 9)
Let q(y) be the first derivative of -2*y**3/27 - 13*y**2/9 - 8*y/3 - 200. Factor q(t).
-2*(t + 1)*(t + 12)/9
Let v(k) be the first derivative of k**4/14 - 52*k**3/21 + 169*k**2/7 + 131. Factor v(n).
2*n*(n - 13)**2/7
Let b(n) be the second derivative of -n**6/30 + n**5/20 + 4*n**4/3 + 10*n**3/3 - 11*n - 8. Suppose b(k) = 0. What is k?
-2, 0, 5
Let c be (-11)/((-55)/(-3)) - (-28)/40. Let u(h) be the second derivative of 0 + 1/5*h**3 - h + 1/50*h**5 + c*h**4 + 1/5*h**2. Suppose u(l) = 0. Calculate l.
-1
Let a(f) be the first derivative of -f**4/2 - 2*f**3 - 3*f**2 - 2*f + 113. Solve a(c) = 0.
-1
Let v(b) be the second derivative of -b**5/130 - 5*b**4/78 + 19*b**3/13 - 99*b**2/13 + 271*b. Find i such that v(i) = 0.
-11, 3
Let k(c) be the second derivative of c**4/84 - c**3/6 + 3*c**2/7 - 2*c - 23. Factor k(q).
(q - 6)*(q - 1)/7
Determine r, given that 4/3*r + 0 + 2/3*r**2 = 0.
-2, 0
Let i(n) be the first derivative of 2*n**6/27 - 4*n**5/3 + 3*n**4 - 52*n**3/27 + 43. Solve i(c) = 0.
0, 1, 13
What is j in -5*j**2 - 172*j**3 + 47*j**3 - 2659 + 125*j + 5*j**4 + 2659 = 0?
-1, 0, 1, 25
Let o(x) be the second derivative of -1/80*x**5 + 0 - 5*x + 1/48*x**4 + 0*x**2 - 1/120*x**6 + 1/24*x**3. Factor o(m).
-m*(m - 1)*(m + 1)**2/4
Let i = 75 + -43. Factor -i + 8*w**3 + w**4 - 21*w**2 - 11*w**2 + 25*w**4 + 2*w**5 - 64*w - 16*w**4.
2*(w - 2)*(w + 1)*(w + 2)**3
Let u(z) = -8*z**3 + 21*z**2 + 6*z + 4. Let x(v) = -5 - 10*v - 2 + 17*v**3 - 2*v - 237*v**2 + 195*v**2. Let a(m) = 7*u(m) + 4*x(m). Suppose a(w) = 0. What is w?
-1/4, 0, 2
Let h(l) = 4*l**2 - 11*l - 10. Let s be h(-1). Suppose 3*n + 4*a = 18, n - 2*n = s*a - 17. Factor n*g**3 + 2/7*g**4 + 16/7*g**2 - 32/7*g + 0.
2*g*(g - 1)*(g + 4)**2/7
Let r(c) = -15*c - 64 - 92 + 2*c**3 + 28 + 35*c**2 + 116*c. Let i(t) = t**2 + t. Let b(d) = 10*i(d) - 2*r(d). Factor b(q).
-4*(q - 1)*(q + 8)**2
Let s(t) = t + 5. Let d be s(-3). Let y(h) = -3 - 1 + 2*h**d - 3*h + 2 - h**2. Let o(f) = f + 1. Let g(i) = -2*o(i) - y(i). Factor g(u).
-u*(u - 1)
Let u(p) be the third derivative of -3/5*p**3 + 2/15*p**4 + 1/150*p**5 + p**2 + 0*p - 7. Factor u(n).
2*(n - 1)*(n + 9)/5
Suppose -5*q + c + 4*c = 15, -3 = -q - c. Suppose p + 5*p - 18 = q. Factor -2/3*m**p + 2*m**2 + 0 - 4/3*m.
-2*m*(m - 2)*(m - 1)/3
Let b(s) be the second derivative of s**4/72 - s**3/18 - 9*s - 4. Find d, given that b(d) = 0.
0, 2
Suppose -5 = y + 3*l - 24, -3*y - 5*l = -37. Let a(c) be the first derivative of 0*c + 0*c**2 + 3/4*c**y - 10 + 4*c**3. Factor a(s).
3*s**2*(s + 4)
Let h(i) be the second derivative of 17*i + 0*i**3 + 0*i**2 + 0 + 1/180*i**5 + 1/54*i**4. Suppose h(j) = 0. What is j?
-2, 0
Let j(a) be the second derivative of 2*a**7/21 + 62*a**6/5 + 2114*a**5/5 - 2302*a**4/3 - 1410*a**3 + 4418*a**2 - 98*a. Solve j(n) = 0 for n.
