iven that p(q) = 0.
-1, 1
Let b = 23 + -21. Factor b*p**4 - 4/5*p + 0 - 18/5*p**3 + 14/5*p**2 - 2/5*p**5.
-2*p*(p - 2)*(p - 1)**3/5
Suppose -1/5*s**2 + 2/5*s - 1/5 = 0. Calculate s.
1
Let g(h) be the first derivative of -9*h**5/10 - 3*h**4/8 + 9. Factor g(x).
-3*x**3*(3*x + 1)/2
Let u(b) = 3*b**5 + 3*b**4 - 3*b**3 + 3. Let l(p) = -6*p**5 - 7*p**4 + 6*p**3 - 7. Let h(q) = -3*l(q) - 7*u(q). Factor h(d).
-3*d**3*(d - 1)*(d + 1)
Let r(w) be the third derivative of w**7/2520 - w**6/180 + w**5/30 - w**4/8 - 5*w**2. Let x(a) be the second derivative of r(a). Factor x(k).
(k - 2)**2
Let o(p) be the third derivative of p**7/105 - p**6/60 - p**5/30 + p**4/12 + 8*p**2. Determine q, given that o(q) = 0.
-1, 0, 1
Let o = -11/2 + 6. Let l = o - 0. Factor l - 3/4*g - 5/4*g**2.
-(g + 1)*(5*g - 2)/4
Let -9*v + 3*v**3 + 11*v - 7*v**3 + 2*v**5 = 0. Calculate v.
-1, 0, 1
Let -10/3*a**2 + 0 + 4/3*a + 2/3*a**3 - 2*a**5 + 10/3*a**4 = 0. What is a?
-1, 0, 2/3, 1
Let l(u) = u**2 - u. Let b(y) be the second derivative of 7*y**4/6 - 8*y**3 + 8*y**2 + y. Let k(g) = -b(g) + 4*l(g). Factor k(o).
-2*(o - 4)*(5*o - 2)
Let i(z) be the third derivative of z**5/270 + 4*z**4/27 + 64*z**3/27 + 22*z**2. Factor i(q).
2*(q + 8)**2/9
Let a = -8 - -10. Let d(f) be the second derivative of 5/3*f**3 - 1/7*f**7 - 2*f**a + 3*f + 0*f**4 + 0 - f**5 + 2/3*f**6. Solve d(x) = 0.
-2/3, 1
Suppose 5*y = 2*y - 3. Let c be (2 + -1)/y - -6. Factor -1 - c*p**2 - 2*p + 2*p**2 + 2*p**2.
-(p + 1)**2
Let y(i) be the third derivative of 1/30*i**3 + 3/200*i**6 + 0*i - 1/24*i**4 + 0 + 1/100*i**5 + 3*i**2. Factor y(p).
(p + 1)*(3*p - 1)**2/5
Let d(k) = -50*k**4 + 15*k**3 + 50*k**2 + 15*k - 15. Let v(c) = -7*c**4 + 2*c**3 + 7*c**2 + 2*c - 2. Let w(y) = 2*d(y) - 15*v(y). Suppose w(g) = 0. What is g?
-1, 0, 1
Suppose -9 = -2*y - 3. Suppose 3*z - 9 = -y. Factor 4*p - p**3 + 4*p**2 + 2*p**z + 3*p**3.
2*p*(p + 1)*(p + 2)
Let m = -9 + 14. Suppose 0 = 5*z - 20 + m. Find g such that 2/5*g**2 + 0 - 2/5*g**z + 0*g = 0.
0, 1
Factor -6/13 - 16/13*k - 6/13*k**2 + 4/13*k**3.
2*(k - 3)*(k + 1)*(2*k + 1)/13
Determine s so that -2*s + s**2 + 3*s**2 - 3*s**2 - 2*s**2 = 0.
-2, 0
Factor -3/5*w**3 + 0*w + 0*w**2 - 3/5*w**5 + 0 - 6/5*w**4.
-3*w**3*(w + 1)**2/5
Let z be (-3)/(63/(-6)) - (-3)/(-35). Suppose 2/5*x**3 + 0*x + 0 - z*x**4 - 1/5*x**2 = 0. What is x?
0, 1
Let g(a) be the third derivative of -a**7/3780 + a**6/1620 - 7*a**3/6 - a**2. Let l(n) be the first derivative of g(n). Let l(t) = 0. What is t?
0, 1
Let k(p) = -p**3 + 3*p**2 + 6*p - 5. Let u be k(4). Suppose -u*j = -j. Factor j*m - 2/3*m**2 + 1/3*m**4 + 1/3 + 0*m**3.
(m - 1)**2*(m + 1)**2/3
Suppose h + 19 = 5*v - 0, -3*h + 3 = 0. Determine c so that 0 + 0*c + 0*c**2 + 1/3*c**v - 1/3*c**3 = 0.
