p**2 + 22*p - 14. Let o(t) = 14*f(t) + 5*k(t). Factor o(j).
-2*j*(j - 3)*(j + 1)*(j + 2)
Let x be (8 + (-3384)/420)*(-14)/24. Let q(s) be the third derivative of 0*s + 0*s**3 - x*s**6 + 1/5*s**5 + 0 - 1/3*s**4 - 8*s**2. Find p such that q(p) = 0.
0, 1, 2
Suppose 5*r + 10*r - 11*r = 0. Let v(o) be the first derivative of -3/4*o**4 + 3/5*o**5 - 2*o**3 - 4 + 0*o**2 + r*o. Suppose v(l) = 0. What is l?
-1, 0, 2
Let n(u) = 12*u + 12*u + 37*u**2 + 10*u**3 - 10*u - u. Let v(j) = 5*j**3 + 19*j**2 + 6*j. Let t(d) = 4*n(d) - 7*v(d). Factor t(i).
5*i*(i + 1)*(i + 2)
Let r(s) = s**2 - 379*s + 1872. Let x be r(5). Find w, given that -10*w**x + 0 + 8/3*w**3 - 8/3*w = 0.
-1/4, 0, 4
Let c(k) = -3*k - 24. Let q be c(-7). Let h be 67/12 - q*(-6)/72. Factor 176/3*s + 224*s**2 + 980/3*s**3 + 343/3*s**4 + h.
(s + 2)*(7*s + 2)**3/3
Suppose 5*r = 13 + 2. Suppose -z = -0*z - r. Factor y**3 - 3*y**4 - z*y + 3*y + 2*y**4.
-y**3*(y - 1)
Factor 9*h**2 + 3/4*h**3 + 0 + 0*h.
3*h**2*(h + 12)/4
Let o(t) = 4*t**5 + 8*t**3 + 12*t**2 + 12*t - 12. Let b(q) = -q**3 - q**2 - q + 1. Let u(m) = 12*b(m) + o(m). Factor u(i).
4*i**3*(i - 1)*(i + 1)
Suppose 4*h + 3*v + 24 = 6, -h = 5*v + 13. Let z be 5/20*h*2/(-3). Factor 0*c**2 + 0*c - 1/2*c**4 + 0 + z*c**3.
-c**3*(c - 1)/2
Let n(p) = 4*p**4 - 4*p**3 + 4*p**2 - 6*p + 18. Let j(m) = -12*m**4 + 10*m**3 - 12*m**2 + 17*m - 51. Let w(t) = 6*j(t) + 17*n(t). Factor w(v).
-4*v**2*(v + 1)**2
Let v = -2/8279 + 16564/24837. Let l = 70/3 + -23. Factor 1/3*f**2 + l + v*f.
(f + 1)**2/3
Let i(o) be the second derivative of -o**6/195 - 3*o**5/65 - 3*o - 2. Let i(c) = 0. What is c?
-6, 0
Solve 4/9*i**4 + 8/9*i + 4/9*i**5 - 4/9*i**2 - 4/3*i**3 + 0 = 0.
-2, -1, 0, 1
Suppose 0*f - 8/13*f**2 - 8/13*f**3 + 0 - 2/13*f**4 = 0. What is f?
-2, 0
Let s(j) be the first derivative of -j**6/27 + 4*j**4/9 + 4*j**3/9 - 7*j**2/9 - 4*j/3 + 543. Solve s(a) = 0.
-2, -1, 1, 3
Let x = -531 - -535. Let g(u) be the first derivative of 4/3*u**x + 7 + 32/3*u**2 - 32/3*u - 2/15*u**5 - 16/3*u**3. Find r, given that g(r) = 0.
2
Let b(t) be the second derivative of t**4/90 - 4*t**3/15 + 4*t**2/3 - 126*t. Find l, given that b(l) = 0.
2, 10
Let y(k) = 17*k**2 - 951*k - 56. Let b be y(56). What is j in 5/2*j**3 + 0 + b*j + 5/2*j**2 = 0?
-1, 0
Suppose 0 = -k - 5*i, -10*k + 7*k = 5*i. Factor 4*z**2 - 7*z + k*z + 3*z - z**3.
-z*(z - 2)**2
Let k(w) be the first derivative of -13 + 0*w - 14/9*w**3 + 1/3*w**2. Find r such that k(r) = 0.
0, 1/7
Let d(c) be the second derivative of 5*c**4/12 - 85*c**3/6 + 180*c**2 - 727*c. Factor d(v).
5*(v - 9)*(v - 8)
Let r(x) be the first derivative of -x**5/50 - x**4/30 + x**3/3 - 3*x**2/5 - 16*x + 3. Let d(p) be the first derivative of r(p). What is s in d(s) = 0?
