ative of -h**6/51 + 6*h**5/85 + 27*h**4/17 - 252*h**3/17 + 891*h**2/17 - 1458*h/17 - 133. Factor y(t).
-2*(t - 3)**4*(t + 9)/17
Let h(w) be the first derivative of 4/9*w**3 + 8/3*w - 2*w**2 - 12. Factor h(o).
4*(o - 2)*(o - 1)/3
Let k(o) = -2*o**2 + o - 7. Let v(r) = 9*r**2 - 3*r + 36. Let s(l) = 24*k(l) + 5*v(l). Factor s(w).
-3*(w - 4)*(w + 1)
Let b(y) be the first derivative of -y**4/6 + 4*y**3/9 - 43. Factor b(d).
-2*d**2*(d - 2)/3
Let x(m) be the third derivative of m**5/30 + 149*m**4/6 + 22201*m**3/3 - 150*m**2. Find a, given that x(a) = 0.
-149
Let p(g) be the third derivative of g**8/2016 - g**7/420 - g**6/720 + g**5/120 - g**2 - 455. What is l in p(l) = 0?
-1, 0, 1, 3
Let b(v) be the second derivative of 3*v**5/50 - 3*v**4/10 - 6*v**3/5 + 24*v**2/5 + 17*v. Factor b(n).
6*(n - 4)*(n - 1)*(n + 2)/5
Let -10*r**2 + 19*r**2 - 6*r + 0*r + 3*r**3 - 12*r**2 = 0. What is r?
-1, 0, 2
Let a(s) be the second derivative of 11*s + 0*s**2 + 0 - 1/24*s**3 - 1/48*s**4. Factor a(x).
-x*(x + 1)/4
Let m = -4863/7 + 695. Factor 2/7*r**2 - m*r + 0.
2*r*(r - 1)/7
Let d = 66113/15 + -13331/3. Let s = -106/3 - d. Factor 2/5*r**4 - 6/5*r**3 + 0 + s*r**2 + 0*r.
2*r**2*(r - 2)*(r - 1)/5
Let l(v) be the second derivative of v**3/2 + 3*v**2 - 10*v. Let o be l(-2). Suppose -1/6 + 1/6*k**2 + o*k = 0. What is k?
-1, 1
Let 3*x**5 + 11*x**2 + 9*x**2 - 3*x**3 - 23*x**2 + 3*x**4 = 0. What is x?
-1, 0, 1
Let m = -17 - -5. Let w be -4 + (-52)/m - (-2 + 2). Suppose w*z + 1/3*z**2 + 0 = 0. Calculate z.
-1, 0
Let h(q) be the third derivative of -q**8/168 + 4*q**7/105 - q**6/20 + 22*q**2 + 3. Factor h(g).
-2*g**3*(g - 3)*(g - 1)
Let d be (-8)/14 + 352/616. Let s(t) be the third derivative of -13/12*t**4 + 7*t**2 + d + 2/3*t**3 + 11/30*t**5 + 0*t. Factor s(y).
2*(y - 1)*(11*y - 2)
Suppose 83*y + 0*y - 260 = -47*y. Determine q, given that -1/4*q**y - 16 - 4*q = 0.
-8
Let m(i) be the first derivative of -i**4/12 + 2*i**3/3 - 4*i**2/3 - 438. Factor m(q).
-q*(q - 4)*(q - 2)/3
Let s(m) = -m - 14. Let r be s(-2). Let x(b) = -b**2 - 16*b - 45. Let u be x(r). Determine f so that 1/3*f**5 + 1/3 - f - f**4 + 2/3*f**u + 2/3*f**2 = 0.
-1, 1
Let k(i) be the first derivative of i**7/2940 - i**6/252 + i**5/140 + 3*i**4/28 - 2*i**3 - 12. Let l(a) be the third derivative of k(a). Factor l(o).
2*(o - 3)**2*(o + 1)/7
Let w(g) = -23*g + 84. Let i be w(11). Let z = 171 + i. Factor 0 - 4*y**3 - 8/5*y**z + 0*y - 16/5*y**4 - 4/5*y**5.
-4*y**2*(y + 1)**2*(y + 2)/5
Let z(v) = v**4 - 7*v**2 - 8*v - 2. Let a be -2*7/6 - 5/(-15). Let j(s) = -15*s**4 + 111*s**2 + 129*s + 33. Let c(p) = a*j(p) - 33*z(p). Factor c(n).
-3*n*(n - 2)*(n + 1)**2
Let c(h) be the third derivative of h**6/240 - h**5/120 - 5*h**4/24 - 2*h**3/3 - 15*h**2 + 5. Factor c(b).
(b - 4)*(b + 1)*(b + 2)/2
Let h(a) be the second derivative of -a**5/140 - 7*a**4/12 - 575*a**3/42 + 625*a**2/14 - 140*a. Factor h(t).
