 of l(i). Find j, given that u(j) = 0.
-3, 0
Let k(p) be the second derivative of p**10/30240 - p**9/15120 - p**8/6720 + p**7/2520 - p**4/12 - p. Let b(z) be the third derivative of k(z). Factor b(q).
q**2*(q - 1)**2*(q + 1)
Let m = -197/2 + 100. Let x(w) = -w. Let c be x(-1). Factor -7/2*f**2 - 3/2*f + 5/2*f**4 + m*f**3 + c.
(f - 1)*(f + 1)**2*(5*f - 2)/2
Let l(y) be the first derivative of 3 - 1/6*y**6 + 0*y + 1/4*y**4 - 1/3*y**3 + 1/5*y**5 + 0*y**2. Determine r so that l(r) = 0.
-1, 0, 1
Find u, given that 144/5*u**2 + 42/5*u**3 + 3/5*u**4 - 42/5*u - 147/5 = 0.
-7, -1, 1
Let s(c) = -c**3 + 2*c**2 + 2*c. Let y be s(2). Factor -2 + 6*i + y*i**2 - 6*i - 2*i**4.
-2*(i - 1)**2*(i + 1)**2
Let c(x) = -x**2 + 5*x - 1. Let l be c(4). Let l*a - 3*a**3 - 4/3*a**4 + 2/3*a**2 + 2/3 = 0. Calculate a.
-2, -1, -1/4, 1
Let b(i) = -12*i**4 - 3*i**3 + 15*i**2 + 15*i + 15. Let o(w) = 3*w**4 + w**3 - 4*w**2 - 4*w - 4. Let t(u) = 4*b(u) + 15*o(u). Factor t(g).
-3*g**3*(g - 1)
Let j(n) be the third derivative of 0 + 0*n - 1/6*n**3 + 0*n**5 - 2*n**2 - 1/24*n**4 + 1/360*n**6. Let o(q) be the first derivative of j(q). Factor o(r).
(r - 1)*(r + 1)
Let q(u) = -5*u + 21. Let r(z) = -6*z + 22. Let c(w) = 5*q(w) - 4*r(w). Let y be c(15). Factor 1/4*l**y - 1/4 + 0*l.
(l - 1)*(l + 1)/4
Factor 2/5*j - 2/5 - 2/5*j**3 + 2/5*j**2.
-2*(j - 1)**2*(j + 1)/5
Let q(m) be the first derivative of -m**3/18 + 3*m**2/2 - 27*m/2 - 20. Determine k so that q(k) = 0.
9
Let f(b) = b**3 + 5*b**2 - 5*b + 6. Let w(a) = -3*a**2 + 3*a. Let p be w(2). Let l be f(p). Factor -2/3*d**4 - 5/3*d**3 - 2/3*d**2 + l*d + 0.
-d**2*(d + 2)*(2*d + 1)/3
Let j be (-14)/(-78) + 14/91. Let i(o) be the first derivative of 2/3*o**3 + 1/3*o**4 + j*o + 1/15*o**5 - 2 + 2/3*o**2. Determine l, given that i(l) = 0.
-1
Determine x, given that 16/7*x**2 - 8/7*x - 2/7*x**3 + 0 - 6/7*x**4 = 0.
-2, 0, 2/3, 1
Factor 4/5*n**2 + 0 - 2/5*n.
2*n*(2*n - 1)/5
Factor 0 - 4/7*x**3 + 2/7*x + 0*x**2 + 0*x**4 + 2/7*x**5.
2*x*(x - 1)**2*(x + 1)**2/7
Let c(z) = -24*z**4 + 36*z**3 - 6*z**2 - 6*z - 3. Let h(u) = -23*u**4 + 36*u**3 - 7*u**2 - 6*u - 2. Let b(x) = -2*c(x) + 3*h(x). Factor b(j).
-3*j*(j - 1)**2*(7*j + 2)
Let y(v) = v**3 - 5*v**2 - 8*v + 6. Let s be y(6). Let w be (1/s)/(3/(-12)). Factor -5/3*l**2 - l + w.
-(l + 1)*(5*l - 2)/3
Factor -20*f**2 - 9*f + 2*f - 5*f + 9*f**3 + 8*f**2.
3*f*(f - 2)*(3*f + 2)
Suppose l + 25*l = -4*l. Let -2/3*u**4 - 4/3*u**3 + 4/3*u + 2/3 + l*u**2 = 0. What is u?
-1, 1
Let j = 7 - 5. Factor -3*q**4 + 2*q**4 - 6*q**3 + 3*q**3 - 4*q**2 + q**j - q.
-q*(q + 1)**3
Let a(i) = -6*i**2 - 16*i + 16. Let h be (-1 + 1)/(10/5). Let w = h + -16. Let l(p) = p**2 + 3*p - 3. Let z(m) = w*l(m) - 3*a(m). Factor z(d).
