**3 + 7*r**2. Let s(x) = 5*x**3 + 17*x**2. Let v(c) = -4*c**3 - 18*c**2. Let g(k) = -5*s(k) - 4*v(k). Let u(p) = 11*b(p) + 6*g(p). Factor u(n).
n**2*(n - 1)
Let t(y) be the second derivative of -y**4/3 - 2*y**3 - 10*y. Factor t(w).
-4*w*(w + 3)
Let o be (16/136)/(24/102). Let -o*b + 3/4*b**2 - 1/4*b**3 + 0 = 0. What is b?
0, 1, 2
Let r = -59 + 60. Find f such that r + 7/4*f**2 + 4*f = 0.
-2, -2/7
Let j = -1/145 + 6/29. Let d(i) be the first derivative of -1 + 0*i**4 - 1/4*i**2 - j*i**5 + 1/12*i**6 + 0*i + 1/3*i**3. Factor d(o).
o*(o - 1)**3*(o + 1)/2
Let i(q) = q**3 - 2*q**2 + 11*q - 7. Let h(f) = f**2 + 16*f + 2 - 15*f + 2 - 5. Suppose 5*w = 44 - 14. Let o(p) = w*h(p) - 2*i(p). Factor o(y).
-2*(y - 2)**2*(y - 1)
Factor -2*c**5 + 10*c**2 - 8*c**4 + 2 - 3*c**5 + 4*c**3 + c - 4.
-(c - 1)*(c + 1)**3*(5*c - 2)
Suppose 0 = -2*c + 4 + 4. Find z, given that 12*z**3 - c*z**2 - 2*z - 2*z**2 + z**2 = 0.
-1/4, 0, 2/3
Let i(b) be the third derivative of b**5/100 - 3*b**4/40 + b**3/5 - 20*b**2. Factor i(z).
3*(z - 2)*(z - 1)/5
Let n(p) = -3*p**3 - 3*p**2 + 7*p - 5. Let x(f) = -2*f**3 - 3*f**2 + 6*f - 4. Let l(h) = h - 2. Let o be l(5). Let d(y) = o*n(y) - 4*x(y). Factor d(s).
-(s - 1)**3
Let k be (1485/105 + -15)/((-2)/7). Factor -20/3*h**4 - 40/3*h**k - 20/3*h - 4/3*h**5 - 4/3 - 40/3*h**2.
-4*(h + 1)**5/3
Let o be ((-40)/(-12))/((-16)/(-12)). Factor x**3 + 0*x**2 + 3/2*x**5 + o*x**4 + 0*x + 0.
x**3*(x + 1)*(3*x + 2)/2
Let m(b) be the second derivative of 3*b**5/20 + b**4/2 - b**3 - 8*b. Let h(n) = -3*n**3 - 5*n**2 + 5*n. Let r(j) = 6*h(j) + 5*m(j). Factor r(k).
-3*k**3
Let s be (5 + -4)*(0 - 4). Let c be ((-12)/(-20))/((-6)/s). Factor 1/5*m**2 + 3/5*m + c.
(m + 1)*(m + 2)/5
Let n = 4 + -1. Solve -n*t + 0*t**2 + 3*t**2 - t**3 + t = 0.
0, 1, 2
Let i(m) be the third derivative of m**8/2800 - m**7/1400 - 2*m**3/3 + 5*m**2. Let b(s) be the first derivative of i(s). Determine y so that b(y) = 0.
0, 1
Let i = -119/15 - -2233/30. Let n = -63 + i. Solve -u**2 + 0 + 11/2*u**3 + 0*u - 8*u**4 + n*u**5 = 0 for u.
0, 2/7, 1
Let o(d) be the second derivative of d**9/52920 - d**8/11760 - d**7/8820 + d**6/1260 + d**4/3 - 5*d. Let y(c) be the third derivative of o(c). Factor y(t).
2*t*(t - 2)*(t - 1)*(t + 1)/7
Let l = 71/35 - 163/119. Let v = 2/255 + l. Solve -2/9*m**2 + 0 - v*m**4 - 2/9*m**5 + 0*m - 2/3*m**3 = 0 for m.
-1, 0
Let c(v) be the first derivative of v**5/30 + v**2/2 - v - 2. Let x(i) be the first derivative of c(i). Let d(s) be the first derivative of x(s). Factor d(j).
2*j**2
Let p(b) be the second derivative of -b**9/12096 + b**8/3360 - b**6/720 + b**5/480 - 2*b**3/3 + 4*b. Let t(v) be the second derivative of p(v). Factor t(w).
