*r**2 - 2*r + 1. Let s be y(-4). Suppose 0 = 7*x - s*x + 8. Factor 2/7*l**5 + 0*l**x + 0 - 4/7*l**3 + 2/7*l + 0*l**2.
2*l*(l - 1)**2*(l + 1)**2/7
Let q(h) be the second derivative of -3*h + 0*h**3 - 1/10*h**2 + 0 + 1/60*h**4. What is v in q(v) = 0?
-1, 1
Let l(a) = -a - 2. Let p be l(-7). Let d(y) be the second derivative of 0*y**4 + 0*y**2 + 0 - 1/15*y**3 + 1/50*y**p + y. Solve d(x) = 0 for x.
-1, 0, 1
Suppose 0 = -4*p - p - 4*y - 6, -y = 4. Factor -6*b**2 - 1 - p + 4*b**2 + 5.
-2*(b - 1)*(b + 1)
Let w(b) be the third derivative of b**6/1080 + b**5/270 - 16*b**2. What is s in w(s) = 0?
-2, 0
Let a(n) be the third derivative of -n**11/166320 + n**10/37800 - n**9/30240 + 2*n**5/15 + 9*n**2. Let q(f) be the third derivative of a(f). Factor q(h).
-2*h**3*(h - 1)**2
Let s(d) be the second derivative of d**7/14 + 5*d. Factor s(a).
3*a**5
Let c(u) be the third derivative of u**6/300 - 7*u**5/300 + u**4/40 + 12*u**2. Factor c(n).
n*(n - 3)*(2*n - 1)/5
What is x in 20*x**3 - 9/2*x**2 - 1 - 8*x**4 - 13/2*x = 0?
-1/4, 1, 2
Let c(s) = s**3 + 7*s**2 - 9*s - 10. Let o be c(-8). Let a be 1 + (-2)/(1*o). Factor 1 + a*p**3 - 2 - 2*p + 2*p**4 - p**4.
(p - 1)*(p + 1)**3
Let p(r) = -3*r**2 + 17*r - 7. Let f(t) = -8*t**2 + 52*t - 22. Suppose 0 = -15*v + 19*v - 12. Let c(i) = v*f(i) - 10*p(i). Solve c(l) = 0.
1/3, 2
Let r(t) be the second derivative of t**4/3 + 2*t**3 + 4*t**2 - 12*t. Suppose r(i) = 0. What is i?
-2, -1
Suppose -3*c + 7*c = 0. Let a be (-5 - 366/(-54)) + 2/9. Let c*f + 2/7*f**a + 0 = 0. What is f?
0
Let a(q) = q**3 - q. Suppose -2*l + 35 = 5*l. Let b(i) = -15*i**2 - 3*i**3 - 19*i - 12 - 8*i**3 + 3*i**3. Let x(s) = l*a(s) + b(s). Solve x(k) = 0.
-2, -1
Let g(b) be the third derivative of b**7/30 + 2*b**6/15 + b**5/15 - 19*b**2. Let g(z) = 0. What is z?
-2, -2/7, 0
Let d(g) be the third derivative of -g**4/24 - 5*g**3/6 - 3*g**2. Let m be d(-5). Factor 0 + 1/2*h**3 + 1/2*h**4 + m*h**2 + 0*h.
h**3*(h + 1)/2
Suppose 14 = 3*g - 19. Let m = g - 8. Let 7*z**4 + z + z**m - z - 8*z**4 = 0. Calculate z.
0, 1
Let i = -134 - -134. Factor 0*v + i - 1/2*v**3 - 1/2*v**2.
-v**2*(v + 1)/2
Let a(o) be the second derivative of -o**5/70 + o**4/2 - 7*o**3 + 49*o**2 - 2*o + 2. Factor a(x).
-2*(x - 7)**3/7
Let a(i) be the second derivative of i**6/10 - 9*i**5/20 - 24*i. Solve a(w) = 0 for w.
0, 3
Let i be (-8 + 10)*(9/(-12) - -1). Factor i*b + 0 - 2/3*b**2 + 1/6*b**3.
b*(b - 3)*(b - 1)/6
Let u(r) = -r**2 - 2*r - 1. Let c(o) = -o**2 - o. Let a be 10/(-4) - (-9)/6. Let v(z) = a*u(z) + 2*c(z). Factor v(i).
-(i - 1)*(i + 1)
Suppose 152 = -4*p + 160. Factor 0*m - 1/4 + 1/4*m**p.
(m - 1)*(m + 1)/4
Let b(m) = 2 - 2*m**2 - 5*m - m**3 - 4*m**2 + 4. Let c = -6 - 0. Let s(y) = 2*y**3 + 11*y**2 + 9*y - 11. Let n(p) = c*s(p) - 11*b(p). Factor n(r).
