3/3 - 41*s**2. Find h, given that r(h) = 0.
-2, -1, 1
Let m = -10839 - -75882/7. Find w such that -m + 9/7*w**2 - 3/7*w + 3/7*w**3 = 0.
-3, -1, 1
Let c be (0/3)/4 + 27. Let x = -51/2 + c. Factor -x*w**3 + 3/2*w**2 + 0 + 0*w.
-3*w**2*(w - 1)/2
Suppose -15 = -42*f + 39*f. Let g(q) be the third derivative of 3*q**2 + 0*q + 1/20*q**f + 3/4*q**4 + 0 + 9/2*q**3. Factor g(v).
3*(v + 3)**2
Let f(s) = -153*s - 5045. Let h be f(-33). Factor 2*b**2 - 38/3*b + h.
2*(b - 6)*(3*b - 1)/3
Let z = 213 + -213. Let d(n) be the second derivative of -1/3*n**2 + 0 + z*n**3 + 1/18*n**4 - 3*n. Solve d(s) = 0.
-1, 1
Let -4/5*q**2 + 4/5*q**4 + 1/5*q**5 - 3/5*q + 2/5*q**3 + 0 = 0. Calculate q.
-3, -1, 0, 1
Determine k, given that -k**5 + 522*k**2 - k**5 + 18*k**3 - 24 - 16*k - 496*k**2 - 2*k**4 = 0.
-2, -1, 1, 3
Suppose 7 = 6*i - 5. Let z(a) be the third derivative of 0 + 0*a - 7*a**i + 32/3*a**3 + 1/15*a**5 - 4/3*a**4. Let z(b) = 0. What is b?
4
Let r(z) be the first derivative of 5/12*z**4 - 5/2*z**2 + 10 + 0*z**3 + 10/3*z. Determine o, given that r(o) = 0.
-2, 1
Let b(r) be the third derivative of r**6/30 + 16*r**5/15 - 17*r**4/6 - 37*r**2 - r. Factor b(d).
4*d*(d - 1)*(d + 17)
Let h be (-18)/(-14) - (29 - 29). Factor 6/7 + h*d - 6/7*d**2.
-3*(d - 2)*(2*d + 1)/7
Suppose 3*q = 2*g + 7*q - 40, -3*q = -5*g + 100. Let u = 22 - g. Factor -8*a**3 + 9*a**3 - a + a**u - 2*a**2 + 1.
(a - 1)**2*(a + 1)
Let k(y) be the first derivative of 1/3*y**3 + 1/6*y**4 - 5*y + 2 - 2*y**2. Let v(n) be the first derivative of k(n). Factor v(x).
2*(x - 1)*(x + 2)
Let h(o) be the first derivative of o**6/360 + o**5/40 + o**4/12 + 2*o**3/3 + 5. Let t(d) be the third derivative of h(d). Factor t(k).
(k + 1)*(k + 2)
Let f(q) be the second derivative of 8*q - 1/10*q**5 + 2 + 0*q**4 + q**3 + 2*q**2. Factor f(p).
-2*(p - 2)*(p + 1)**2
Let n be -2 - (-1)/(-7)*-13. Let i = n + 10/21. Factor 0 + i*z**3 + 0*z**2 + 0*z.
z**3/3
Factor 13 + 4*u**2 + 19 - 26*u + 25 - 17 - 18*u.
4*(u - 10)*(u - 1)
Let i be (-748)/6120 - 1*2/(-9). Let q(r) be the third derivative of -1/40*r**6 + 0*r + 2*r**2 + 0*r**4 + 0*r**3 + 0 - i*r**5. Find j such that q(j) = 0.
-2, 0
Let a(i) be the first derivative of 2*i**3/33 - 194*i**2/11 + 18818*i/11 + 134. Factor a(u).
2*(u - 97)**2/11
Let l(q) be the third derivative of -1/672*q**8 - 1/48*q**6 - 9*q**2 + 1/60*q**5 + 0*q**4 + 0 + 1/105*q**7 + 0*q + 0*q**3. Let l(u) = 0. Calculate u.
0, 1, 2
Suppose f - h + 2*h = 5, 0 = -4*h + 12. Factor -21*k**2 + k**4 + 4*k**4 - 5*k**3 + 5*k + 16*k**f.
5*k*(k - 1)**2*(k + 1)
Let h(z) be the first derivative of 1/3*z**3 + 21 + 0*z + 1/2*z**2. Solve h(d) = 0 for d.
-1, 0
Let w(g) be the first derivative of 2/65*g**5 + 1/39*g**6 - 6/13*g + 4/39*g**3 + 3 + 5/13*g**2 - 3/13*g**4. Let w(j) = 0. What is j?