-w*(w - 1)**3*(w + 1)/4
Let r(g) be the first derivative of 3/5*g**5 + 1 + 3/4*g**4 - 1/2*g**6 - g**3 + 0*g + 0*g**2. Factor r(i).
-3*i**2*(i - 1)**2*(i + 1)
Let i = 1 + 2. Let r = -4 + i. Let b(x) = x**3 + x**2 + x + 1. Let o(y) = y**3 + y + 2. Let n(c) = r*o(c) + 2*b(c). Suppose n(w) = 0. What is w?
-1, 0
Let y(n) be the first derivative of -n**6/27 - 2*n**5/9 - n**4/2 - 14*n**3/27 - 2*n**2/9 + 6. Factor y(d).
-2*d*(d + 1)**3*(d + 2)/9
Let m be ((-6)/(-5))/((-66)/(-40)). Let i = -2/33 + m. Determine h so that -i*h**3 + 2*h**2 + 2/3 - 2*h = 0.
1
Let w = 0 + 2. Let o(y) be the first derivative of 0*y + 3/4*y**4 + y**5 + 1 + 0*y**w - 2/3*y**3. Factor o(h).
h**2*(h + 1)*(5*h - 2)
Let r(p) be the first derivative of 1/3*p**2 + 1/2*p**4 + 0*p + 1 + 2/15*p**5 + 2/3*p**3. Factor r(t).
2*t*(t + 1)**3/3
Determine l, given that 0 - 2/9*l**3 + 0*l**2 + 0*l + 2/9*l**4 = 0.
0, 1
Let h(n) be the first derivative of n**4/3 - 16*n**3/9 + 10*n**2/3 - 8*n/3 + 22. What is i in h(i) = 0?
1, 2
Let j(w) be the third derivative of 0*w**4 + 1/168*w**8 + 0*w**7 + 0*w + 0*w**3 + 0 - 1/15*w**5 - 1/20*w**6 - 4*w**2. Factor j(o).
2*o**2*(o - 2)*(o + 1)**2
Suppose 2*q - 1 = 5*a - 0*q, 8 = 2*a - 5*q. Let h be 5 - a - (-10)/(-5). Determine z, given that 6*z**2 + h*z + 0*z + 0 - 2 = 0.
-1, 1/3
Let d(a) be the second derivative of -a**7/168 + a**6/40 - a**5/40 - a**4/24 + a**3/8 - a**2/8 + 3*a. Find y such that d(y) = 0.
-1, 1
Let l(v) be the third derivative of -v**2 - 1/40*v**6 + 0 - 1/20*v**5 + 0*v + 1/8*v**4 + 1/2*v**3. Determine k, given that l(k) = 0.
-1, 1
Factor -40/7*r - 4*r**2 - 16/7 - 6/7*r**3.
-2*(r + 2)**2*(3*r + 2)/7
Let u be 23/7 + (-14)/49. Factor 10*m + 4 + 12*m**2 + 2*m + m**u + 3*m**3.
4*(m + 1)**3
Let j(x) be the third derivative of 1/72*x**4 - 1/1008*x**8 + 0 + 0*x + 0*x**3 - 1/315*x**7 + 1/90*x**5 + 2*x**2 + 0*x**6. Solve j(i) = 0.
-1, 0, 1
Let z(f) be the second derivative of -f**6/150 - f**5/100 + f**4/20 + f**3/30 - f**2/5 + 11*f. Solve z(b) = 0.
-2, -1, 1
Let d(w) be the second derivative of -w**5/80 + w**4/12 + 26*w. Factor d(u).
-u**2*(u - 4)/4
Let v(t) be the first derivative of -t**5/40 + 3*t**4/16 - t**3/2 - t**2 - 1. Let l(w) be the second derivative of v(w). Solve l(u) = 0 for u.
1, 2
Let q(i) be the first derivative of 9*i**7/280 - 3*i**6/20 + 3*i**5/10 - i**4/3 + 2*i**3/3 - 1. Let s(d) be the third derivative of q(d). Factor s(z).
(3*z - 2)**3
Factor 0*g - 1/2*g**3 + 0*g**2 + 0.
-g**3/2
Let l = 3 - -2. Suppose 3*w - 14 = 2*s, 0*w + 2*w - l*s = 24. Factor -6*x**3 - x + 4*x**3 + 3*x - 2*x**4 + 0*x**2 + w*x**2.
-2*x*(x - 1)*(x + 1)**2
Suppose 4*v = -4, z + z = -v + 3. Let d be 1 + 10/(-28)*2. Determine x, given that -2/7*x - d*x**z + 0 = 0.
