e p.
-1
Let s(z) be the first derivative of -1/6*z**4 - 1/6*z**5 + 0*z**3 - 1/2*z**2 - 1/20*z**6 + 0*z + 1. Let l(r) be the second derivative of s(r). Solve l(h) = 0.
-1, -2/3, 0
Suppose p + 24 = 4*z, 2*p + 42 = -z + 6*z. Let a = -13 - p. Factor 3/2*b - 3/2*b**4 + 1/2 + b**2 - b**a - 1/2*b**5.
-(b - 1)*(b + 1)**4/2
Suppose -10 = -4*t - 2. Factor -h**4 - h + h**2 + 0*h**3 + 3*h**3 - t*h**3.
-h*(h - 1)**2*(h + 1)
Let o = -908/7 + 130. Determine a, given that o - 2/7*a**3 + 6/7*a**2 - 6/7*a = 0.
1
Let u(s) be the first derivative of s**4/4 - 11*s**3/9 + s**2 + 4. Factor u(c).
c*(c - 3)*(3*c - 2)/3
Let n(f) be the first derivative of 2 - 2/27*f**3 + 0*f**2 + 2/9*f. Let n(z) = 0. Calculate z.
-1, 1
Factor -2*n + 2/7*n**3 - 8/7*n**2 + 20/7.
2*(n - 5)*(n - 1)*(n + 2)/7
Factor -4/5*u**2 - 8/5*u + 0.
-4*u*(u + 2)/5
Let g(t) be the second derivative of -t**6/30 - t**5/10 - t**4/12 - 6*t. Factor g(d).
-d**2*(d + 1)**2
Let -1/5*r**5 - r**3 - 2/5*r**2 + 0*r - 4/5*r**4 + 0 = 0. What is r?
-2, -1, 0
Let a(r) be the third derivative of 1/18*r**4 + 1/90*r**5 + 0*r + 1/9*r**3 + 0 - 3*r**2. Find y such that a(y) = 0.
-1
Let d(b) be the second derivative of -b**6/60 - b**5/20 + b**4/6 + b**3/6 - 3*b**2/4 - 8*b. Factor d(i).
-(i - 1)**2*(i + 1)*(i + 3)/2
Let a(s) be the third derivative of -s**5/300 + s**4/30 - 2*s**3/15 - 6*s**2. Solve a(t) = 0.
2
What is d in 10*d**3 + 6*d**4 - 3*d**4 + d**4 - 2*d**4 = 0?
-5, 0
Let o be 0 + (5 - (-39)/(-9)). Factor 0*j - 2/3*j**4 - 2/3*j**5 + 0 + 2/3*j**2 + o*j**3.
-2*j**2*(j - 1)*(j + 1)**2/3
Let v(p) = 3*p**2 - 9*p + 6. Let w(o) = o - 1. Let f(c) = -v(c) - 3*w(c). Find s such that f(s) = 0.
1
Factor -16*a - 1/3*a**5 + 56/3*a**2 - 32/3*a**3 + 3*a**4 + 16/3.
-(a - 2)**4*(a - 1)/3
Determine z so that 1/9*z**2 + 1/3 + 4/9*z = 0.
-3, -1
Suppose -4*f + 7 + 9 = 0. Find k, given that -14*k**2 - f*k + 6*k**2 - 7*k**3 + 3*k**3 = 0.
-1, 0
Let d be (-4)/18 - 1066/(-585). Factor -2/5*s**2 - 8/5 - d*s.
-2*(s + 2)**2/5
Suppose -3*g + 77 = -2*i, -i - i = 2. Factor 2 - 14*u - g*u**2 + 7*u**2 + 20*u + 10*u**3.
2*(u - 1)**2*(5*u + 1)
Let r(z) be the third derivative of z**5/180 - z**4/24 + z**3/9 - 9*z**2. Factor r(i).
(i - 2)*(i - 1)/3
Solve 2/5*p**3 - 14/5*p - 4 + 8/5*p**2 = 0 for p.
-5, -1, 2
Let l be (-1)/((-2)/8) + -1. Suppose 3*p - 5*i = -16 + 2, -l*p + 4*i = 10. Let p*d - d + 2*d**2 - 2*d**4 - d**3 - 6*d**2 + 6*d**3 = 0. Calculate d.
0, 1/2, 1
Let p = 11 + -7. Let b = p + -7/2. Factor b - z + 1/2*z**2.
(z - 1)**2/2
Suppose -w - 5*r + r + 24 = 0, -2*w = 3*r - 23. Solve b**w + b - 4*b**2 + 2 - b**3 + 5*b**2 - 7*b**2 + 3*b**2 = 0.
-1, 1, 2
Let o be (-4 + 1 + 4)*0. Let q(u) be the first derivative of o*u**3 + 1/12*u**4 + 0*u - 2 - 1/6*u**2. Determine a so that q(a) = 0.
