/30*j**4 + 0*j**2 + 4*j. Factor o(c).
-2*c*(c - 3)/5
Let j(y) be the first derivative of 5*y**6/6 + 2*y**5 - 10*y**3/3 - 5*y**2/2 + 15. Factor j(g).
5*g*(g - 1)*(g + 1)**3
Determine q, given that 2/9*q**3 + 4/3*q**2 + 2*q + 8/9 = 0.
-4, -1
Let g(f) = 7*f**2 - 19*f + 3. Let v(x) be the second derivative of -5*x**4/3 + 28*x**3/3 - 4*x**2 + 7*x. Let m(p) = 8*g(p) + 3*v(p). Find w such that m(w) = 0.
0, 4
Let x(l) = l**2 + l. Let p(a) = 16*a**2 + 12*a. Let o(r) = -p(r) + 12*x(r). Factor o(b).
-4*b**2
Suppose 42 - 52 = -2*l. Let h(u) be the third derivative of 3*u**2 - 1/3*u**3 + 0*u - 1/120*u**6 + 0 - 5/24*u**4 - 1/15*u**l. Determine z, given that h(z) = 0.
-2, -1
Find f, given that 0 + 12/7*f**3 + 8/7*f - 20/7*f**2 - 4/7*f**5 + 4/7*f**4 = 0.
-2, 0, 1
Factor -10/17*k**3 - 8/17*k - 16/17*k**2 - 2/17*k**4 + 0.
-2*k*(k + 1)*(k + 2)**2/17
Suppose 0 = 2*f - 2*g - 22, 10 = -3*g + 4. Suppose 2*y - 3 = j, -j - f = -5*y + 2*j. Factor -2*m**4 + y*m**2 + 18/7*m**5 + 0 + 0*m - 4/7*m**3.
2*m**3*(m - 1)*(9*m + 2)/7
Let t(x) be the first derivative of -7/2*x**2 - x**3 + 1 + 6*x. Let t(v) = 0. What is v?
-3, 2/3
Let j = -2 + 5. Let q be 2 + (2 - j/3). Determine y, given that 2/5*y + 1/5 - 4/5*y**q + 4/5*y**4 - 3/5*y**2 = 0.
-1/2, 1
Let k(i) be the first derivative of 7*i**4/8 - 2*i**3 + 3*i**2/4 + i - 5. Solve k(b) = 0.
-2/7, 1
Suppose -5 - 1 = -2*y. Let q(v) = -v - 2. Let p be q(-5). What is h in -2 - 3*h - 2*h**2 - 2*h**y - p*h - 4*h**2 = 0?
-1
Factor w**3 - w**3 + 2*w**3 + 2*w**2.
2*w**2*(w + 1)
Let r(p) be the third derivative of 9*p**7/245 - 9*p**6/70 - 27*p**5/70 - p**4/21 + 4*p**3/7 + 4*p**2. Let r(n) = 0. What is n?
-2/3, 1/3, 3
Suppose 6 = n + 12*a - 13*a, 0 = -3*n - 5*a - 6. Factor -8/15*p**n + 0 + 2/15*p**2 - 2/5*p**4 + 4/15*p.
-2*p*(p + 1)**2*(3*p - 2)/15
Let f = 2/29 - -17/174. Let g(b) be the second derivative of 3/10*b**5 + 1/3*b**4 + 0 + 2/15*b**6 + 0*b**2 + 3*b + 1/42*b**7 + f*b**3. Factor g(h).
h*(h + 1)**4
Let z(p) = -p**3 + 4*p**2 + 7*p + 2. Let i(y) = 6*y**3 - 19*y**2 - 34*y - 9. Let u(f) = -4*i(f) - 22*z(f). Factor u(m).
-2*(m + 1)**2*(m + 4)
Let p = 332 + -2984/9. Let g(u) be the first derivative of -8/9*u - 2/27*u**3 + 2 + p*u**2. Determine s so that g(s) = 0.
2
Determine w, given that -846*w + 4*w**2 + 12 + 834*w - w**2 = 0.