0, 1
Let q(v) = -9*v**3 - 2*v**2 - 9*v. Let h(l) = l**3 + l. Let t = 15 - 39. Let f(i) = t*h(i) - 3*q(i). Factor f(p).
3*p*(p + 1)**2
Let q(y) be the first derivative of -y**6/180 + y**5/60 - 4*y**3/3 + 1. Let j(h) be the third derivative of q(h). Let j(k) = 0. Calculate k.
0, 1
Let a(i) be the third derivative of -i**2 + 0*i - 1/80*i**5 - 1/160*i**6 + 0 + 1/32*i**4 + 1/8*i**3. Factor a(y).
-3*(y - 1)*(y + 1)**2/4
Factor -3*z**3 - 7*z**3 + 0*z**5 + 2*z**5 + 2*z**2 + 14*z**4 - 8*z**5.
-2*z**2*(z - 1)**2*(3*z - 1)
Let i be 1 + -3 + -1 - (3 + -6). Let c(z) be the second derivative of 2*z + i*z**4 + 1/25*z**5 + 0*z**3 + 0 + 0*z**2 + 1/75*z**6. Factor c(h).
2*h**3*(h + 2)/5
Let g(v) be the second derivative of -1/30*v**5 + 2*v + 1/2*v**2 + 1/3*v**3 + 0 + 0*v**4. Let r(i) be the first derivative of g(i). Suppose r(y) = 0. What is y?
-1, 1
Suppose -6 = -0*z - 3*z. Suppose 9*j - 4*j - 10 = 0. Suppose -f + 5*f + f**j - z - 3*f**2 = 0. What is f?
1
Let a(p) = 3*p**2 - 6*p + 1. Let h(f) = -2*f**2 + 3*f - 1. Let r(n) = 3*a(n) + 5*h(n). Factor r(c).
-(c + 1)*(c + 2)
Let j(q) = -10*q - 6 - 5*q**2 + 4*q**2 - 3. Let y be j(-9). Determine f so that f**2 + y*f**2 + 0*f**2 + 2*f = 0.
-2, 0
Let l(s) be the third derivative of 0 + 1/210*s**7 + 0*s**4 + 0*s - 1/60*s**5 + 10*s**2 + 1/336*s**8 - 1/120*s**6 + 0*s**3. Determine a so that l(a) = 0.
-1, 0, 1
Factor 6/7 - 3/7*k**2 - k.
-(k + 3)*(3*k - 2)/7
Suppose -v + 2*j + 8 = 0, -4*j - 22 + 90 = 4*v. Let y be 49/v - 3/1. Factor y - 3/4*d + 1/4*d**2.
(d - 2)*(d - 1)/4
Let q(u) = 4*u - 2. Let l(j) = -j**2 + 9*j - 5. Let i(a) = -4*l(a) + 10*q(a). Solve i(k) = 0.
-1, 0
Suppose 3*d = 0, 13 = -3*f + 3*d - 41. Let i be 15*(-2)/f*3. Factor 2*u**3 + 3*u**3 - 4*u**4 + i*u**5 - 4*u**5 - 2*u**2.
u**2*(u - 2)*(u - 1)**2
Let q(o) be the first derivative of -3*o**4/8 - 3*o**3/2 + 15*o**2/2 - 11. Factor q(i).
-3*i*(i - 2)*(i + 5)/2
Let o(k) = k**3 + 11*k**2 - 13*k - 10. Let w be o(-12). Find n, given that -4*n**2 + 8 + 0*n**2 + 8*n + 6*n**w = 0.
-2
Let g(z) be the second derivative of 2*z + 2/5*z**6 - 53/24*z**4 + 7/3*z**3 + 0 - z**2 + 7/20*z**5. Find w such that g(w) = 0.
-2, 1/4, 1/2, 2/3
Let o(c) be the second derivative of 5*c**7/42 + c**6/2 + c**5/4 - 5*c**4/4 - 5*c**3/3 + 16*c. Factor o(h).
5*h*(h - 1)*(h + 1)**2*(h + 2)
Let d = 3 - 2. Factor d - n**2 + 4*n - 4*n.
-(n - 1)*(n + 1)
Suppose -4*c - 10 = -2*c. Let r = -3 - c. Factor 0*i - 2*i**r - i + i.
-2*i**2
Factor -24*h**2 - 24*h**2 + 50*h**2 - 8*h.
2*h*(h - 4)
Let n(z) be the second derivative of z**4/3 + 10*z**3/3 + 12*z**2 + 2*z - 10. What is t in n(t) = 0?
-3, -2
Let 6*r**2 - 2*r - 8*r**3 + 6*r**3 - 4*r + 2*r**2 = 0. Calculate r.
0, 1, 3
Suppose -3*u = -f - 9, 4*u - 3*u + 1 = -f. Factor -2 - n**2 + 4*n**u - n**2.