2*d**2
Suppose -5*y = -2*y - 3. Let l = y + 1. Factor -5*n + 7*n + 2*n**2 - 2*n**3 + l - 4*n**2.
-2*(n - 1)*(n + 1)**2
Suppose d - 2*k = 2, 4*d - 20 = -4*k - 0. What is c in 0 + 2/3*c**d + 2*c**2 + 2/3*c + 2*c**3 = 0?
-1, 0
Let a(r) be the first derivative of -r**7/1680 + r**6/288 - r**5/240 + r**3/3 + 2. Let o(w) be the third derivative of a(w). Suppose o(c) = 0. Calculate c.
0, 1/2, 2
Suppose -8*x + 3*x + 15 = 0. Let t(m) be the third derivative of 1/8*m**4 + 1/5*m**5 + 7/120*m**6 - 1/3*m**x + 0*m + 0 + m**2. Factor t(i).
(i + 1)**2*(7*i - 2)
Factor 18*t**2 - 3*t + 0 - 105/4*t**3.
-3*t*(5*t - 2)*(7*t - 2)/4
Let g be (-82)/(-48) - (-42)/(-112). Determine a, given that -14/3*a**2 - 8/3*a**3 + 2/3 - g*a = 0.
-1, 1/4
Let x = 6 + -9. Let m be -1 + -4*3/x. Factor -1/4*u**2 - 1/2*u + 0 + 1/4*u**m.
u*(u - 2)*(u + 1)/4
Let u(m) = -7*m**2 - 3 - 4 - 4 + 7 + 16*m. Let d be (2/5)/(1/(-55)). Let j(f) = 35*f**2 - 80*f + 20. Let o(p) = d*u(p) - 4*j(p). Factor o(a).
2*(a - 2)*(7*a - 2)
Suppose c + 34 = 36. Let g = 1118/9 - 124. Determine r so that 0*r + 2/9*r**4 - g*r**c - 2/9*r**5 + 2/9*r**3 + 0 = 0.
-1, 0, 1
Let z = 799 + -799. Factor 5/9*h**2 + z + 1/9*h**4 - 2/9*h - 4/9*h**3.
h*(h - 2)*(h - 1)**2/9
Let v(z) = -z**4 - z**2 - z. Let w(h) = -h**3 + 7*h**2 + 7*h + 11. Let n be w(8). Let g(u) = 4*u**4 + 8*u**2 + 7*u. Let y(x) = n*g(x) + 15*v(x). Factor y(s).
-3*s*(s - 2)*(s + 1)**2
Let x be ((-3)/2)/(-3 + (-42)/(-16)). Solve 2/3*d**x + 4/3*d**3 - 4/3*d + 0*d**2 - 2/3 = 0 for d.
-1, 1
Let -2/5 - 4/5*z - 2/5*z**2 = 0. What is z?
-1
Let x(d) be the third derivative of 0 + 0*d**4 - 1/1260*d**6 + 0*d - 1/420*d**5 - d**2 - 1/3*d**3. Let q(s) be the first derivative of x(s). Factor q(l).
-2*l*(l + 1)/7
Let k(n) be the second derivative of -4*n + 0 + 1/6*n**2 - 1/18*n**4 + 0*n**3 + 1/90*n**6 + 0*n**5. Determine j so that k(j) = 0.
-1, 1
Let k(w) be the second derivative of 2*w**7/21 + 2*w**6/5 + w**5/5 - w**4 - 4*w**3/3 - w. Find s, given that k(s) = 0.
-2, -1, 0, 1
Let o(t) = -t**4 - t**3 + t**2 - t + 1. Let v(b) = -5*b**5 + 15*b**4 + 30*b**3 - 25*b**2 + 15*b - 15. Let h(z) = 15*o(z) + v(z). Determine m so that h(m) = 0.
-2, 0, 1
Let x(c) = 5*c**2 - 14*c + 5. Let j(n) = 5*n**2 - 15*n + 5. Let a(v) = 4*j(v) - 5*x(v). Factor a(f).
-5*(f - 1)**2
Let h(z) be the third derivative of -z**5/60 + z**4/4 - 4*z**3/3 - 19*z**2. Factor h(v).
-(v - 4)*(v - 2)
Factor -16 + 26*c**2 + 73*c + 4 + c.
2*(c + 3)*(13*c - 2)
Let f = -17 + 52/3. Let m(r) be the first derivative of 1/5*r**5 - f*r**3 + 0*r - 1/3*r**6 - 3 + 0*r**2 + 1/2*r**4. Find z such that m(z) = 0.
-1, 0, 1/2, 1
Let b(o) = o**2 + 2*o + 2. Let m be b(-2). Let z be (4/(-36))/(m/(-6)). Factor -1/3*c**5 + 1/3*c**2 + 0 + 0*c + z*c**3 - 1/3*c**4.