2
Factor -32/3*x**3 - 576 - 384*x - 4/9*x**4 - 96*x**2.
-4*(x + 6)**4/9
Let q(c) be the third derivative of -c**5/150 + c**3/15 + 15*c**2. Determine i so that q(i) = 0.
-1, 1
Find k such that 16/7*k**4 + 0 + 0*k + 20/7*k**3 + 8/7*k**2 + 4/7*k**5 = 0.
-2, -1, 0
Let m(g) be the third derivative of -1/12*g**4 - 3*g**2 + 0 + 0*g - 1/60*g**5 + 0*g**3. Determine l, given that m(l) = 0.
-2, 0
Let k(f) = 13*f + 6. Let s(n) = -2*n**2 + 53*n + 24. Let p(u) = -9*k(u) + 2*s(u). Determine m so that p(m) = 0.
-2, -3/4
Let f(i) be the first derivative of -i**7/105 - 2*i**6/75 + i**4/15 + i**3/15 - 4*i - 2. Let j(b) be the first derivative of f(b). Solve j(v) = 0.
-1, 0, 1
Let b(u) = -u**2 - 10*u + 12. Let j be b(-12). Let g be (-2)/(-3) + j/(-9). Find d, given that -1 + 0 + 3*d**3 + 3 + 9*d**g + 1 + 9*d = 0.
-1
Let j = 1 - -1. Determine t, given that 3*t**2 + 3*t**5 - 2*t**2 - 3*t**4 + j*t**2 - 3*t**3 = 0.
-1, 0, 1
Factor -x**2 + 3 - 1 - 2*x**2 - 2*x**2 - 3*x.
-(x + 1)*(5*x - 2)
Let d(i) = -i**2 + 7*i - 6. Let a be d(6). What is o in -1/4*o**2 + a + 0*o + 1/4*o**3 = 0?
0, 1
Let c = -24 + 29. Suppose 5*v - c = 10. Find w, given that 0*w + 2/9*w**4 + 0 - 4/9*w**v + 2/9*w**2 = 0.
0, 1
Let u be 22/(-77)*7/(-3). Factor 8/9*s - 2/9 - u*s**2.
-2*(s - 1)*(3*s - 1)/9
Suppose -4*d - d = 0. Suppose -5*w + 20 = -d. Let -2 + 4*a**2 - 5*a**2 - a**2 - w*a = 0. Calculate a.
-1
Let n = 9 - 6. What is x in x**n + x**3 + x**2 - 3*x**3 = 0?
0, 1
Suppose 0 = -4*n + 8 + 4. Factor 0*k + 0*k + 8*k**n - 6*k**3.
2*k**3
Let z(v) be the third derivative of -v**8/1176 - 2*v**7/735 + v**5/105 + v**4/84 + 33*v**2. Suppose z(j) = 0. What is j?
-1, 0, 1
Let b(c) be the first derivative of -c**6/540 - c**5/180 - c**3 + 4. Let t(w) be the third derivative of b(w). Factor t(p).
-2*p*(p + 1)/3
Let f(k) be the first derivative of -4*k**5/5 - k**4 + 4*k**3 + 10*k**2 + 8*k + 3. Let f(d) = 0. What is d?
-1, 2
Factor -8/7*h - 8/7*h**2 + 0 - 2/7*h**3.
-2*h*(h + 2)**2/7
Let u be 66/15 - 1 - (-3)/5. Let v(i) be the first derivative of 0*i**2 + 1/15*i**6 - 3 + 2/15*i**3 + 0*i - 2/25*i**5 - 1/10*i**u. Determine b so that v(b) = 0.
-1, 0, 1
Let s = 245/6 + -1213/30. Factor s*h**2 + 2/5*h + 0.
2*h*(h + 1)/5
Let f = -10513 - -94718/9. Let t = f - 11. Factor 2/9*u - 2/9*u**3 + 0 + t*u**4 - 2/9*u**2.
