rivative of i**8/4200 - i**6/450 + i**4/60 + i**3 + 3*i. Let q(u) be the second derivative of v(u). Factor q(o).
2*(o - 1)**2*(o + 1)**2/5
Let z(d) be the first derivative of -d**5/20 + d**4/8 + d**2 + 4. Let f(k) be the second derivative of z(k). Find q, given that f(q) = 0.
0, 1
Let q(c) be the first derivative of c**8/4200 + c**7/700 + c**6/300 + c**5/300 - c**3 + 1. Let m(z) be the third derivative of q(z). What is s in m(s) = 0?
-1, 0
Let x(f) be the second derivative of -f**4/84 - 4*f**3/21 + 9*f**2/14 - 4*f. Factor x(w).
-(w - 1)*(w + 9)/7
Let x be 3 + 0 + 2/2. Suppose -3*w + d + 10 = -0*d, -x*d - 20 = -2*w. Factor 0 + 1/3*r + 1/3*r**w.
r*(r + 1)/3
Let p(v) be the third derivative of v**10/75600 - v**9/30240 - v**8/5040 + 7*v**5/60 + 3*v**2. Let m(w) be the third derivative of p(w). Factor m(z).
2*z**2*(z - 2)*(z + 1)
Suppose 11 + 49 = -4*k. Let a be 10/k - (-7)/3. Find d such that 2/3*d**4 + 10/3*d**3 + 2/3 - 4/3*d**2 - 5/3*d**5 - a*d = 0.
-1, 2/5, 1
Let y(w) be the second derivative of w**7/28 + w**6/20 - 3*w**5/20 - w**4/4 + w**3/4 + 3*w**2/4 - w. Factor y(d).
3*(d - 1)**2*(d + 1)**3/2
Let l(s) be the third derivative of s**6/600 + s**5/300 - 34*s**2. Find w, given that l(w) = 0.
-1, 0
Suppose 2*k + 23 = -5. Let a = 5 - k. Factor -a + 19 - 2*o**2.
-2*o**2
Let q be 10 - (-2 - 3/(-1)). What is y in -7 + y**2 + q - 1 + 2*y = 0?
-1
Let i(b) be the second derivative of 0*b**2 - 1/20*b**5 + 6*b + 1/6*b**4 + 0*b**3 + 0. Factor i(r).
-r**2*(r - 2)
Let q(z) be the first derivative of -2*z**5/45 - z**4/18 + 2*z**3/27 + z**2/9 - 7. Suppose q(u) = 0. What is u?
-1, 0, 1
Let d be 55/25 - (-2)/(-10). Factor 8/5*o**d + 4/5*o - 4/5*o**3 - 8/5.
-4*(o - 2)*(o - 1)*(o + 1)/5
Suppose -23 = -2*r + r. What is x in 39 + 4*x**2 - r - 10*x - 6*x = 0?
2
Let m(s) = -s**2 + 6*s - 5. Let z be m(5). Factor l**2 + z*l**4 + 7*l**2 - 8*l**3 + 2*l**4 + 0*l**4.
2*l**2*(l - 2)**2
Let b(f) be the second derivative of f**7/48 + 37*f**6/240 + 73*f**5/160 + 67*f**4/96 + 7*f**3/12 + f**2/4 - 31*f. Factor b(r).
(r + 1)**3*(r + 2)*(7*r + 2)/8
Let d(m) be the first derivative of 0*m**2 + 1/3*m**6 - 2/3*m**3 + 0*m - 6/5*m**5 + 3/2*m**4 - 3. Let d(w) = 0. What is w?
0, 1
Let h(p) be the first derivative of 1/12*p**3 - 1/16*p**4 + 6 + 0*p + 0*p**2. Suppose h(g) = 0. What is g?
0, 1
Let k = 0 - 1. Let m = k - -1. Determine n so that 0 - 4/7*n**4 + 2/7*n**5 - 2/7*n + m*n**3 + 4/7*n**2 = 0.
-1, 0, 1
Let b(u) = 24*u**3 + 40*u**2 + 22*u + 2. Let k(p) = 48*p**3 + 80*p**2 + 44*p + 3. Let a(d) = -5*b(d) + 2*k(d). Factor a(x).
-2*(2*x + 1)**2*(3*x + 2)
Let k(a) be the second derivative of -a**5 + 2*a**4/3 + 10*a**3/3 - 4*a**2 + 8*a. Determine m so that k(m) = 0.
-1, 2/5, 1
Let f(t) = -t**2 + 4*t - 2. Let c(j) = j - 1. Let d(q) = 2*c(q) - f(q). Find o such that d(o) = 0.