-c**2*(c - 1)*(c + 1)**2/3
Let k(h) be the third derivative of -1/30*h**5 - 1/6*h**4 + 0*h - 1/3*h**3 - 3*h**2 + 0. Factor k(d).
-2*(d + 1)**2
Let q(i) = -2*i**3 - i. Let y be q(-1). Let c be (-5)/((-20)/(-12))*-1. Factor 0*x**5 - 4*x**c + 3*x**y + 2*x**4 - x**5 + 0*x**3.
-x**3*(x - 1)**2
Let u(v) = v**3 + 4*v**2 + 4*v + 4. Let x be u(-3). Suppose 0 = -4*f + x + 7. Suppose 4*i + i**4 - 7/3*i**3 - 2*i**f + 8/3 = 0. What is i?
-1, -2/3, 2
What is l in -4*l**3 + 2*l**2 - 3*l**4 - 2*l**2 - 5*l**4 = 0?
-1/2, 0
Let b(u) be the first derivative of -u**6/12 + u**5/8 + 11*u**4/32 - 7*u**3/24 - 7*u**2/16 + u/4 + 5. Determine i so that b(i) = 0.
-1, 1/4, 1, 2
Let w(c) be the second derivative of 0 + 3*c + 0*c**3 + 0*c**2 + 0*c**4 - 1/7*c**7 - 1/3*c**6 - 1/5*c**5. Factor w(j).
-2*j**3*(j + 1)*(3*j + 2)
Let r(j) = 14*j - 96. Let o be r(7). Factor o*h**2 + 0*h**3 - 2/3*h**4 + 4/3*h + 0.
-2*h*(h - 2)*(h + 1)**2/3
Let q(y) = 3*y**2 + 62*y + 180. Let j(a) = 5*a**2 + 125*a + 360. Let l(b) = 2*j(b) - 5*q(b). Find p such that l(p) = 0.
-6
Let t(s) = 13*s**2 - 13*s. Let c be t(1). Factor 1/4*w**4 - 1/4*w**2 + 0*w**3 + c + 0*w.
w**2*(w - 1)*(w + 1)/4
Let 6*b + 5*b**2 - 15*b + 20 + 7*b - 18*b = 0. What is b?
2
Let a(b) be the third derivative of b**8/168 + b**7/21 + 3*b**6/20 + 7*b**5/30 + b**4/6 - 41*b**2. Suppose a(g) = 0. What is g?
-2, -1, 0
Factor -8/3*x**3 + 2/3*x**4 - 8/3 + 8/3*x + 2*x**2.
2*(x - 2)**2*(x - 1)*(x + 1)/3
Suppose -8/7*a**4 - 12/7*a**3 - 2/7*a**5 - 2/7*a - 8/7*a**2 + 0 = 0. What is a?
-1, 0
Let k(j) = j**2 + j. Let v be k(0). Let a(p) be the third derivative of 1/60*p**5 + 0 + 0*p**4 - 2*p**2 + 1/60*p**6 + 0*p**3 + v*p + 1/210*p**7. Factor a(l).
l**2*(l + 1)**2
Suppose 2*p + 0*p + 8 = -2*s, 2*p = 5*s + 34. Let h = s + 10. Determine b so that 3*b - 6*b**2 + b**h - 6*b**3 - 5*b - 3*b**4 = 0.
-1, 0
Let w(o) be the second derivative of o**7/3780 - o**6/360 + o**5/90 - 7*o**4/12 - 6*o. Let f(n) be the third derivative of w(n). Find q such that f(q) = 0.
1, 2
Let n be 69/(-2)*6/(-9). Let q = -35 + 58. What is f in 4*f**2 + q + 2*f + 2*f**3 - n = 0?
-1, 0
Let w(x) be the first derivative of x**4/24 + x**3/2 + 9*x**2/4 + 9*x/2 + 7. Factor w(v).
(v + 3)**3/6
Determine s, given that -19 - 14*s - 12*s**3 - 25*s**2 + 0*s + 10 + 8 = 0.
-1, -1/12
Let p(l) be the third derivative of -1/336*l**8 + 0*l**7 + 0*l**3 + 1/60*l**6 + 0*l - 1/24*l**4 + 0 + 0*l**5 - 2*l**2. Find s such that p(s) = 0.
-1, 0, 1
Let o(v) be the third derivative of -1/12*v**3 + 0*v - 3*v**2 + 1/32*v**4 + 0 - 1/240*v**5. Determine q so that o(q) = 0.
1, 2
Let p(z) be the second derivative of -z**10/70560 - z**9/35280 - z**4/4 + 2*z. Let t(v) be the third derivative of p(v). Solve t(m) = 0 for m.
-1, 0
Let r be 63/(-35) - -2*1. Factor 1/5*l**4 - 2/5*l**3 + 2/5*l + 0*l**2 - r.
(l - 1)**3*(l + 1)/