or c(v).
-4*(v - 1)**2*(v + 1)/3
Suppose 40 = 7*p - 2. Let w(f) be the first derivative of -1/4*f**5 + 1 + 5/8*f**2 + 5/8*f**4 - 1/4*f + 1/24*f**p - 5/6*f**3. Factor w(k).
(k - 1)**5/4
Suppose 3*k + 2 = i, -4*i = -8*i + 5*k + 8. Factor -4/3*c**3 + 2/9*c**4 - i + 4/3*c + 16/9*c**2.
2*(c - 3)**2*(c - 1)*(c + 1)/9
Determine d, given that 24 - 5*d**2 - 4*d**2 + 5*d**2 + 33*d - 37*d = 0.
-3, 2
Let t be -4 - 26*10/(-60). Determine r, given that -2/3*r**2 + t + 1/3*r**4 + 0*r + 0*r**3 = 0.
-1, 1
Let x(g) be the first derivative of 2/35*g**5 + 0*g**2 - 1/7*g**4 + 5 + 2/21*g**3 + 0*g. Factor x(u).
2*u**2*(u - 1)**2/7
Let y(g) be the third derivative of 0 + 0*g + g**2 + 0*g**3 - 1/15*g**5 + 1/12*g**4. Let y(o) = 0. What is o?
0, 1/2
Let b be 1*1/2*4. Let o + 6*o**2 + 2*o**4 - 3*o - 8*o**3 + b*o**3 = 0. What is o?
0, 1
Let q = 3 - 7/3. Factor -q*y + 4/3*y**2 + 0 - 2/3*y**3.
-2*y*(y - 1)**2/3
Let k(l) be the second derivative of l**7/1680 - l**6/360 + l**5/240 + l**3/2 + l. Let a(p) be the second derivative of k(p). Factor a(n).
n*(n - 1)**2/2
Let f(t) = t**3 + 7*t**2 - t - 8. Let j be f(-7). Let y(h) = 4*h**2 - 1. Let a be y(j). Determine b, given that -4*b - 4*b**2 + 5*b + b**a - 2 + 4*b = 0.
1, 2
Let q(z) be the second derivative of -z**6/255 - z**5/170 + z**4/34 + 5*z**3/51 + 2*z**2/17 + 11*z. Factor q(o).
-2*(o - 2)*(o + 1)**3/17
Let u(t) = 8*t**5 + 2*t**4 - 5*t**3 - 8*t**2 - 3*t. Let v(d) = 17*d**5 + 3*d**4 - 10*d**3 - 17*d**2 - 7*d. Let r(s) = -7*u(s) + 3*v(s). Factor r(p).
-5*p**2*(p - 1)*(p + 1)**2
Let i be 0 - 5 - (-1056)/198. Factor -1/3*r**2 + 1/3*r**3 + 1/3*r**4 - i*r**5 + 0 + 0*r.
-r**2*(r - 1)**2*(r + 1)/3
Let v(w) be the second derivative of -5/27*w**3 + 0 - 2/9*w**2 + 7/54*w**4 - 5*w. Factor v(t).
2*(t - 1)*(7*t + 2)/9
Let q(s) be the third derivative of s**5/330 - 4*s**2. Factor q(m).
2*m**2/11
Let q be (4 - 6)*(2 - 6). Factor -2*f**5 + 4*f**3 - 2*f**4 - q*f**3 + 8*f**4.
-2*f**3*(f - 2)*(f - 1)
Let n be 1/(-3) + (-2)/(-6). Suppose -2*h = 4*m + 16, -3*m = -h - 0*m + 17. Determine x, given that 0 + 2/7*x**h + n*x = 0.
0
Let a(x) be the first derivative of -x**5/40 - x**4/24 + x**3/12 + x**2/4 - x + 2. Let i(g) be the first derivative of a(g). Let i(k) = 0. What is k?
-1, 1
Suppose 3*u - 5*u - 26 = -4*n, u = n - 9. Let w be u/10 - (-3)/6. Factor -3/2*k**3 + w + 3/2*k - 3/2*k**4 + 3/2*k**2.
-3*k*(k - 1)*(k + 1)**2/2
Let w(z) be the first derivative of -5*z**6/8 - 3*z**5/2 - 3*z**4/2 - 4*z**3/5 - z**2/2 - 2. Let b(h) be the second derivative of w(h). Factor b(d).
-3*(5*d + 2)**3/5
Factor 2*y + 5*y + 3*y - 9*y**2 - 4*y.
-3*y*(3*y - 2)
Let s be -1 + (3 - 4/3). Suppose -s + 31/6*w**4 - 5/6*w**3 - 9/2*w**2 + 10/3*w - 5/2*w**5 = 0. What is w?
-1, 2/5, 2/3, 1
Let p(x) be the third derivative of 25*x**8/336 + 2*x**7/7 + x**6/6 - 2*x**2 - 45. Find g, given that p(g) = 0.