0, 2
Let w(r) = r**4 + r**2. Let c(n) = -12*n**4 + 18*n**3 - 16*n**2 + 2*n. Suppose -5*u + 6 - 1 = 0. Let s(p) = u*c(p) + 4*w(p). What is k in s(k) = 0?
0, 1/4, 1
Let t = -66 - -66. Factor 0*h**2 + 0*h**4 + 2/11*h**5 + 0*h - 2/11*h**3 + t.
2*h**3*(h - 1)*(h + 1)/11
Let s = -2/553 - -1116/2765. Factor 2/5*b**2 - s*b - 4/5.
2*(b - 2)*(b + 1)/5
Suppose 4*u = 3*m - 5, 0 = -2*u + 7*u - 5. Let n be (-6)/(-8) + (-3)/6. Suppose 0*b**2 - 1/4*b**4 - n*b**m + 0*b + 0 = 0. What is b?
-1, 0
Let x(j) be the second derivative of 0*j**3 + 0 - 1/42*j**4 + 2*j + 0*j**2 + 1/70*j**5. Factor x(h).
2*h**2*(h - 1)/7
Let v(x) be the third derivative of -x**5/60 - x**4/8 - x**3/3 + 32*x**2. Determine s so that v(s) = 0.
-2, -1
Let c(t) = 2 + t**3 - 2*t**2 - 5*t**3 + 3*t**3. Let z be c(-2). What is l in l - l + z*l**4 - 2*l**3 = 0?
0, 1
Let x(j) be the first derivative of 5*j**6/33 + 26*j**5/55 - j**4/22 - 34*j**3/33 - 4*j**2/11 + 8*j/11 + 33. Let x(w) = 0. What is w?
-2, -1, 2/5, 1
Let c(s) be the third derivative of s**6/600 + s**5/300 - s**4/24 + s**3/10 + 23*s**2 - 2. Factor c(i).
(i - 1)**2*(i + 3)/5
Let h(n) be the second derivative of n**6/75 + n**5/50 - n**4/10 - n**3/3 - 2*n**2/5 + 5*n. Factor h(a).
2*(a - 2)*(a + 1)**3/5
Let b be -2 + 9 + -2 + 0. Let g be (b/(-10))/(2/(-12)). Factor -16*u**2 + 0*u**3 - 2*u**g + 16*u**2 - 2*u**4.
-2*u**3*(u + 1)
Let v(g) be the second derivative of -g**6/15 - 3*g**5/10 - g**4/2 - g**3/3 + 56*g. Factor v(p).
-2*p*(p + 1)**3
Let i be 1*2 + 185/(-10). Let t = i - -17. Suppose -t*w**3 - 3/2*w + 1/2 + 3/2*w**2 = 0. Calculate w.
1
Suppose 15 = 2*h - 7*h. Let o be h/9 - (-20)/6. Factor -4*i**3 - o*i + 2*i**3 - 3*i**4 - 8*i**2 - i**2 - 7*i**3.
-3*i*(i + 1)**3
Factor 0*m**3 + 0*m + 1/5*m**4 + 0 - 1/5*m**2.
m**2*(m - 1)*(m + 1)/5
Let v(w) be the first derivative of 3*w**4/16 + 5*w**3/6 + 9*w**2/8 + w/2 - 6. Factor v(r).
(r + 1)*(r + 2)*(3*r + 1)/4
Determine o so that -4*o**2 - 3*o - o + o - o = 0.
-1, 0
Let s(k) = -k**2 - 10*k - 9. Let p be s(-8). Let x(b) = -b**2 + 9*b - 4. Let i be x(p). Solve -6*h - 7*h**2 + 4*h - h**3 + i*h**3 = 0 for h.
-2/9, 0, 1
Factor -3/4*s**3 + 3/4*s**2 + 0 - 3/4*s**4 + 3/4*s.
-3*s*(s - 1)*(s + 1)**2/4
Factor -1/7*h**5 - 1/7*h + 0*h**2 + 0*h**4 + 2/7*h**3 + 0.
-h*(h - 1)**2*(h + 1)**2/7
Let z(w) be the second derivative of -w**6/75 - 7*w**5/50 + w**4/30 + 7*w**3/15 + 41*w. Factor z(q).
-2*q*(q - 1)*(q + 1)*(q + 7)/5
Let w(c) be the third derivative of -c**6/60 + c**5/16 - c**4/16 - 2*c**3/3 - 2*c**2. Let t(y) be the first derivative of w(y). Factor t(p).
-3*(p - 1)*(4*p - 1)/2
Factor -8 + 983*g**4 + 4*g**3 - 21*g + 5*g - 981*g**4 - 6*g**2.
2*(g - 2)*(g + 1)**2*(g + 2)
Let u = -1 + 3. Let n be (-8)/9*21/(-28). Factor -1/3*b**u - 1/3 - n*b.