-(t - 1)*(t + 25)**2/7
Determine y so that -479*y + 2764*y**2 + 13*y**4 - 624*y - 1201*y + 188*y**3 - 652*y**2 - 9*y**4 = 0.
-24, 0, 1
Let j(g) be the second derivative of -g**7/70 + g**5/20 + g**2 - 11*g. Let w(t) be the first derivative of j(t). Solve w(s) = 0.
-1, 0, 1
Let w(x) be the third derivative of -x**8/560 - x**7/70 - 3*x**6/100 - 45*x**2 - x. Factor w(n).
-3*n**3*(n + 2)*(n + 3)/5
Let m(x) be the third derivative of -x**6/960 - x**5/160 - x**4/64 + 5*x**3/3 + 7*x**2. Let i(t) be the first derivative of m(t). Find v such that i(v) = 0.
-1
Suppose 0 = -o - 2*y - 2, 0 = -4*y + 2*y - 4. Determine x so that 3/7*x**o + 0 - 3/7*x**3 + 0*x = 0.
0, 1
Let o(d) = 6*d**4 - 10*d**3 + 12*d**2 + 2. Let h(f) = 25*f**4 - 39*f**3 + 50*f**2 + 9. Let b(m) = 2*h(m) - 9*o(m). Solve b(l) = 0 for l.
0, 1, 2
Let a(j) be the first derivative of -j**4/14 - 2*j**3/21 + 10*j**2/7 - 16*j/7 + 83. Suppose a(q) = 0. What is q?
-4, 1, 2
Let b = -2/6281 + 37696/31405. Factor 2/5*y**4 - 19/5*y - 4*y**2 - 6/5 - b*y**3 + 1/5*y**5.
(y - 3)*(y + 1)**3*(y + 2)/5
Factor -184/7*c**2 - 48/7*c**3 - 100/7 - 240/7*c - 4/7*c**4.
-4*(c + 1)**2*(c + 5)**2/7
Let d be 24/(-20)*225/(-27). Let j(g) be the third derivative of 1/50*g**5 + 0*g - 1/200*g**6 + 0 - 1/40*g**4 - d*g**2 + 0*g**3. Factor j(u).
-3*u*(u - 1)**2/5
Let n be 2 + (2 - (-1599)/(-15)). Let h = -102 - n. Factor 0 + h*y + 3/5*y**2.
3*y*(y + 1)/5
Let g be (7/(-56))/(15/(-40)). Let v(w) be the first derivative of 0*w - 2 + 0*w**2 - 4/5*w**5 - 2*w**4 + 16/3*w**3 + g*w**6. Factor v(z).
2*z**2*(z - 2)**2*(z + 2)
Let z = -145 - -148. Let d(h) = -h**3 + 5*h**2 - h - 13. Let m be d(z). Factor 1/3*o**m + o**3 + 0*o + 0.
o**2*(3*o + 1)/3
Let o be -1 + (11/(-3))/(3/(-18)). Let u = o + -17. Factor -2/7*x + 2/7*x**5 - 4/7*x**u + 4/7*x**2 + 0 + 0*x**3.
2*x*(x - 1)**3*(x + 1)/7
Let b = 290 - 286. Let t(f) be the second derivative of 4*f**2 + f + 0 + 5/6*f**b - 1/10*f**5 - 8/3*f**3. Suppose t(v) = 0. What is v?
1, 2
Suppose 5*q = -4*f + 21, f - 5*q - 5 = -6*q. Let g = 3 + 0. Factor 3*m**f - m**4 + 23*m**3 - 21*m**g.
2*m**3*(m + 1)
Suppose -303*u - 38*u + 1044 = -80*u. Determine q, given that 98/11*q**u - 16/11*q - 156/11*q**3 + 8*q**2 - 20/11*q**5 + 0 = 0.
0, 2/5, 1/2, 2
Suppose 32 = 2*p - 3*z, -p + 32 = p + 5*z. Suppose p = 6*x - 20. Solve -3/2*g + 0 + 3/2*g**3 - 6*g**4 + x*g**2 = 0 for g.
-1, 0, 1/4, 1
Let a(g) be the third derivative of -11*g**5/50 - 167*g**4/60 - 2*g**3/3 + 429*g**2 + 1. Factor a(o).
-2*(o + 5)*(33*o + 2)/5
Let x be (-123)/(-30) + (-2)/(-5). Let m = 1358 + -1354. Determine y, given that 0 - 3/2*y - 9/2*y**2 - x*y**3 - 3/2*y**m = 0.
-1, 0
Let p be 5*(12/14 - 25/(-175)). Let j(u) be the first derivative of 1/30*u**4 - 6 + 0*u**2 + 0*u**3 + 0*u - 1/45*u**6 + 0*u**p. Factor j(i).