-3, -1, 1
Let z be (-18)/(-15)*((-5)/(-15) - 0). Factor 0 + z*k**2 + 2/5*k.
2*k*(k + 1)/5
Let n(j) = -8*j**3 + 4*j**2 + 14*j + 2. Let g(d) = -d - 1. Let x be (2 + -2 - -1) + 0. Let o be (-14 + 40/8)/((-6)/4). Let r(q) = o*g(q) + x*n(q). Factor r(u).
-4*(u - 1)*(u + 1)*(2*u - 1)
Let j = -2600 - -13002/5. Factor 0 - 2/5*z - j*z**2.
-2*z*(z + 1)/5
Let b(l) be the first derivative of l**6/180 - l**5/30 - 19*l**3/3 - 26. Let y(x) be the third derivative of b(x). Factor y(z).
2*z*(z - 2)
Let 4/3*f**4 + 32/3 + 62/3*f - 62/3*f**3 - 12*f**2 = 0. What is f?
-1, -1/2, 1, 16
Let q(j) be the third derivative of -j**5/12 - 25*j**4/24 + 125*j**3/3 - 202*j**2. Solve q(z) = 0.
-10, 5
Factor -55*w**3 - 30*w**2 + 30*w**2 + 14*w**4 - 20*w + w**4 + 60*w**2.
5*w*(w - 2)*(w - 1)*(3*w - 2)
Let x(h) = -65*h - 455. Let y be x(-7). Let f(m) be the first derivative of y*m**2 + 0*m - 3 - 2/3*m**3. Factor f(g).
-2*g**2
Let p be (25/(25/(-6)))/(-2 - (3 - 3)). Factor -4/9*l**4 + 4/3*l**2 + 4/9*l**p + 8/9 - 20/9*l.
-4*(l - 1)**3*(l + 2)/9
Let i = 1753 - 8763/5. Factor i - 4/15*h - 2/15*h**2.
-2*(h - 1)*(h + 3)/15
Let c(t) be the first derivative of -t**4/7 + 8*t**3/21 - 2*t**2/7 - 650. Factor c(o).
-4*o*(o - 1)**2/7
Let i = -891 + 891. Let n(a) be the first derivative of -1/20*a**4 + 0*a + i*a**2 - 5 + 1/15*a**3. Solve n(u) = 0 for u.
0, 1
Let m be (12 + 0)/(-3 + 4). Let n = 14 - m. Factor -r + 2*r**3 - 3*r**2 + 3*r + 7*r**n.
2*r*(r + 1)**2
Let q(t) = -t + 7. Let d be q(6). Let s be 5/25*d*15. Factor -5 + 8 - 9*w**4 - s*w**5 - 3.
-3*w**4*(w + 3)
Let m = -7 + 17. Suppose 3*v - 8 = m. Suppose -v*c**2 + 3 + c**2 - c**2 + 3*c**2 = 0. Calculate c.
-1, 1
Let a(r) be the second derivative of 0 + 0*r**2 - 5/8*r**4 - 1/28*r**7 + 9/40*r**5 + 1/2*r**3 + 7*r + 1/20*r**6. Factor a(c).
-3*c*(c - 1)**3*(c + 2)/2
Solve 0 - 7/2*h + 2*h**2 = 0 for h.
0, 7/4
Let d be 1 + 61/(-105) + (-4)/14. Let v(u) be the second derivative of -1/5*u**2 + 0 + 6*u + d*u**3 - 1/30*u**4. Factor v(o).
-2*(o - 1)**2/5
Let l be (25 + 0)*(4 - -1) + 3. Let v = -1404/11 + l. What is q in v*q**2 - 2/11*q**4 + 0*q**3 - 2/11 + 0*q = 0?
-1, 1
Let t(a) be the second derivative of -a**4/72 - 91*a**3/36 - 15*a**2/2 + 527*a. Determine p so that t(p) = 0.
-90, -1
Let f(h) be the first derivative of -h**4/8 - h**3/2 + 2*h - 47. Factor f(y).
-(y - 1)*(y + 2)**2/2
Let s(d) = -3*d - 13. Let v(r) = r + 4. Let u(f) = -4*s(f) - 11*v(f). Let g be u(-8). Factor c**2 + 0*c**2 + 3 - 1 + g*c**2 + 3*c.
(c + 1)*(c + 2)
Let b(c) = -7*c**3 - 74*c**2 + 148*c - 73. Let l(i) = -76*i**3 - 812*i**2 + 1628*i - 804. Let o(a) = -32*b(a) + 3*l(a). Factor o(r).
-4*(r - 1)**2*(r + 19)
Let j(h) be the second derivative of -3*h**5/20 + 93*h**4/4 - 1104*h**3 + 3174*h**2 + 235*h + 2. Factor j(p).