-(b + 1)**2/3
Let r(y) be the second derivative of 4*y**4/9 + 4*y**3/3 + 3*y**2/2 + 33*y. Let r(h) = 0. Calculate h.
-3/4
Suppose 0 = 4*u + u - 3*f - 120, -2*u + 48 = -3*f. Let d be (4/(-9))/(u/(-108)). Find w, given that 0*w - 1/4*w**5 + 1/4*w**d + 3/4*w**4 - 3/4*w**3 + 0 = 0.
0, 1
Let n(x) = x**2 + 8*x - 12. Let j be n(-9). Let u = 0 - j. Let 3/4 - 3/2*t**u - 3/4*t**4 + 3/2*t + 0*t**2 = 0. What is t?
-1, 1
Let b(c) be the first derivative of -c**6/240 - c**5/80 + c**4/8 - 2*c**3/3 - 4. Let u(z) be the third derivative of b(z). Factor u(m).
-3*(m - 1)*(m + 2)/2
Let y(t) = 4*t**3 - 2*t - 2. Let s(o) = -9*o**3 + 4*o + 5. Suppose -5*b = -2*l + 6*l, -1 = -3*l - 4*b. Let i(r) = l*y(r) - 2*s(r). Factor i(f).
-2*f*(f - 1)*(f + 1)
Let r(c) be the first derivative of 3*c**4/20 + c**3 + 12*c**2/5 + 12*c/5 + 15. Suppose r(g) = 0. Calculate g.
-2, -1
Let b(i) be the second derivative of i**5/90 + 5*i. Factor b(n).
2*n**3/9
Let o(q) be the third derivative of 2*q**2 - 1/840*q**7 + 1/48*q**4 + 1/24*q**3 + 0 + 0*q**5 + 0*q - 1/240*q**6. What is w in o(w) = 0?
-1, 1
Suppose -w + 0 = -4. Let y(h) be the third derivative of 7/108*h**w - h**2 + 0*h + 1/180*h**6 - 2/27*h**3 - 4/135*h**5 + 0. Factor y(d).
2*(d - 1)**2*(3*d - 2)/9
Let o = -359/5 + 72. Factor 2/5*l**4 - 1/5*l**2 + o*l**3 + 0*l + 0.
l**2*(l + 1)*(2*l - 1)/5
Factor 0 - 2*x**4 - 22*x**3 - x**2 + 0 + 25*x**3.
-x**2*(x - 1)*(2*x - 1)
Find z, given that z + 252*z**2 - z - 251*z**2 - 1 = 0.
-1, 1
Factor 22*o**3 - o**2 - 26*o**3 + 3*o**2.
-2*o**2*(2*o - 1)
Let b be (16/20)/((-4)/50). Let l = 21/2 + b. Determine v so that 1/2 - 1/2*v**2 - 1/2*v + l*v**3 = 0.
-1, 1
Let w be (-7)/(-9)*(4/14 - 0). Determine a, given that 0 + 2/9*a - w*a**2 - 2/9*a**3 + 2/9*a**4 = 0.
-1, 0, 1
Let p be (-45)/(-84) + 6/(-21). Factor 0*g**2 + p*g**4 - 1/4 + 1/2*g**3 - 1/2*g.
(g - 1)*(g + 1)**3/4
Let h(b) be the third derivative of b**7/42 - b**6/24 - b**5/12 + 5*b**4/24 + b**2 - 2*b. Factor h(q).
5*q*(q - 1)**2*(q + 1)
Let w = -41 + 43. Solve 2/5 + 32/5*f**w - 16/5*f = 0 for f.
1/4
Let v(b) be the second derivative of b**7/28 - b**6/20 - 3*b**5/40 + b**4/8 - 2*b. Factor v(a).
3*a**2*(a - 1)**2*(a + 1)/2
Let r(j) be the first derivative of -4*j**3/3 - 2*j**2 + 24*j + 14. Factor r(q).
-4*(q - 2)*(q + 3)
Factor -11*d**3 + d**4 - 4*d**3 - 24*d**2 - 17*d**4 - 4*d - 21*d**3.
-4*d*(d + 1)**2*(4*d + 1)
Let a(b) be the second derivative of -b**5/20 - b**4/8 + 2*b**2 - 9*b. Let c(k) be the first derivative of a(k). Factor c(u).
-3*u*(u + 1)
Let b(k) = -10*k**3 + 2*k**2. Let c(x) = x**3. Suppose -2*m + s - 4 = -6*m, 20 = 5*s. Suppose -2*g + m = -2. Let d(w) = g*b(w) + 4*c(w). Solve d(u) = 0.
0, 1/3
Suppose -1/3 + 2*p**2 + 5/3*p = 0. What is p?
-1, 