-1, 0, 1
Let h(l) = -l**3 - 4*l**2 + 5*l + 2. Let g(y) = -6*y**2 + y. Let s be g(1). Let n be h(s). Factor 2*w**3 - 6*w**3 + 2*w**3 - 2 + 2*w**n + 0*w + 2*w.
-2*(w - 1)**2*(w + 1)
Let b(m) be the first derivative of -1/80*m**5 + 1/24*m**4 + 0*m**2 - m - 2 - 1/24*m**3. Let g(n) be the first derivative of b(n). Factor g(w).
-w*(w - 1)**2/4
Let m(g) be the third derivative of -g**7/840 + g**6/360 - 7*g**3/6 - g**2. Let u(p) be the first derivative of m(p). Let u(a) = 0. Calculate a.
0, 1
Let v(f) = f**3 + 2*f**2 - 4*f - 3. Let h be v(-2). Factor 0*y**2 + y**2 - 5*y**2 - h*y**2 - 2*y.
-y*(9*y + 2)
Suppose 2*w = 4*w - 30. Let j be (-1 + -1)*w/(-10). Factor 2*a**2 + 0*a**3 - 8*a**2 + a**3 + 2*a**j.
3*a**2*(a - 2)
Let q(h) = -h**2 - 2*h - 1. Let t be q(-1). Let w be t/(-3 + 1 - -1). Find a such that a**2 + w*a + 2*a - 1 - 2*a**2 = 0.
1
Let n(d) be the second derivative of -d**7/21 - 19*d**6/105 - 3*d**5/14 - d**4/42 + 2*d**3/21 + 5*d. Let n(v) = 0. What is v?
-1, 0, 2/7
Let b(p) be the first derivative of -2/3*p**3 + 1/4*p**4 - 1/2*p**2 + 1 + 2*p. Factor b(z).
(z - 2)*(z - 1)*(z + 1)
Let m(f) be the first derivative of 4*f**3/3 + 2*f**2 + 6. Factor m(i).
4*i*(i + 1)
Let x = -13 + 26. Let u = 17 - x. Find w such that -2/3*w - 8*w**3 - u*w**2 - 16/3*w**4 + 0 = 0.
-1/2, 0
Let z(y) be the third derivative of y**6/40 + 9*y**5/20 + 15*y**4/8 - 25*y**3/2 - 16*y**2. Factor z(m).
3*(m - 1)*(m + 5)**2
Let g(c) be the third derivative of -3*c**6/80 - c**5/40 + 3*c**4/4 + c**3 - 8*c**2. Factor g(p).
-3*(p - 2)*(p + 2)*(3*p + 1)/2
Let -17*d**2 - 3 + 3*d - 10*d**2 + 6*d**3 - 21*d - 18*d**3 = 0. Calculate d.
-1, -1/4
Let n(j) be the first derivative of -j**6/10 + 13*j**5/20 - 11*j**4/8 + j**3 - 5*j**2/2 + 1. Let c(h) be the second derivative of n(h). Factor c(d).
-3*(d - 2)*(d - 1)*(4*d - 1)
Factor 3*o**3 - 28*o**4 + 21*o**2 - 5*o**2 + 45*o**3.
-4*o**2*(o - 2)*(7*o + 2)
Let w(v) be the third derivative of -1/210*v**7 - 3*v**2 + 0 - 1/10*v**5 + 1/6*v**4 + 1/30*v**6 - 1/6*v**3 + 0*v. What is k in w(k) = 0?
1
Let l be 36/14 - (3 - (-5 - -6)). Suppose -2/7*z**2 - l*z - 2/7 = 0. Calculate z.
-1
Let m(r) = -r**3 - 10*r**2 + 12*r + 11. Let b be m(-11). Let z(a) be the first derivative of -2 + 0*a - 1/4*a**4 + b*a**2 + 1/10*a**5 + 1/6*a**3. Factor z(i).
i**2*(i - 1)**2/2
Find r, given that 0 - 6/13*r - 2/13*r**2 = 0.
-3, 0
Let d(t) be the second derivative of 1/2*t**4 + 5*t + 0 - 3/20*t**5 + 0*t**2 + 0*t**3. Factor d(s).
-3*s**2*(s - 2)
Let t be -35 - -40 - (-22)/(-5). Factor -t*m**2 + 0 - 1/5*m**4 + 3/5*m**3 + 1/5*m.
-m*(m - 1)**3/5
Let g(y) = -y**2 - 16*y + 80. Let a be g(-20). Let q(r) be the third derivative of 0*r**3 + 1/105*r**5 + a*r + 2*r**2 + 1/420*r**6 + 0 + 0*r**4. Solve q(s) = 0.
-2, 0
Let w be (-6)/(-9) - (-82)/(-150). Let t(h) be the first derivative of -w*h**5 - 3/5*h**2 + 3/10*h**4 + 3/5*h + 0*h**3 - 1. Factor t(s).
