b**4 + 0*b**3 + 0 - 2/9*b.
2*b*(b - 1)**3*(b + 1)/9
Suppose 9 = 6*s + 3. Let l(r) be the first derivative of 1/2*r**2 + 1/6*r**3 + s - 1/8*r**4 + 0*r. Factor l(j).
-j*(j - 2)*(j + 1)/2
Factor 2/13*a**2 + 10/13 + 12/13*a.
2*(a + 1)*(a + 5)/13
Let s(k) = -k + 1. Let a be s(-1). Let d(g) be the second derivative of -3*g + 0 + 0*g**a - 1/24*g**3 + 1/48*g**4. Factor d(u).
u*(u - 1)/4
Let g(n) be the third derivative of -n**5/300 - 52*n**2. Let g(t) = 0. Calculate t.
0
Let a(m) be the first derivative of 2 + 4/3*m - m**2 + 2/9*m**3. Factor a(b).
2*(b - 2)*(b - 1)/3
Let j(t) be the first derivative of -t**4/2 - 2*t**3 - 2*t**2 - 7. Factor j(w).
-2*w*(w + 1)*(w + 2)
Let d = -101/259 + 25/37. Find t, given that -1/7*t**2 - 3/7*t - d = 0.
-2, -1
Factor 2/5*r - 2/5*r**3 - 2/5*r**2 + 2/5*r**4 + 0.
2*r*(r - 1)**2*(r + 1)/5
Let t(c) be the second derivative of c**5/20 - 4*c**4/21 + 11*c**3/42 - c**2/7 + 25*c. Let t(v) = 0. What is v?
2/7, 1
Suppose 2*x = x + 3. Let q(n) be the second derivative of 2*n + 0 - 4/3*n**x - 1/15*n**6 + 4*n**2 + 2/5*n**5 - 1/2*n**4. Let q(t) = 0. What is t?
-1, 1, 2
Let k(p) be the first derivative of p**5/10 + p**4/2 - p**3/2 - 9*p**2/2 + 32. Factor k(q).
q*(q - 2)*(q + 3)**2/2
Factor v**3 - 2*v + 50*v**2 + v - 48*v**2 - 2.
(v - 1)*(v + 1)*(v + 2)
Let b = -15 - -47/3. Factor 1/3*q**3 + 1/3*q + b*q**2 + 0.
q*(q + 1)**2/3
Let m be -2 - -4 - (0 - 0). Factor 12*q**3 + 7*q + 40*q**m + q + 22*q**3 + 8*q**4.
2*q*(q + 2)**2*(4*q + 1)
Let m(x) be the second derivative of 5*x**4/12 - 5*x**3 - 35*x**2/2 + 25*x. Find a, given that m(a) = 0.
-1, 7
Let k(q) be the third derivative of q**9/4536 + q**8/2520 + q**3/6 + 3*q**2. Let i(v) be the first derivative of k(v). Find g such that i(g) = 0.
-1, 0
Let c(b) be the first derivative of b**4/12 - 2*b**3/9 + 3. Factor c(r).
r**2*(r - 2)/3
Let d(n) be the second derivative of n**5/10 + n**4/3 + n**3/3 + 13*n. Let d(z) = 0. What is z?
-1, 0
Let s = -4/31 - -82/155. What is w in -s*w**3 + 0 + 0*w + 2/5*w**2 = 0?
0, 1
Let p = 93 + -91. Let s(d) be the third derivative of -3*d**p + 0 + 1/100*d**5 + 0*d**3 + 0*d + 0*d**4. Suppose s(c) = 0. What is c?
0
Let z(q) = -q**2 - q + 1. Let o(w) = 3*w**2 + 1. Let f(m) = 5*o(m) - 5*z(m). Factor f(x).
5*x*(4*x + 1)
Let h be (-21)/(-6)*(-72)/(-462) - -6. Determine x so that -18/11*x**5 + 78/11*x**4 + 0 - 16/11*x - 116/11*x**3 + h*x**2 = 0.
0, 2/3, 1, 2
Factor 5*w**2 + 23 - 15*w + 6 - 49.
5*(w - 4)*(w + 1)
Let d(z) be the third derivative of z**10/226800 - z**9/22680 + z**8/6048 - z**7/3780 - z**5/30 - z**2. Let g(w) be the third derivative of d(w). Factor g(p).
2*p*(p - 2)*(p - 1)**2/3
Let r = 142 + -140. Suppose -2/7*q**r + 4/7 + 2/7*q = 0. Calculate q.
-1, 2
Solve 59*p + 243 - 6*p + p + 2*p**2 + p**2 = 0 for p.
-9
Let g(u) be the third derivative of 0 + 0*u**3 - 4*u**2 - 1/75*u**5 - 1/1050*u**7 + 0*u**4 + 0*u - 1/150*u**6. Find b, given that g(b) = 0.
-2, 0
Let l(m) be the second derivative of -m**7/1260 + m**6/360 + m**5/30 + m**4/12 - 5*m. Let r(h) be the third derivative of l(h). Solve r(z) = 0.
-1, 2
Let q(g) be the first