ative of -r**4/8 - 206*r + 1. Factor w(p).
-3*p**2/2
Let s be 406/(-6) + (4/(-2) - -1). Let o = 2284/33 + s. Determine z so that o*z**3 - 2/11*z**4 + 2/11*z + 0 - 6/11*z**2 = 0.
0, 1
Suppose 0 = 7*m - 11*m + 52. Determine q so that -m + 13 + 2*q**2 + 8*q**5 - 8*q**3 - 2*q**4 = 0.
-1, 0, 1/4, 1
Let t(a) be the second derivative of 2*a - 1/28*a**4 + 0 - 3/7*a**2 - 3/14*a**3. What is h in t(h) = 0?
-2, -1
Suppose -56*x + 222*x = 498. Factor 1/4*l**x + 0 + 1/4*l**2 - 1/2*l.
l*(l - 1)*(l + 2)/4
Let j(u) = -u**2 - 1. Let q = 33 - 43. Let v(c) = 5*c**2 + 0*c**3 - 2*c**3 + 4*c + 6*c**3 + 13*c**2 + 10. Let s(f) = q*j(f) - v(f). Factor s(y).
-4*y*(y + 1)**2
Let x = 98 + -97. Let l be x*(-14)/4*8/(-14). Factor -3/2*o + 1/4*o**l + 9/4.
(o - 3)**2/4
Let w be 1269/(-564) + (-45)/(-20). Factor -1/7*p**4 + w*p**2 + 0*p + 0 - 3/7*p**3.
-p**3*(p + 3)/7
Let y be 2 - (-5 + 0) - 4. Find u, given that u**2 + 20*u - 6*u**2 - 39*u**3 + 20 + 34*u**y = 0.
-2, -1, 2
Suppose -p - 29 = -6. Let s = -14 - p. Factor -3*y**2 + 3*y + 3*y**5 - s*y**3 + 3*y**4 + 3*y + 0*y**5.
3*y*(y - 1)**2*(y + 1)*(y + 2)
Factor 4/7*c**3 + 12*c + 40/7 + 48/7*c**2.
4*(c + 1)**2*(c + 10)/7
Let m(x) be the first derivative of x**5/120 + x**4/48 + x**2/2 + 15. Let a(b) be the second derivative of m(b). Factor a(d).
d*(d + 1)/2
Let j(z) be the third derivative of -z**6/320 + 17*z**5/160 + 9*z**4/32 + 282*z**2. Determine n so that j(n) = 0.
-1, 0, 18
Find g such that 42/5 + 33/5*g**2 + 237/5*g = 0.
-7, -2/11
Factor 0*w + 0 - 3/5*w**3 + 3*w**2.
-3*w**2*(w - 5)/5
Suppose 17/5*a**2 - 19/5*a + 2/5 = 0. Calculate a.
2/17, 1
Let d(g) = g**3 + 3*g**2. Let m be d(-3). Suppose -4 = -2*u - m. Solve 0*z**3 - 5*z**3 + 5*z**3 - z**u - z**3 = 0 for z.
-1, 0
Let r(j) be the first derivative of j**6/135 - j**5/270 - 4*j**4/27 + 4*j**3/27 - 35*j**2/2 + 5. Let s(l) be the second derivative of r(l). Solve s(z) = 0.
-2, 1/4, 2
Let g(t) be the third derivative of t**5/240 + 35*t**4/96 + 35*t**2 - 3*t. Solve g(r) = 0.
-35, 0
Let b be (-1)/((-24)/16)*(-4)/(-8). Let o(t) be the first derivative of -1 + 0*t**2 - b*t**3 + 0*t + 1/8*t**4. Factor o(d).
d**2*(d - 2)/2
Let w(p) = -6*p**3 - 13*p**2 + 28*p - 7. Let s(v) = -v**3 + v**2 + 2*v - 1. Let q(z) = 6*s(z) - 3*w(z). Factor q(r).
3*(r - 1)*(r + 5)*(4*r - 1)
Let l(m) be the second derivative of -m**8/13440 + m**7/2016 - m**6/720 + m**5/480 - 4*m**4/3 + 12*m. Let u(j) be the third derivative of l(j). Factor u(y).
-(y - 1)**2*(2*y - 1)/4
Let p(c) = -4*c**2 + c + 3. Let g(r) = r**2 + 1. Let m(u) = -3*g(u) - p(u). Let q(i) = 5. Let v(z) = 5*m(z) + 6*q(z). Factor v(x).
5*x*(x - 1)
Let t be 9/(-15) + 1028/(-20). Let k = -48 - t. Suppose 2/7*d + 0 + 48/7*d**k + 18/7*d**5 + 44/7*d**3 + 16/7*d**2 = 0. What is d?