-r*(r - 1)*(r + 1)
Let u be 1 + 1 - (-7 + -21). What is c in -82/3*c**2 + 18*c**5 - 2*c**3 - 8/3 - 16*c + u*c**4 = 0?
-1, -2/3, -1/3, 1
Determine h, given that 0*h + 0 + 1/3*h**3 - 1/3*h**2 = 0.
0, 1
Let y be 5 + -2*2697/1080. Let v(j) be the third derivative of 0*j**7 + 0*j**5 + 0*j - j**2 + 0*j**4 + 0 - 1/504*j**8 + 0*j**3 + y*j**6. Factor v(w).
-2*w**3*(w - 1)*(w + 1)/3
Let u(w) = -w + 10. Let o be u(7). Factor 3*b**4 - 2*b**3 - o*b + b - 4*b**2 + 4*b + 1.
(b - 1)**2*(b + 1)*(3*b + 1)
Let w be (-2)/(-8) - (-84)/(-16). Let d = w + 7. Solve 2/9*h**4 + 0 + 2/9*h**3 + 0*h + 0*h**d = 0.
-1, 0
Let g = 38 + -75/2. Suppose 0 - 3*p**3 + 2*p**2 - 1/2*p**5 - g*p + 2*p**4 = 0. Calculate p.
0, 1
Let j = 6 + -7. Let i(s) = -3*s**3 - s**2 - s. Let o be i(j). Solve -2/3*l**2 - 2/3*l**o + 0 + 2/3*l + 2/3*l**4 = 0.
-1, 0, 1
Let p = 112/927 + -1/103. Let o(u) be the first derivative of -p*u**3 + 0*u**2 + 1/15*u**5 + 0*u - 1/12*u**4 + 1/18*u**6 - 2. Determine b so that o(b) = 0.
-1, 0, 1
Let g(r) be the second derivative of -r**6/240 + 3*r**5/160 + r**4/48 - r**3/4 + r**2/2 - 38*r. Factor g(q).
-(q - 2)**2*(q - 1)*(q + 2)/8
Let g(k) be the second derivative of -k**5/40 - 2*k**4/3 - 29*k**3/12 - 7*k**2/2 - 11*k. Solve g(q) = 0.
-14, -1
Let d = 68/5 - 267/20. Suppose 1/4*k**2 - d*k + 0 = 0. Calculate k.
0, 1
Let f(t) be the first derivative of t**7/245 + t**6/60 + t**5/42 + t**4/84 + 2*t**2 + 3. Let y(b) be the second derivative of f(b). Solve y(q) = 0.
-1, -1/3, 0
Let j be ((-1)/18)/((-60)/9). Let r(k) be the third derivative of 0 - 1/336*k**8 - j*k**6 + 0*k**4 + 2*k**2 + 0*k + 1/105*k**7 + 0*k**5 + 0*k**3. Factor r(z).
-z**3*(z - 1)**2
Let o(z) = 4*z**4 + 5*z**3 - 14*z**2 + 2*z - 2. Let m(g) = g**4 - g**2 - g. Let q(y) = -20*m(y) + 4*o(y). Factor q(x).
-4*(x - 2)*(x - 1)**3
Let s(u) be the first derivative of u**4/6 + u**3/3 + 4*u - 1. Let q(h) be the first derivative of s(h). Factor q(w).
2*w*(w + 1)
Let z(k) be the third derivative of 5*k**8/168 + 8*k**7/105 + k**6/60 - k**5/15 - 4*k**2. Factor z(x).
2*x**2*(x + 1)**2*(5*x - 2)
Suppose 4*t + 10 = a, 4*a + 0*a - 4*t = 28. Suppose -3*u + 2*v + 2 = -a*u, -3 = u + 3*v. Determine l, given that 0 - 1/4*l**2 + u*l = 0.
0
Let x(l) = l**3 - 3*l**2 - 9*l - 5. Let b(f) = -6*f**3 + 14*f**2 + 46*f + 26. Suppose 4*z + 19 = 7. Let j(m) = z*b(m) - 16*x(m). Factor j(w).
2*(w + 1)**3
Let x(g) = 3*g**3 + 17*g**2 - 3*g - 17. Let v(z) = z**3 + 9*z**2 - z - 9. Let a(s) = -7*v(s) + 4*x(s). Suppose a(j) = 0. What is j?
-1, 1
Suppose 5*a - 5*m + m = 20, m + 5 = -5*a. Suppose a = -2*d - d + 6. Determine f, given that 3 + 3*f**2 + 4*f**2 - 4*f**d + 6*f = 0.
-1
Suppose -5*f - 6 + 21 = 0. Let m = 436/3 + -144. Factor m*g**f - 4/3*g + 2/3 - 2/3*g**4 + 0*g**2.
-2*(g - 1)**3*(g + 1)/3
Let w = -3 + 5. Suppose 5*i - 12 = -w. Factor 2*l**5 - i*l**2 + 3*l**3 - 5*l**3 + 2*l**4 + 0*l**4.