2*(n - 1)*(n + 1)
Factor 7 - 4 + 5*w**2 + 9 + 10*w - 3*w**2.
2*(w + 2)*(w + 3)
Suppose -2*i = 5*w - 7, -3*i + 23 = -7*w + 2*w. Let f(n) = -7*n**2 + 7. Let c(r) = -20*r**2 + 20. Let a(b) = i*c(b) - 17*f(b). Determine o, given that a(o) = 0.
-1, 1
Let o(f) be the third derivative of f**5/60 + f**3/6 + 2*f**2. Let l(j) = 5*j**2 + 4*j + 5. Let g(a) = -l(a) + 3*o(a). Factor g(w).
-2*(w + 1)**2
Let j(r) be the second derivative of r**6/45 - r**4/9 + r**2/3 - 3*r. Factor j(a).
2*(a - 1)**2*(a + 1)**2/3
Suppose 4*j - 5*r - 6 = -3*r, -5*j = -3*r - 6. Let t be 2/2 + 0 + 1. Factor n**4 - n**t + j*n**3 - n**3 + 3*n**4 - 5*n**4.
-n**2*(n - 1)**2
Let b(m) = 48*m**3 - 81*m**2 - 129*m. Let v(l) = -3*l**3 + 5*l**2 + 8*l. Let d(g) = 2*b(g) + 33*v(g). Solve d(p) = 0 for p.
-1, 0, 2
Let x(q) = -q**3 + 3*q**2 - 1. Let k be x(2). Factor k*a + a**3 - 8*a**3 + 8*a - 2 - 4*a + 2*a**2.
-(a - 1)*(a + 1)*(7*a - 2)
Suppose 5*o - 28 = -3. Let y(x) be the third derivative of -3*x**2 + 0 + 0*x**4 - 1/6*x**3 + 0*x + 1/60*x**o. Find b, given that y(b) = 0.
-1, 1
Let 3 + 0*l**2 + 3*l**2 + 6*l + 0*l = 0. What is l?
-1
Find p such that 13*p**2 - 5*p**4 - 5 - 43*p**2 - 3*p - 20*p**3 - 17*p = 0.
-1
Let j(r) = -5*r**5 + 21*r**4 + 21*r**3 - 5*r**2 - 9*r. Let t(i) = -i**5 + 5*i**4 + 5*i**3 - i**2 - 2*i. Let n(m) = -4*j(m) + 18*t(m). Factor n(x).
2*x**2*(x + 1)**3
Solve 0*b**3 + 2*b**2 + b**4 - 2*b**2 - 3*b**3 - b + 3*b**2 = 0.
0, 1
Let g(l) be the first derivative of -l - 1/10*l**5 + 1/8*l**4 - 1/4*l**2 + 1/2*l**3 + 2. Factor g(c).
-(c - 2)*(c - 1)*(c + 1)**2/2
Let d(c) = -6*c**2 + 7*c. Let t be ((-2)/(-4))/((-4)/168). Let b(x) = x**2 - x. Let f(r) = t*b(r) - 3*d(r). Factor f(q).
-3*q**2
Factor -1/2*i - 3/2*i**3 + 0 - 2*i**2.
-i*(i + 1)*(3*i + 1)/2
Let u(x) be the second derivative of x**5/5 - 2*x**4/3 + 2*x**3/3 + x. Factor u(a).
4*a*(a - 1)**2
Let d(w) be the first derivative of w**5/4 + 15*w**4/16 + 5*w**3/12 - 15*w**2/8 - 5*w/2 + 16. Factor d(j).
5*(j - 1)*(j + 1)**2*(j + 2)/4
Factor -g + 3*g**2 - 6*g**2 + 2*g**2 - g.
-g*(g + 2)
Let g(r) be the first derivative of 2*r**3/15 + 4*r**2/5 + 8*r/5 + 8. Determine z, given that g(z) = 0.
-2
Let p(s) be the third derivative of s**6/60 - s**5/30 - 5*s**4/12 - s**3 - s**2 + s. Factor p(z).
2*(z - 3)*(z + 1)**2
Suppose 2*w = 11 + 1. Let i = -3 + w. Factor -4*h**2 - 3*h**i + 11*h**2 + 5*h**2 + 6 - 15*h.
-3*(h - 2)*(h - 1)**2
Solve 2/9*i**2 + 0*i**3 - 2/9*i**4 + 0*i + 0 = 0 for i.
-1, 0, 1
Let x(a) be the first derivative of -a**5/70 - a**4/14 + 2*a + 5. Let q(h) be the first derivative of x(h). Factor q(l).
-2*l**2*(l + 3)/7
Let s = 4/433 - 110431/1732. Let z = 65 + s. Factor -z*n + 1/2 - n**2 + 3/4*n**3.
(n - 2)*(n + 1)*(3*n - 1)/4
Let u(d) = -4*d**3 - 6*d**2 + 20*d - 10. Let l(i) = -5*i**3 - 6*