-1, -1/3, 0
Suppose -28/9*u - 16/3 + 2/9*u**3 + 2/9*u**2 = 0. What is u?
-3, -2, 4
Let x = -21 - -21. Suppose 27*v**2 - 3*v + x*v + 2 - 26*v**2 = 0. What is v?
1, 2
Suppose -37*f = -83 - 65. Factor -2/5*r**3 + 4/5*r + 3/5*r**2 - 4/5 - 1/5*r**f.
-(r - 1)**2*(r + 2)**2/5
Let w be ((-66)/45)/(-11) + 7/(-45). Let s = 1/5 - w. Suppose 2/9*j**4 + 2/9*j**3 - s*j**2 + 0*j - 2/9*j**5 + 0 = 0. What is j?
-1, 0, 1
Let f(c) be the second derivative of c**8/5040 - c**7/630 + c**6/360 - 4*c**3 + 13*c. Let n(r) be the second derivative of f(r). Factor n(a).
a**2*(a - 3)*(a - 1)/3
Let b be (-8)/((-240)/(-310)) - -11. Factor -b + 2/3*h**3 - 2/3*h + 2/3*h**2.
2*(h - 1)*(h + 1)**2/3
Let h = 3025/8 + -378. Let p(y) be the first derivative of -h*y**2 - 1 - 1/2*y + 1/12*y**3. Determine k, given that p(k) = 0.
-1, 2
Let a(t) be the first derivative of -t**7/63 + 2*t**6/45 - t**5/30 + t - 24. Let h(y) be the first derivative of a(y). Find b, given that h(b) = 0.
0, 1
Solve -4*i**3 + i**4 - 2 + 1/2*i**5 + i**2 + 7/2*i = 0.
-4, -1, 1
Let t(f) = 2*f**3 - 22*f**2 + 4. Let r be t(11). Let n(v) be the second derivative of 1/2*v**2 + 0 + 1/12*v**3 - 1/24*v**r - 7*v. Suppose n(b) = 0. What is b?
-1, 2
Let o(y) be the third derivative of 0 - 1/40*y**4 + 28*y**2 + 1/100*y**5 + 0*y + 0*y**3. Factor o(m).
3*m*(m - 1)/5
Let v(q) be the first derivative of -q**5/15 + q**4/4 - q**3/3 + q**2/6 - 72. Factor v(l).
-l*(l - 1)**3/3
Let h(k) = -k**3 - 1. Let v(d) = 5*d**3 - 96*d**2 + 768*d + 2. Let b(o) = -2*h(o) - v(o). Factor b(q).
-3*q*(q - 16)**2
Suppose -2/5*s**2 + 24 + 34/5*s = 0. What is s?
-3, 20
Let q = -272 + 274. Let a be q/3*(21 - 15). Factor 1/2 + 1/4*h**3 - 1/4*h - 3/4*h**2 + 1/4*h**a.
(h - 1)**2*(h + 1)*(h + 2)/4
Let i be (-8)/20*5 + (-38)/(-9). Let o(h) be the first derivative of 26/15*h**5 + 8/9*h**3 - 7 + i*h**4 + 0*h**2 + 0*h + 1/3*h**6. Find x, given that o(x) = 0.
-3, -2/3, 0
Let y be (-24 - (-2840)/120)/((-1)/2). Solve -10/9*i - 8/9 + 10/9*i**3 + 2/9*i**4 + y*i**2 = 0 for i.
-4, -1, 1
Let -180 + c**3 + 4*c**3 - 105*c**2 - 54*c + 84*c + 250*c = 0. Calculate c.
1, 2, 18
Let 111/7*q**3 + 60/7*q + 0 + 177/7*q**2 - 6/7*q**4 = 0. Calculate q.
-1, -1/2, 0, 20
Let v be (3 - 11) + (-8 - -16). Let o(s) be the third derivative of -6*s**2 + 0 + 2/45*s**5 + 0*s - 1/36*s**4 + v*s**3. Factor o(i).
2*i*(4*i - 1)/3
Let k be (-1)/3 + (52/104)/((-18)/(-44)). Factor k*v**2 + 0 + 2/9*v**3 + 2/3*v.
2*v*(v + 1)*(v + 3)/9
Let x(h) be the first derivative of h**5/105 + 2*h**4/21 + 2*h**3/7 + 2*h**2 + 6. Let i(v) be the second derivative of x(v). Determine t, given that i(t) = 0.
-3, -1
Let y(l) = -l**2 - 67*l - 191. Let s be y(-3). Let h(t) be the first derivative of -1/12*t**6 - 2/3*t**3 + 0*t**4 - s + 0*t**2 + 3/10*t**5 + 0*t. Factor h(n).