-2*i**3*(i - 1)*(i + 1)/15
Let g(a) be the second derivative of -3*a**5/20 + 3*a**4 - 18*a**3 + a + 39. Suppose g(t) = 0. What is t?
0, 6
Suppose l - 2*s + 3*s + 8 = 0, 2*l - 4*s + 16 = 0. Let o be l/48 + (-38)/(-12). Factor 20*i**3 + 55*i**o - 48*i - 8*i**2 + 12 + 23*i**2.
3*(i + 1)*(5*i - 2)**2
Let b(h) = 14*h**4 + 244*h**3 + 248*h**2 - 252*h - 254. Let o(a) = -9*a**4 - 163*a**3 - 165*a**2 + 168*a + 169. Let f(m) = 5*b(m) + 8*o(m). Factor f(g).
-2*(g - 1)*(g + 1)**2*(g + 41)
Let s be 2*5/(-35) - (-132)/21. Factor 2*h**2 + s*h**2 - 5*h**3 - 10*h + 7*h**2.
-5*h*(h - 2)*(h - 1)
Suppose -909*s = -897*s. Solve 0*n + 4/5*n**2 - 6/5*n**3 + s*n**4 + 2/5*n**5 + 0 = 0 for n.
-2, 0, 1
Let d(l) = 2*l**2 - 150*l + 703. Let x be d(5). Factor -4/3*g + 0 - 8/3*g**x - 6*g**2.
-2*g*(g + 2)*(4*g + 1)/3
Let g(x) be the second derivative of 4/5*x**6 + 31*x + 0*x**2 + 2/21*x**7 + 0 + 0*x**3 + 0*x**4 + x**5. Factor g(c).
4*c**3*(c + 1)*(c + 5)
What is c in -10*c**5 - 2*c**5 + 12*c**3 - 54 - 58*c**4 + 66*c**2 + 19*c**4 + 27 = 0?
-3, -1, 3/4, 1
Let m(p) = p**5 + p**4 - p**3 + p**2 - 1. Let h(r) = -5*r**5 + 2*r**4 - 8*r**3 + 6*r**2 - 3*r + 4. Let f(c) = h(c) + 4*m(c). Suppose f(k) = 0. Calculate k.
0, 1, 3
Let x be (-18)/(-30) + (-4)/(-10). Let m = x - -5. Factor -4*j**4 - m*j**2 + 7*j**2 - j**5 + 3*j**4 + j**3.
-j**2*(j - 1)*(j + 1)**2
Let o(i) be the second derivative of 13*i + 0*i**2 + 1/4*i**5 + 5/4*i**4 + 0 + 0*i**3. Factor o(w).
5*w**2*(w + 3)
Let c be 4*3/(-54)*110/(-101). Let i = c + -2/101. Factor -i*s**3 + 0 - 2/3*s**2 - 4/9*s.
-2*s*(s + 1)*(s + 2)/9
Let h(g) be the first derivative of -g**4/6 + 4*g**3/3 - 3*g**2 + 8*g/3 + 92. Suppose h(u) = 0. Calculate u.
1, 4
Suppose 8*r = 75 - 51. Let v(c) be the first derivative of 1/24*c**4 - 8 - 1/6*c**r - 1/6*c + 1/4*c**2. Solve v(o) = 0.
1
Suppose -3*u = -17 + 5. Let b be 2/7 - 114/(-532). Suppose -q**3 - b + 0*q**2 + q + 1/2*q**u = 0. What is q?
-1, 1
Suppose -30 = -3*t - 6. Let l be 1/6*(11 - t). Solve 1/4 - 1/4*s**5 + 1/4*s**4 + 1/2*s**3 - 1/4*s - l*s**2 = 0.
-1, 1
Let k = 7022 + -7018. Determine n, given that 4/3*n**k - 4/3 - 2/3*n**5 + 14/3*n + 4/3*n**3 - 16/3*n**2 = 0.
-2, 1
Let m(s) = 6*s**4 - 42*s**3 - 3*s**2 - 3*s + 6. Let z(n) = -n**4 - 2*n**3 + n**2 + n - 2. Let w(d) = -m(d) - 3*z(d). Suppose w(f) = 0. Calculate f.
0, 16
Let g = -1206 + 3619/3. Factor 1 - g*w**3 - w**2 + 1/3*w.
-(w - 1)*(w + 1)*(w + 3)/3
Let l(k) = -22*k**2 + 140*k - 490. Let r(a) = 196 + 11*a**2 - 68*a + 2*a**2 + 12*a - 4*a**2. Let c(p) = 5*l(p) + 12*r(p). Suppose c(f) = 0. What is f?
7
Let c be (-8)/36 - (-16)/(-36)*-5. Su