-2, -2/5, 0
Let i = 193 + -193. Let m(s) be the third derivative of i*s**4 - 1/210*s**5 + 0*s + 1/21*s**3 + 4*s**2 + 0. Factor m(t).
-2*(t - 1)*(t + 1)/7
Let w(p) be the third derivative of -2*p**2 + 1/70*p**7 + 1/16*p**4 + 0*p**6 + 0*p**3 - 1/224*p**8 + 0 - 1/20*p**5 + 0*p. Suppose w(i) = 0. What is i?
-1, 0, 1
Let o(g) be the third derivative of -1/672*g**8 + 0*g**4 - 1/240*g**6 + 0*g**3 + 0 + 5*g**2 + 0*g - 1/210*g**7 + 0*g**5. Determine w, given that o(w) = 0.
-1, 0
Let h(q) = 9*q**2 + 14*q - 4. Let d(r) = r**2 + r - 1. Let n(v) = -4*d(v) + h(v). Factor n(z).
5*z*(z + 2)
What is g in 5/4 + 9/4*g + 3/4*g**2 - 1/4*g**3 = 0?
-1, 5
Suppose 3*r - 2 - 4 = 0. Let 3*k**3 - r*k - 4*k - 3*k + 6*k = 0. Calculate k.
-1, 0, 1
Let c be (-4)/22 + (-12)/(-33). Find p, given that 0 + 0*p + c*p**2 = 0.
0
Let s(i) be the first derivative of -i**5/30 + i**4/24 + i**3/18 - i**2/12 - 7. Suppose s(p) = 0. What is p?
-1, 0, 1
Suppose 8*x = 7*x. Suppose 2*i**3 - 3*i - 10*i**5 - 14*i**2 + 9 + 5*i**4 + 11*i**5 + x*i**3 = 0. Calculate i.
-3, -1, 1
Let n = 42 - 28. Let q be 6/21 + (-4)/n. Solve -5*v**4 + 4*v**2 + 3*v**4 - 2 + q*v**2 = 0 for v.
-1, 1
Let f(i) be the third derivative of -1/24*i**4 + 1/40*i**5 - 1/180*i**6 + 0 + 1/6*i**3 + 0*i - i**2. Let q(a) be the first derivative of f(a). Factor q(o).
-(o - 1)*(2*o - 1)
Let y(u) be the first derivative of -u**5/50 - u**4/40 - 15. Solve y(n) = 0 for n.
-1, 0
Let w = -1/3 - -5/6. Factor 1/2 - z + w*z**2.
(z - 1)**2/2
Let q = 19 + -13. Solve -84*t**3 + 8*t - 45*t**4 + 22*t**3 + 13*t**4 + 2*t**2 + q*t**2 + 30*t**5 = 0.
-1, -1/3, 0, 2/5, 2
Let w be ((-7)/9)/(133/(-114)). Let -8*p**4 + 0 + 0*p - 16/3*p**5 - w*p**2 + 5*p**3 = 0. What is p?
-2, 0, 1/4
Let h(w) = -w + 2. Let c(a) = 2*a - 2. Let z(j) = 4*c(j) + 5*h(j). Let u be z(2). Factor u*t**2 + 2*t - 3*t - 9*t**2.
-t*(t + 1)
Let i(v) be the first derivative of -2*v**3/45 + v**2/15 + 2. Find z such that i(z) = 0.
0, 1
Let s(g) be the first derivative of 5*g**6/39 - 16*g**5/65 + g**4/26 + 4*g**3/39 - 3. Factor s(r).
2*r**2*(r - 1)**2*(5*r + 2)/13
Suppose -3*j + 3 = -6. Let r(v) = v**2 + 3*v + 2. Let a be r(-3). Factor 4/9*m**4 - 2/9*m**5 + 0 - 4/9*m**a + 0*m**j + 2/9*m.
-2*m*(m - 1)**3*(m + 1)/9
Let s(v) be the first derivative of 7*v**6/2 - 36*v**5/5 - 3*v**4 - 19. Determine n so that s(n) = 0.
-2/7, 0, 2
Let n = -1 - -1. Suppose -m - 2 + 4 = n. Factor 2/5*l**m + 0*l + 0.
2*l**2/5
Let d(s) = 5*s**3 - 7*s**2 + 13*s + 13. Let l(m) = 6*m**3 - 7*m**2 + 15*m + 14. Let b(j) = -7*d(j) + 6*l(j). Factor b(v).
(v - 1)*(v + 1)*(v + 7)
Suppose -v + 18 + 12 = 0. Let q be ((-10)/4)/(v/(-6)). Find b such that -q*b**4 - b**5 + b**2 - 1/2 + 2*b**3 - b = 0.