-n**2*(n - 2)**2*(n + 1)/2
Factor -647*n**2 - 647*n**2 + 1936*n**2 - 21675 + 510*n - 645*n**2.
-3*(n - 85)**2
Let u(h) = h**3 + 9*h**2 + 10*h + 19. Let c be u(-8). Let 2*q**2 - 3*q**2 + 6*q + 4 - c*q + 0*q**2 = 0. Calculate q.
-1, 4
Let q(a) = 365*a - 360. Let g(k) = -k**2 - k + 1. Let h(f) = 5*g(f) + q(f). Solve h(i) = 0.
1, 71
Let i be (-148)/(-222) - (0 + (-2)/(-3)). Factor 4/15*w + 2/15*w**2 + i.
2*w*(w + 2)/15
Determine q so that 1/2*q**2 - 9*q + 16 = 0.
2, 16
Let n(u) be the first derivative of -u**3/3 - 5*u**2/2 + 4. Let h be n(-4). Factor 2*q**5 - 3*q**2 + 4*q**3 + 6*q**h + 3*q**2.
2*q**3*(q + 1)*(q + 2)
Let k(z) be the second derivative of -z**6/90 + z**4/2 + 16*z**3/9 + 5*z**2/2 + 83*z. Let k(d) = 0. Calculate d.
-3, -1, 5
Let n(s) be the third derivative of s**8/560 - s**7/350 - s**6/200 + s**5/100 - 68*s**2. Factor n(i).
3*i**2*(i - 1)**2*(i + 1)/5
Let j(t) be the second derivative of -t**6/2 + 171*t**5/20 - 11*t**4/2 + 4*t + 2. Factor j(v).
-3*v**2*(v - 11)*(5*v - 2)
Let y = 130 - 128. Let c(k) = 7*k**5 - 17*k**4 + 3*k**3 + 15*k**2 - 8*k. Let x(s) = s**5 - s**4 - s**3 + s. Let i(v) = y*x(v) - c(v). Solve i(b) = 0 for b.
-1, 0, 1, 2
Let k(i) be the second derivative of -i**5/30 - 7*i**4/9 - 8*i**3/3 - 27*i + 3. Factor k(q).
-2*q*(q + 2)*(q + 12)/3
Let k be 68 + (-30)/25*-5. Let m = k - 71. Suppose -t - 1/2*t**4 + 5/2*t**2 - 3/2*t**m + 0 + 1/2*t**5 = 0. Calculate t.
-2, 0, 1
Let t(k) be the first derivative of -5*k**3/3 - 25*k**2 - 105*k - 144. Determine h, given that t(h) = 0.
-7, -3
Let t(l) be the first derivative of -4/15*l**3 - 7 + 0*l**2 + 1/25*l**6 + 0*l**4 + 7/50*l**5 - 11*l. Let y(s) be the first derivative of t(s). Solve y(p) = 0.
-2, -1, 0, 2/3
Let m(x) = -30*x**3 - 54*x**2 + 4*x - 14. Let o(a) = -6*a**3 - 11*a**2 + a - 3. Let c be -6 + 2 + 1 + 0. Let s(y) = c*m(y) + 14*o(y). Let s(p) = 0. What is p?
-1, -1/3, 0
Let s(z) be the third derivative of -z**7/105 - 17*z**6/60 - 31*z**5/30 - 5*z**4/4 - 43*z**2 - 2. Factor s(g).
-2*g*(g + 1)**2*(g + 15)
Let h be 2 - (-2)/(796/260 + -3). Let w = -34 + h. Find j such that -3/2*j**2 + 0*j**3 + 0 - j + w*j**4 = 0.
-1, 0, 2
Let g = 249 + -247. Let f be (g/(-8))/(29/(-435)). Factor 0*i**2 + 0 + 3/2*i**5 - 9/4*i**3 + f*i**4 + 0*i.
3*i**3*(i + 3)*(2*i - 1)/4
Suppose -3*r - 3*c = -51, 4*r - 49 = 3*c + 5. Solve 20 - 5*i**3 - r*i**3 + 0*i**3 + 85*i**2 - 80*i - 5*i**3 = 0 for i.
2/5, 1, 2
Let h(k) be the second derivative of -1/180*k**5 - 1/18*k**2 + 0 + 42*k - 1/18*k**3 - 1/36*k**4. Suppose h(l) = 0. What is l?
-1
Let f = 64 - 59. Suppose -q - 5 = -3*i - 0*q, -4*i - f*q = 25. Factor -4/5*m + i + 2/5*m**2.
2*m*(m - 2)/5
Factor 3*r**5 - 1941*r**2 + 4427*r**2 + 768*r - 1910*r**2 + 12*r**3 - 36*r**4.
3*r*(r - 8)**2*(r + 2)**2
Let 2/7