2*l**2*(l - 1)*(l + 1)**2
Let n(h) be the second derivative of 1/21*h**7 + 3*h + 3*h**3 + 2/5*h**6 + 8/3*h**4 + 2*h**2 + 7/5*h**5 + 0. Factor n(k).
2*(k + 1)**4*(k + 2)
Let u = -16 + 27. Suppose u = 5*y + 1. Suppose 0*s + s**2 - 3*s**y - 1 - 1 + 4*s = 0. What is s?
1
Factor 39*j**2 - 19*j**2 - 4 - 16*j**2.
4*(j - 1)*(j + 1)
Let u be (-9)/(-7) + (3 + -4)*1. Suppose 0*s + 2/7*s**4 - u*s**3 + 0 + 0*s**2 = 0. Calculate s.
0, 1
Let r(j) be the third derivative of j**6/200 + j**5/10 + 17*j**4/40 + 4*j**3/5 + 20*j**2. Determine n, given that r(n) = 0.
-8, -1
Let o(m) = m**3 + 4*m**2 + 2*m. Let r be o(-3). Find n, given that n**3 + 0*n**3 - r*n**3 + 0*n**3 = 0.
0
Suppose -4/7*f - 18/7*f**2 + 8/7 + 10/7*f**4 + 3/7*f**5 + 1/7*f**3 = 0. What is f?
-2, -1, 2/3, 1
Factor -7*y**2 - 9 + 15*y - 79*y**3 - 73*y**3 + 153*y**3.
(y - 3)**2*(y - 1)
Factor 18/7*c**2 - 12/7*c - 8/7*c**3 + 2/7.
-2*(c - 1)**2*(4*c - 1)/7
Factor -8/21*l + 2/21*l**4 + 0 + 16/21*l**2 - 10/21*l**3.
2*l*(l - 2)**2*(l - 1)/21
Factor 0 + 8/9*n - 28/9*n**2.
-4*n*(7*n - 2)/9
Let c be (-8)/(-20) + (-13)/(-5). Factor p**2 + 9*p - 4*p**3 - 5*p**c + 6*p**3 - 7*p**2.
-3*p*(p - 1)*(p + 3)
Let g(j) = j**4 + j**2 + 1. Let m(b) = -5*b**5 - 31*b**4 - 75*b**3 - 41*b**2 + 4. Let y(q) = 4*g(q) - m(q). What is t in y(t) = 0?
-3, -1, 0
Let t = 6346/27 + -235. Let y(c) be the third derivative of 0*c - 11/540*c**6 + 2*c**2 - 1/108*c**4 + 0 - 4/945*c**7 - 1/30*c**5 + t*c**3. Solve y(p) = 0 for p.
-1, 1/4
Let t(s) be the first derivative of s**6/4 + s**5/15 - 3*s**4/4 - 2*s**3/9 + 3*s**2/4 + s/3 - 8. Solve t(a) = 0.
-1, -2/9, 1
Let w(s) be the third derivative of -1/945*s**7 + 0*s**6 + 0 + 0*s**3 + 4*s**2 + 0*s**4 + 1/270*s**5 + 0*s. Let w(c) = 0. Calculate c.
-1, 0, 1
Let a = -986/5 + 198. Suppose -2/5*v**2 + a + 2/5*v = 0. What is v?
-1, 2
Factor -1 + 18*r + 4*r**3 - 4*r**4 - 14*r + 3*r**4 - 6*r**2.
-(r - 1)**4
Let q(b) = -2*b**3 - 3*b**2 - 2*b. Let x be q(-2). What is h in x*h**2 + h**2 + 3*h + 3*h**2 - 9*h**3 - 6 = 0?
-2/3, 1
Let r(s) = s**3 - 2*s**2 - s + 1. Let u be r(0). Let i be 6/(-9)*u/(-2). Factor 1/3*n + 2/3 - i*n**2.
-(n - 2)*(n + 1)/3
Let a be 4/14 + 10/14. Let m(z) = z**4 - z**3 + z**2 - z + 1. Let k(b) = -b**5 + 2*b**4 - 7*b**3 + 7*b**2 - 2*b + 6. Let r(p) = a*k(p) - 5*m(p). Factor r(w).
-(w - 1)*(w + 1)**4
Let w = -3 - -2. Let g be 2 + (-1 - w) + 0. Factor -3*f**g - 4 + 2*f**2 + 2*f + 3.
-(f - 1)**2
Let 0 - 2/7*q**2 + 8/7*q = 0. What is q?
0, 4
Let x(v) be the second derivative of -4/15*v**3 + 0 - 6*v - 8/5*v**2 - 1/60*v**4. Solve x(h) = 0 for h.
-4
Let v(q) be the third derivative of 0 - 1/24*q**4 - q**2