-3, 1
Let n be (-1 + (3 - 2))*1. Let f(k) be the second derivative of 0 - 4*k + 1/10*k**4 + n*k**2 - 1/50*k**5 - 2/15*k**3. Suppose f(t) = 0. What is t?
0, 1, 2
Let d(u) be the second derivative of u**4/18 + u**3 + 6*u**2 - u + 119. Factor d(p).
2*(p + 3)*(p + 6)/3
Let k = 24 + -647/27. Let w(c) be the second derivative of c + k*c**3 + 0 - 1/9*c**2 - 1/90*c**5 + 1/54*c**4. Suppose w(n) = 0. Calculate n.
-1, 1
Let 0*g**4 - 1/6*g**5 + 1/3*g**3 + 0*g**2 - 1/6*g + 0 = 0. What is g?
-1, 0, 1
Let z(b) be the first derivative of -b**6/30 - 9*b**5/80 - b**4/8 - b**3/24 + 2*b - 6. Let n(g) be the first derivative of z(g). Factor n(y).
-y*(y + 1)**2*(4*y + 1)/4
Let r(n) be the second derivative of -3*n**4/2 - 286*n**3/3 + 64*n**2 - 305*n. Solve r(d) = 0 for d.
-32, 2/9
Suppose -6*y = -2*y - 2*y. Suppose y = -2*x + 27 - 7. Factor 8/3*d**4 + 14/3*d + 26/3*d**3 + x*d**2 + 2/3.
2*(d + 1)**3*(4*d + 1)/3
Solve 3775 + 19*b - 4*b**2 + 17*b - 3807 = 0 for b.
1, 8
Let 303/8*y**4 + 21/4*y**5 + 36*y**3 - 129/8*y**2 - 15*y + 9/2 = 0. Calculate y.
-6, -1, 2/7, 1/2
Let r(t) be the first derivative of t + 1/3*t**3 - t**2 + 8. Factor r(s).
(s - 1)**2
Let u(a) be the third derivative of 0*a + 9*a**2 - 1/100*a**6 + 0*a**4 + 1/100*a**5 + 1/350*a**7 + 0*a**3 + 0. What is r in u(r) = 0?
0, 1
Let m(w) be the third derivative of w**7/70 - 2*w**6/45 - 31*w**5/180 - w**4/12 - 2*w**2 - 13. Let m(d) = 0. Calculate d.
-1, -2/9, 0, 3
Let h(n) be the second derivative of -10/9*n**6 - 5/3*n**5 + 8/9*n**3 - 4*n - 16/3*n**2 + 0 + 6*n**4. Suppose h(g) = 0. Calculate g.
-2, -2/5, 2/5, 1
Let a(x) = x**2 + 16*x + 15. Let w(s) = s**2 - 2*s - s + 3*s + s. Let d(z) = -a(z) - 2*w(z). Determine l so that d(l) = 0.
-5, -1
Let h = 31321/72 - 435. Let v(i) be the second derivative of h*i**4 + 0*i**2 + 10*i + 0*i**3 + 0. Factor v(n).
n**2/6
Let p(m) be the third derivative of 1/3*m**3 - 4*m**2 - 1/240*m**6 + 0*m + 0 + 1/24*m**5 - 1/6*m**4. Factor p(z).
-(z - 2)**2*(z - 1)/2
Let h(r) = -2*r**2 + 2*r. Let s(k) = 9*k**2 - 9. Let q(p) = -6*h(p) - s(p). Factor q(m).
3*(m - 3)*(m - 1)
Suppose 6*w + 517 + 221 = 0. Let y = w + 127. Factor -2/5*l**y + 0 + 0*l + 4/5*l**2 - 2/5*l**3.
-2*l**2*(l - 1)*(l + 2)/5
Let p = -19 + 17. Let n be (-3)/(-6) - (p + 2). Factor 3/4*m**2 + n*m**4 - 1/4 - 5/4*m**3 + 1/4*m.
(m - 1)**3*(2*m + 1)/4
Let w = -460 + 76359/166. Let z = 169/498 + w. Solve 0 - 1/3*t**3 + 1/3*t**2 - z*t**4 + 1/3*t = 0.
-1, 0, 1
Let h(f) be the third derivative of -f**6/180 - f**5/30 + f**4/4 - 5*f**3/9 + 5*f**2 - 23*f. Factor h(d).
-2*(d - 1)**2*(d + 5)/3
Let t = 63 - 60. Determine p so that 4*p**2 + 24*p**t + 25*p**3 + 21*p**3 - 74*p**3 = 0.
0, 1
Let g(h) be the first derivative of h**3/7 + 93*h**2/14 - 96*h/7 + 109. Factor g(r).