-1, -1/2, 1
Let u be 2*(132/(-42) + 4). Factor 2/7*q**2 - u*q + 18/7.
2*(q - 3)**2/7
Factor 2/15*u**2 + 4/3*u + 10/3.
2*(u + 5)**2/15
Let w(u) be the second derivative of 1/42*u**4 - 2/7*u**2 + 1/21*u**3 + 11*u + 0. Factor w(k).
2*(k - 1)*(k + 2)/7
Solve 20 - 15/2*o**3 + 5/4*o**2 + 5/4*o**4 + 30*o = 0.
-1, 4
Suppose 4*c = -0*c - 5*g + 37, -4*c + 2*g = -2. Let l(r) be the first derivative of -c - 1/4*r**2 + 0*r + 1/12*r**3. Factor l(j).
j*(j - 2)/4
Let s(i) be the third derivative of -5*i**8/168 + i**7/35 + 7*i**6/60 - i**5/10 - i**4/6 + 4*i**2. Solve s(n) = 0.
-1, -2/5, 0, 1
Let n(p) be the third derivative of p**8/224 - p**7/140 - 3*p**6/40 + 7*p**5/20 - 11*p**4/16 + 3*p**3/4 - 13*p**2. Let n(r) = 0. What is r?
-3, 1
Let u(y) = y**2 + 6*y + 4. Let v(l) = -l**2 - 7*l - 5. Suppose 0 = p + r - 1, -4*p + 10 = r - 3. Let f(g) = p*v(g) + 5*u(g). Factor f(t).
t*(t + 2)
Factor -6*w**2 + 2*w**2 + 3*w**2 + 5*w + 14.
-(w - 7)*(w + 2)
Let o = 1042 + -1040. Factor 10/3*q**2 + 2/3*q**3 + o*q - 6.
2*(q - 1)*(q + 3)**2/3
Let h be -2*4/(6*-6). Factor -4/9*y**3 + 4/9*y + 2/9*y**4 - h + 0*y**2.
2*(y - 1)**3*(y + 1)/9
Factor -2/3*p**3 - 2/3*p**4 + 0 + 0*p + 0*p**2.
-2*p**3*(p + 1)/3
Let p be (-6)/6 - (-1 + -3). Suppose 0*l = -p*l. Factor 2/9*x**4 - 2/9*x**2 + 2/9*x + l - 2/9*x**3.
2*x*(x - 1)**2*(x + 1)/9
Suppose -5*f + 15 = 0, 0*f = 3*i - 3*f - 69. Factor 0*l - 80/9*l**3 - i*l**4 - 18*l**5 - 8/9*l**2 + 0.
-2*l**2*(l + 1)*(9*l + 2)**2/9
Suppose -4*p - p = -15, -5*p = -5*i. Let g(c) be the second derivative of -1/10*c**5 + 0 + 0*c**2 + 1/3*c**4 - 1/3*c**3 + i*c. Factor g(v).
-2*v*(v - 1)**2
Let v(x) = -4*x**2 - 16*x + 6. Let c(d) = d**3 - 12*d**2 + 12*d - 14. Let p be c(11). Let a(t) = -t**2 - 3*t + 1. Let n(f) = p*v(f) + 14*a(f). Factor n(m).
-2*(m - 2)*(m - 1)
Let k(c) be the third derivative of 2/45*c**6 - 8*c**2 + 1/504*c**8 + 0 + 1/12*c**4 + 0*c + 1/18*c**3 + 7/90*c**5 + 1/70*c**7. Factor k(o).
(o + 1)**4*(2*o + 1)/3
Let i(m) be the second derivative of 7/10*m**5 + 0 + 1/3*m**4 - 7/3*m**3 + 2*m - 2*m**2. Factor i(t).
2*(t - 1)*(t + 1)*(7*t + 2)
Suppose 4*l - 10 = 2*l. Let b(m) = -m**2 + 1. Let q(j) = 20*j**2 - 30*j + 14. Let r(z) = l*b(z) - q(z). Determine s, given that r(s) = 0.
3/5
Let x(h) be the first derivative of -8/5*h**4 + 0*h - 8/15*h**3 + 0*h**2 + 1 - 14/25*h**5. Factor x(b).
-2*b**2*(b + 2)*(7*b + 2)/5
Let k(x) be the first derivative of 5/6*x**6 + 3 - 2/5*x**5 - 5/2*x**4 + 4/3*x**3 + 5/2*x**2 - 2*x. Let k(z) = 0. Calculate z.
-1, 2/5, 1
Let i be (-4)/(-6)*(-2 + 5). Suppose 2*x - 4*x**3 - 6*x**2 + 9*x**4 + 7*x**3 - i*x = 0. What is x?
-1, 0, 2/3
Let q(j) be the first derivative of -j**4/4 - j**3/2 - 4*j - 3. Let f(s) be the first derivative of q(s). Find t, given that f(t) = 0