-47, -1, 1
Let h(a) be the second derivative of 1/5*a**2 + 1/15*a**3 - 1/50*a**5 + 0 + 9*a - 1/30*a**4. Factor h(c).
-2*(c - 1)*(c + 1)**2/5
Let g(m) be the first derivative of -1/42*m**4 + 2/21*m**3 + 0*m - 2 - 2/21*m**2. Factor g(f).
-2*f*(f - 2)*(f - 1)/21
Let w be 68/306 + 2/(-9). Let i(r) be the second derivative of -r + w - 1/48*r**4 - 1/4*r**2 + 1/8*r**3. Factor i(c).
-(c - 2)*(c - 1)/4
Suppose 380 = 26*w - 22*w. Let n = -281/3 + w. Determine c so that -4/3 - n*c - 1/3*c**2 = 0.
-2
Let q(v) = -4*v**2 - 169*v - 1442. Let t(n) = n**2 + n + 3. Let c(r) = q(r) - t(r). What is o in c(o) = 0?
-17
Let s(q) = q**3 + 20*q**2 - 5*q - 18. Let t(g) = 2*g - 1. Let f(x) = 3*s(x) + 6*t(x). Suppose f(n) = 0. What is n?
-20, -1, 1
Let n be 4/(-10) + 18*13/10. Find b, given that -20 + 50*b**2 - n*b**2 - 23*b**2 + 4 - 12*b = 0.
-1, 4
Let p(f) be the third derivative of -f**7/5040 + f**6/1080 + 3*f**3 - 12*f**2. Let w(b) be the first derivative of p(b). Suppose w(i) = 0. Calculate i.
0, 2
Let u(s) = -54*s**3 - 29*s**2 + 107*s + 15. Let m(p) = -9*p**3 - 5*p**2 + 18*p + 2. Let q(j) = 39*m(j) - 6*u(j). Suppose q(y) = 0. What is y?
-2, 2/9, 1
Let q(z) be the third derivative of 0 + 0*z - 1/3*z**4 + 1/15*z**5 - 2*z**3 - 3*z**2. Factor q(y).
4*(y - 3)*(y + 1)
Suppose -5*u - g + 13 = -2*u, -5*g = -4*u + 11. Suppose 1 = u*h - b - 9, -16 = -2*h - 5*b. Suppose 0 + 1/2*v - 1/2*v**h - v**4 + v**2 = 0. Calculate v.
-1, -1/2, 0, 1
Let s(b) = b**2 + 6*b + 8. Suppose m - 4*m - 2 = -2*d, 0 = 2*d - 5*m - 6. Let z be s(d). Factor 0 + z*h + 2/15*h**2 - 2/15*h**3.
-2*h**2*(h - 1)/15
Let x = 7006/7651 - 64/1093. Factor 1/7*k**2 + x + k.
(k + 1)*(k + 6)/7
Let a(o) be the third derivative of -1/255*o**7 - 1/1428*o**8 - 5/204*o**4 + 2*o + 0 + 16*o**2 - 2/17*o**3 + 1/30*o**5 + 1/340*o**6. Let a(z) = 0. Calculate z.
-3, -2, -1/2, 1
Factor 0 + 2/3*l**2 - 2/3*l**5 + 0*l + 2/3*l**3 - 2/3*l**4.
-2*l**2*(l - 1)*(l + 1)**2/3
Let q(g) be the third derivative of -2*g**7/35 - 3*g**6/8 - 3*g**5/5 + g**4/2 + 71*g**2 - 2*g. Factor q(x).
-3*x*(x + 2)**2*(4*x - 1)
Suppose 2/9*k**3 - 14/9*k**2 + 0 + 4/3*k = 0. Calculate k.
0, 1, 6
Let p(j) be the third derivative of -j**9/10080 - j**8/6720 + 2*j**5/15 - 15*j**2. Let l(x) be the third derivative of p(x). Factor l(g).
-3*g**2*(2*g + 1)
Let l(d) = -d**3 + 12*d**2 + 3. Let y be l(12). Factor 22*w**2 + w**y - 23*w**2 - w**5 + w**4 + 0*w**3.
-w**2*(w - 1)**2*(w + 1)
Let w(d) be the second derivative of -1/600*d**6 + 3*d + 0*d**5 + 0 + 1/2*d**2 + 1/40*d**4 + 1/15*d**3. Let g(x) be the first derivative of w(x). Factor g(s).
-(s - 2)*(s + 1)**2/5
Let k(r) = 2*r**5 + 0*r**5 - r**4 - r**5 + 3 - 2. Let z(j) = -2 + j**3 + 13*j**2 - 5*j**5 - 12*j**2 - 3*j**4 - 2*j**3. Let s(y) = 2*k(y) + z(y). Factor s(n).