3*(r - 1)*(r + 32)/7
Let r(u) be the first derivative of -u**6/3 + 8*u**5/5 + u**4/2 - 8*u**3/3 - 84. Find d, given that r(d) = 0.
-1, 0, 1, 4
Let v = -15 - -18. Suppose -v*t = t. Determine m so that 1/2*m**2 + t + 0*m**3 + 1/4*m**5 - 1/4*m - 1/2*m**4 = 0.
-1, 0, 1
Let o(a) = -a**3 + 8*a**2 - 10*a + 1. Let g be o(7). Let f = g + 49. Factor x**2 + 13 + 12 - 3*x - f.
(x - 4)*(x + 1)
Let k be (4/8)/(1/4). Factor -12*c**3 - 2*c**k + 2*c - 3*c**5 - 10*c**4 - 3*c - 4*c**2.
-c*(c + 1)**3*(3*c + 1)
Suppose k + l + 2 = 4*k, 2*k = 4*l - 12. Factor -g**k + 5*g + 2 + 0 - 4*g + 4.
-(g - 3)*(g + 2)
Let p(q) be the second derivative of -q**6/630 + q**4/42 - q**3/3 - 16*q. Let z(h) be the second derivative of p(h). Determine t so that z(t) = 0.
-1, 1
Let r be -2 + 3/((-3)/(-8)). Suppose -3*v + r*v + 0 + 2 + v**2 = 0. What is v?
-2, -1
Let b(x) = 74*x + 890. Let z be b(-12). Factor 50/9 + 2/9*q**z - 20/9*q.
2*(q - 5)**2/9
Suppose 29*o = 37*o - 32. Determine s, given that -234/7*s**o - 80/7*s - 82/7*s**3 + 8/7 + 226/7*s**2 + 162/7*s**5 = 0.
-1, 2/9, 1
Let -2*j**5 + 66 - 120*j**2 - 66 - 74*j**3 - 72*j - 20*j**4 = 0. Calculate j.
-3, -2, 0
Let c be (9/(-12))/(-1) + (-357)/1020. Solve c*d**2 + 0 - 2/5*d = 0.
0, 1
Let h(x) be the second derivative of 1/12*x**6 + 1/4*x**4 + 0 - 3*x + 1/3*x**3 - 3/10*x**5 - x**2. Let q(z) be the first derivative of h(z). Solve q(k) = 0.
-1/5, 1
Suppose -66*q - 24 = -78*q. Let o(h) be the third derivative of 1/60*h**5 + 0*h + 8*h**q - 1/3*h**3 - 1/24*h**4 + 0. Factor o(a).
(a - 2)*(a + 1)
Let j(n) be the second derivative of 0*n**2 + 0*n**3 - 1/20*n**5 - 11*n + 1/20*n**6 + 0 + 5/84*n**7 + 0*n**4. Factor j(h).
h**3*(h + 1)*(5*h - 2)/2
Factor 21/4*q**3 - 30*q**2 + 33*q + 12.
3*(q - 4)*(q - 2)*(7*q + 2)/4
Let c(v) = -10*v**3 + 45*v**2 + 280*v + 305. Let h(s) = -9*s**3 + 47*s**2 + 280*s + 304. Let z(a) = 4*c(a) - 5*h(a). What is j in z(j) = 0?
-2, 15
Let u = -15 + 18. Let a be ((-12)/(-30))/(u/5). Suppose -2/3*i**2 + 4/3*i - a = 0. What is i?
1
Suppose 8*o + 85 = 25*o. Let m(h) be the third derivative of -4/525*h**7 + 0*h + 0 + 1/60*h**6 - h**2 + 0*h**4 - 1/150*h**o + 0*h**3. What is x in m(x) = 0?
0, 1/4, 1
Suppose -l - 14 = -5*c + 9, 3*l + 4*c - 26 = 0. Let w(o) be the third derivative of -1/40*o**6 + 0*o + 0 - 1/4*o**4 + 3/20*o**5 + 4*o**l + 0*o**3. Factor w(y).
-3*y*(y - 2)*(y - 1)
Let n = 10 + -13. Let b = n + 5. Factor 4*l**2 - 2*l**4 + l**4 - 2*l**b - 1.
-(l - 1)**2*(l + 1)**2
Factor 0 + y**3 + 0*y + 1/2*y**4 + 1/2*y**2.
y**2*(y + 1)**2/2
Let x(t) = t**2 - 6*t + 13. Let a be x(5). Factor -6*u**2 + 10 - 24*u**3 + 18*u**4 + a*u - 8 - 2*u**2 + 4*u**2.
2*(u - 1)**2*(3*u + 1)**2
Let i(n) = n**2 - 34*n + 261. Let w be i(11). Let l(c) be the first derivative of 2/7*c**2 - w - 4/7*c - 1/21*c**3. Factor l(a).
-(a - 2)**