-1, 0
Let b(q) = -q**3 - 1. Let p(f) = -15*f**3 + 78*f**2 - 60*f - 18. Let h(y) = -6*b(y) - p(y). Factor h(w).
3*(w - 2)**2*(7*w + 2)
Let h(o) be the third derivative of 0*o - 1/120*o**6 - 1/30*o**5 - 1/24*o**4 + 0*o**3 + 7*o**2 + 0. Determine s, given that h(s) = 0.
-1, 0
Let p(n) = 7*n**3 - n**2 + n - 2. Let k(l) = 6*l**3 - 2*l**2 + 2*l - 2. Let i = -3 + -2. Let z(y) = i*k(y) + 4*p(y). Determine b, given that z(b) = 0.
1
Let o(x) be the third derivative of x**6/780 - x**5/78 + 7*x**4/156 - x**3/13 + 2*x**2. Factor o(b).
2*(b - 3)*(b - 1)**2/13
Let a(r) be the first derivative of r**3 + 9*r**2/2 + 6*r + 11. Factor a(o).
3*(o + 1)*(o + 2)
Let p(l) be the third derivative of -l**7/420 - l**6/180 + l**5/60 + l**4/12 + l**3/3 - 3*l**2. Let g(f) be the first derivative of p(f). Factor g(r).
-2*(r - 1)*(r + 1)**2
Let d(x) be the third derivative of x**7/525 - x**5/50 - x**4/30 - 2*x**2. Let d(w) = 0. Calculate w.
-1, 0, 2
Let q(z) be the second derivative of -z**4/8 - z**3/4 + 12*z. Find c, given that q(c) = 0.
-1, 0
Let t(o) be the first derivative of -4*o**3/3 - 10*o**2 - 16*o - 10. Factor t(x).
-4*(x + 1)*(x + 4)
Let h(o) be the first derivative of o**3 - 3/2*o**2 + 3/4*o + 1. Factor h(a).
3*(2*a - 1)**2/4
Let q(r) be the third derivative of -1/270*r**6 + 0*r**3 + 1/54*r**4 + 0*r - 1/135*r**7 - r**2 + 0 + 7/270*r**5. Determine w so that q(w) = 0.
-1, -2/7, 0, 1
Let r(w) be the third derivative of -2*w**5/135 + w**4/54 - 43*w**2. Find a, given that r(a) = 0.
0, 1/2
Let o(s) be the third derivative of s**5/30 + s**4/6 + s**3/3 - 3*s**2. Factor o(g).
2*(g + 1)**2
Let y(h) be the third derivative of h**9/20160 - h**8/3360 + h**7/1680 - h**5/15 - 2*h**2. Let j(n) be the third derivative of y(n). Factor j(a).
3*a*(a - 1)**2
Let y(x) = 3*x**2 + x - 4. Let o(n) = 4*n**2 - 4. Let k(t) = -4*o(t) + 5*y(t). Let v be k(3). Find z such that -2*z - 5*z**2 - 2*z**2 - z**v = 0.
-1/4, 0
Suppose -6*f = -2*f - 16. Factor -f - 6*c - 3*c**2 - 4*c - c**2.
-2*(c + 2)*(2*c + 1)
Let m(d) be the first derivative of -d**4/18 + 10*d**3/27 - 3. Let m(g) = 0. What is g?
0, 5
Let b(o) be the third derivative of 0*o + 1/9*o**3 + 1/315*o**7 + 0 - 1/504*o**8 - 1/45*o**5 + o**2 + 1/90*o**6 - 1/36*o**4. Suppose b(d) = 0. Calculate d.
-1, 1
Let r be (-2)/8 + 105/20 + -5. Let w(u) be the second derivative of -1/40*u**5 - 2*u - 1/12*u**3 - 1/12*u**4 + 0 + r*u**2. Factor w(s).
-s*(s + 1)**2/2
Let o(l) be the second derivative of 1/150*l**6 + 2/15*l**3 - l + 2/5*l**2 - 1/50*l**5 - 1/20*l**4 + 0. Find z such that o(z) = 0.
-1, 2
Factor v**5 - 6*v**3 - 10*v**3 + 4*v**2 - 5*v**5 - 4 + 4*v + 2 + 14*v**4.
-2*(v - 1)**4*(2*v + 1)
Let d(t) = 11*t**2 + 70*t - 6. Let z(k) = -23*k**2 - 140*k + 13. Let m(o) = 13*d(o) + 6*z(o). Let m(c) = 0. What is c?
-14, 0
Let g(s) = s**3 + 12*s**2 + 11*s - 4. Let f be g(-9). Suppose 10*p - 5*p = f. Find h such t