-n**2*(n + 1)**2*(3*n - 1)
Find z, given that 842*z - 115*z**2 - 11*z**4 - 812*z + 80*z**3 - 4*z**4 = 0.
0, 1/3, 2, 3
Suppose -i + 11 = 2. Suppose -m + i = -4*m. Let h(u) = -u**4 + 2*u**3 + 6*u + 1. Let r(p) = -p**4 + p**3 + 5*p + 1. Let f(c) = m*h(c) + 4*r(c). Solve f(g) = 0.
-1, 1
Suppose 3*m - h - 1 = 0, 43*m - 2*h = 47*m + 2. Let y(s) be the second derivative of 0*s**2 + m - 1/4*s**4 + 5*s + 1/2*s**3. Factor y(o).
-3*o*(o - 1)
Let a(r) be the second derivative of 23*r**4/12 - 25*r**3/6 + r**2 + 39*r. Factor a(g).
(g - 1)*(23*g - 2)
Solve -4/7 + 0*w**4 + 4/7*w**2 + 6/7*w + 2/7*w**5 - 8/7*w**3 = 0.
-2, -1, 1
Find j, given that 24/11*j - 54/11 - 2/11*j**2 = 0.
3, 9
Let 1 - 3/2*i**3 + 3/2*i - 1/2*i**2 - 1/2*i**4 = 0. Calculate i.
-2, -1, 1
Let x be -8*-7*7/1568. Let 0 - 1/8*b**3 - x*b**2 - 1/8*b = 0. What is b?
-1, 0
Let u(j) be the first derivative of j**6/24 + j**5/4 + 5*j**4/8 + 5*j**3/6 + 7*j**2 + 1. Let b(t) be the second derivative of u(t). Factor b(k).
5*(k + 1)**3
Let n(r) be the first derivative of -17/2*r**2 - 12*r - 5/3*r**3 + 4. Let s(b) = -5*b**2 - 18*b - 13. Let y(h) = 3*n(h) - 2*s(h). Determine z so that y(z) = 0.
-2, -1
Let c(y) be the first derivative of y**6/21 + 8*y**5/35 + 3*y**4/14 - 8*y**3/21 - 4*y**2/7 + 58. Find g such that c(g) = 0.
-2, -1, 0, 1
Let g(y) be the third derivative of -y**10/151200 + y**8/10080 - y**6/720 - y**5/6 + 5*y**2. Let r(f) be the third derivative of g(f). Factor r(m).
-(m - 1)**2*(m + 1)**2
Let l(r) be the first derivative of 2/3*r**3 + 5*r**2 - r**4 + 6 + 4*r. Solve l(d) = 0.
-1, -1/2, 2
Factor -26*t**2 + 6561 + 162*t + 6*t**2 + 21*t**2.
(t + 81)**2
Let s = -199 - -189. Let u be 1 + ((-1175)/s)/5. Factor -21*f - 9/2 - u*f**2.
-(7*f + 3)**2/2
Let k(b) be the third derivative of 0*b - b**2 - 3*b**3 + 7/8*b**4 - 1/20*b**5 + 0. Factor k(u).
-3*(u - 6)*(u - 1)
Let w(k) be the third derivative of -k**8/560 - 2*k**7/175 + 3*k**6/200 + 7*k**5/50 + k**4/5 + 3*k**2 - 2*k. Determine q so that w(q) = 0.
-4, -1, 0, 2
Let b be (((-40)/225)/2)/(2/(-5)). Let c(n) be the second derivative of b*n**4 + 1/20*n**5 + 7/18*n**3 + 5*n + 0 + 1/3*n**2. Factor c(m).
(m + 1)**2*(3*m + 2)/3
Suppose 4 + 10 = 2*a. Suppose 4*d = -5*w - 17, -3*w + 24 = 2*d - a*w. Determine h, given that 0 + 1/5*h + 2/5*h**d = 0.
-1/2, 0
Let o = 2873 - 1624. Find u such that -u**3 - o + 2*u**4 + u - u**4 - 3*u**2 + 1251 = 0.
-1, 1, 2
Let q(m) be the third derivative of m**6/180 + 8*m**5/45 + 16*m**4/9 - 33*m**2. Factor q(y).
2*y*(y + 8)**2/3
Let t(h) be the first derivative of h**6/30 - h**5/10 + h**3/3 - h**2/2 + 2*h + 25. Let z(x) be the first derivative of t(x). Factor z(o).
(o - 1)**3*(o + 1)
Factor 4/3*i + 1/6*i**2 - 65/6.
(i - 5)*(i + 1