-3*(p - 46)**2*(p - 1)
Let a(t) be the second derivative of -t**4/3 - 4*t**3 - 18*t**2 - 19*t. Suppose a(g) = 0. Calculate g.
-3
Factor 273/5*d**2 + 1215 - 3/5*d**3 - 1269*d.
-3*(d - 45)**2*(d - 1)/5
Let r = 1814 - 12697/7. Let s(x) be the first derivative of 3/14*x**2 + r*x**3 + 3 + 0*x. Factor s(b).
3*b*(b + 1)/7
Suppose 0 + x**4 + 5/4*x**3 + 1/2*x**2 + 1/4*x**5 + 0*x = 0. Calculate x.
-2, -1, 0
Find x, given that 32*x**4 - 64/5*x**5 - 4/5*x**3 - 8/5 + 68/5*x - 152/5*x**2 = 0.
-1, 1/4, 1, 2
Let g be -2 - 514/(-176) - 501/1336. Factor 0*h**3 - 6/11 + 0*h + 12/11*h**2 - g*h**4.
-6*(h - 1)**2*(h + 1)**2/11
Let a(p) be the first derivative of -p**4/4 - 8*p**3/3 - 5*p**2/2 + 14*p + 56. Factor a(n).
-(n - 1)*(n + 2)*(n + 7)
Let c(k) = 4*k**2 + 2192*k + 2111. Let w(v) = v**2 + 437*v + 422. Let r(z) = 2*c(z) - 11*w(z). Suppose r(j) = 0. Calculate j.
-140, -1
Let k = -23 + 20. Let f be -1*(-10)/25 - k/(-120). Factor -3/8*p - f*p**2 + 3/4.
-3*(p - 1)*(p + 2)/8
Let i be (2 + -2)*(-5)/30. Let f(h) be the second derivative of -1/14*h**2 + 2*h + i + 1/42*h**3 + 1/84*h**4 - 1/140*h**5. Suppose f(w) = 0. Calculate w.
-1, 1
Let h(n) be the third derivative of -n**6/30 + n**5/15 + n**4/3 - 54*n**2. Find a, given that h(a) = 0.
-1, 0, 2
Let f(n) be the first derivative of n**7/140 + 11*n**6/90 + n**5/12 - 7*n**4/6 + n**3/3 - 15. Let u(t) be the third derivative of f(t). Solve u(j) = 0.
-7, -1, 2/3
Suppose 41*m = 126 + 38. Let j(c) be the second derivative of 0 + 5*c + 0*c**m + 0*c**5 + 0*c**2 + 2/15*c**6 + 2/21*c**7 + 0*c**3. Factor j(z).
4*z**4*(z + 1)
Solve 337/2*k**2 - 21/2*k**3 + 34 + 168*k = 0.
-2/3, -2/7, 17
Let h(f) = f**2 - 58*f + 672. Let u be h(16). Factor 0*p + 1/2*p**3 + 1/4*p**4 + 0*p**2 + u - 1/4*p**5.
-p**3*(p - 2)*(p + 1)/4
Let w be -2*25*8/96*-3. Let o(p) be the first derivative of -7 + 20/3*p**3 - 5/4*p**4 + 10*p - w*p**2. Solve o(f) = 0.
1, 2
Let q be (-1 - (-22)/10)*65/26. Let o(d) be the third derivative of 0*d**q - 1/75*d**5 - 1/40*d**4 - 1/600*d**6 + 0 + 0*d + 10*d**2. Let o(x) = 0. Calculate x.
-3, -1, 0
Let i be ((-10)/(-18))/((-560)/(-1344)). Factor -1/3*x**5 + 4*x**2 - 13/3*x**3 + 0 - i*x + 2*x**4.
-x*(x - 2)**2*(x - 1)**2/3
Factor -32/3 - 8/3*k + 4/3*k**2.
4*(k - 4)*(k + 2)/3
Find k, given that 116*k**3 - 220*k**3 - 2*k**5 + 4*k**4 + 110*k**3 = 0.
-1, 0, 3
Factor 1/3*l**2 - 16/3 + 2*l.
(l - 2)*(l + 8)/3
Let n(f) be the third derivative of f**5/20 - 39*f**4/4 + 1521*f**3/2 - 2*f**2 - 273. Find g, given that n(g) = 0.
39
Let u(i) = 7*i**2 + 336*i - 343. Let s be u(-49). Solve s - 3/4*j**2 + 0*j = 0.
0
Let z = -54 + 48. Let a(x) = -x**4 - x**2 - 1. Let q(h) = 5*h**4 + h**3 + 7*h**2 - h + 6. Let b(w) = z*a(w) - q(w). Suppose b(o) = 0. Calculate o.
-1, 0, 1
Let s