-3*(s - 1)**3*(s + 1)/5
Factor -5*x**2 - 2*x**2 + 3*x + 4*x**2 + 6.
-3*(x - 2)*(x + 1)
Let z be ((-11)/(-3))/(2/(-6)). Let f = -8 - z. Factor 0 - 1 - w**5 - 10*w**2 - 6*w**3 - 5*w - 4*w**f - 5*w**4.
-(w + 1)**5
Suppose 0 - 4 + 4 + 5 - 5*c**2 = 0. Calculate c.
-1, 1
Suppose -2*l - 2*q = -20, l - 3*q + 6 = -0*l. Let k be l/2 + (-3)/3. Solve -3*h**3 + h - k + 2*h**3 - h**4 - 5*h**2 + 8*h**2 = 0 for h.
-2, -1, 1
Let 0 + 2/9*t + 0*t**2 - 2/9*t**3 = 0. Calculate t.
-1, 0, 1
Suppose 0 = -3*t + 24 + 15. Suppose 3*f = -f + c + t, 5*f + 5*c + 15 = 0. Factor 1/4*s**4 + 0 + 0*s - 1/4*s**3 + 0*s**f.
s**3*(s - 1)/4
Find y such that -5*y**3 + 5*y + 0 + 5/2*y**2 - 5/2*y**4 = 0.
-2, -1, 0, 1
Let u(o) be the second derivative of o**7/14 + 3*o**6/10 + 9*o**5/20 + o**4/4 - 21*o. Factor u(h).
3*h**2*(h + 1)**3
Suppose -4*i - 2 - 18 = 0. Let y be -1*8/20*i. Solve 18/5*u**y + 6/5*u**4 - 4/5*u + 0 - 4*u**3 = 0.
0, 1/3, 1, 2
Let m be 12 + -9 + (-26)/9. Let k(q) be the first derivative of m*q**6 - 4/9*q**3 + 2/15*q**5 - 1/3*q**4 + 2/3*q + 3 + 1/3*q**2. Find d such that k(d) = 0.
-1, 1
Let o be 74/14 - 4/14. Factor o*p**3 - 3*p**3 - p - p.
2*p*(p - 1)*(p + 1)
Let s(o) be the third derivative of -o**6/540 - o**5/270 - 2*o**2. Factor s(i).
-2*i**2*(i + 1)/9
Let b(z) be the third derivative of -z**8/560 + z**7/280 + z**6/120 - z**5/40 + z**3 + z**2. Let d(q) be the first derivative of b(q). Factor d(a).
-3*a*(a - 1)**2*(a + 1)
Let l(f) be the third derivative of -f**7/140 + 11*f**6/480 - f**5/60 - f**4/96 + f**2 + 6. Suppose l(o) = 0. Calculate o.
-1/6, 0, 1
Suppose 2*v**3 + 0*v**2 + 0 - 2/3*v + 4/3*v**4 = 0. Calculate v.
-1, 0, 1/2
Let v(n) = -n**2 + 2*n - 9. Let k be v(-4). Let f be (3/k)/(1/(-2)). Let 0*x - 2/11*x**4 + 2/11*x**3 - 2/11*x**5 + f*x**2 + 0 = 0. What is x?
-1, 0, 1
Let k(i) be the third derivative of -i**5/360 - i**4/144 + i**3/18 - 5*i**2. Factor k(t).
-(t - 1)*(t + 2)/6
Let t(w) = w**3 + 4*w**2 + 5*w + 5. Let n be t(-2). Let u be -4 + 0 + 5 + n. Solve -142/5*b**3 + 56/5*b**u - 38/5*b + 24*b**2 + 4/5 = 0.
1/4, 2/7, 1
Suppose 3*i = 24 + 30. Let g = i - 13. Suppose -2*s**4 - s**3 - 2*s**3 + 3*s**g + 2*s**3 = 0. Calculate s.
-1/3, 0, 1
Let a(o) = 0*o - 2 + 4*o - 5*o. Let k be a(-4). Suppose -3*t**2 + 0*t**2 - 4*t**k + 5*t**2 = 0. What is t?
0
Let m = -173 - -1213/7. Determine u so that 8/7*u**2 - 6/7*u - m = 0.
-1/4, 1
Let h(b) = 4*b**2 - 3*b - 7. Let s(o) = 2*o**2 - o - 3. Let z be (-22)/(-99) - (-58)/(-18). Let q(v) = z*h(v) + 5*s(v). Determine u so that q(u) = 0.
-1, 3
Let k = 52/3 - 50/3. Factor 0*a**2 - 1/3*a**4 - k*a**3 + 1/3 + 2/3*a.
-(a - 1)*(a + 1)**3/3
Let i = 7 - 0. Let f be 3*(