2*u*(u - 1)**2*(u + 1)/9
Let w be 10/8*5/((-10)/(-8)). Let f(j) be the second derivative of -3*j + 1/5*j**w - 1/21*j**7 - 1/15*j**6 + 0 + 0*j**2 + 0*j**3 + 0*j**4. Solve f(y) = 0.
-2, 0, 1
Let h = -4 - -4. Suppose 6*c - 4*c - 5*y + 11 = h, 0 = -y + 3. Factor 0*q - 2/5*q**3 + 0 - 2/5*q**c.
-2*q**2*(q + 1)/5
What is f in 240/7*f**2 + 54/7*f + 4/7 + 352/7*f**3 = 0?
-1/4, -2/11
Let x(m) be the first derivative of -m**7/280 + m**6/120 + m**5/40 - m**4/8 + 2*m**3/3 + 3. Let g(b) be the third derivative of x(b). Factor g(k).
-3*(k - 1)**2*(k + 1)
Let k(j) be the first derivative of -j**6/21 - 6*j**5/35 - 3*j**4/14 - 2*j**3/21 - 3. What is o in k(o) = 0?
-1, 0
Let n(d) = d**3 - d**2 - 3*d + 4. Let a be n(2). Factor -q**2 - 3*q**a - q - 2 + 5*q**2.
(q - 2)*(q + 1)
Let x(u) = -5*u**2 - 4. Let v = 5 - 2. Let t(n) = 4*n**2 + 3. Let d(i) = v*x(i) + 4*t(i). Factor d(o).
o**2
Let n(a) be the second derivative of a**4/12 - a**3/3 + 3*a**2/2 - 9*a. Let t be n(2). Factor 0 - 1/2*u**t + 1/2*u + 0*u**2.
-u*(u - 1)*(u + 1)/2
Let h(i) be the third derivative of -2*i**2 - 3/20*i**5 + 1/20*i**6 + 0 + 0*i + 0*i**3 - 1/4*i**4. Find t, given that h(t) = 0.
-1/2, 0, 2
Let g(p) be the first derivative of 22*p**3/45 - 3*p**2/5 - 4*p/15 - 42. Let g(w) = 0. Calculate w.
-2/11, 1
Let w be 9/21 - (-11)/7. Factor 12 + w*i + i**4 + 5*i**2 + 4*i**3 - 12.
i*(i + 1)**2*(i + 2)
Suppose 0 = 2*v + 4*v - 24. Determine b so that 3 + 4 + 9*b**v + 3*b - 15*b**3 - 7 + 3*b**2 = 0.
-1/3, 0, 1
Let d(f) = -f**2 - 6*f - 5. Let b be d(-5). Let k be -1 + (b - 2*-1). Factor -3*a**2 + 7*a**2 - k - 1 - 2*a**4.
-2*(a - 1)**2*(a + 1)**2
Let p(l) = -4 - 5*l**2 - 4*l**3 + l**2 - 5*l + 3*l**3. Let h be p(-3). Solve 2*f + 3 + 3 - 2 - 4*f - 2*f**h = 0 for f.
-2, 1
Let x be 1/((5/(-2))/(-5)). Suppose 5 = -3*j + k, -4 = -x*j + 5*k - 29. Factor j*p**2 + p + 0*p + p**2.
p*(p + 1)
Let h be ((-14)/(-4))/(9/18). Suppose -6 = -h*f + 4*f. Determine v so that 0 + 1/4*v**3 - 1/4*v - 1/4*v**4 + 1/4*v**f = 0.
-1, 0, 1
Solve 0*p**3 - 3*p**3 - 11*p - 15*p**2 - 3 - p - 3*p**3 = 0 for p.
-1, -1/2
Let q(h) be the third derivative of 1/1260*h**6 + 0*h + 4*h**2 + 1/84*h**4 + 0 - 1/210*h**5 + 1/3*h**3. Let a(d) be the first derivative of q(d). Factor a(n).
2*(n - 1)**2/7
Suppose -5*s + 15 = 0, -5*a - 3*s + 22 + 7 = 0. Factor -8*o**5 - 30*o**2 + 32*o**2 - o + o - 4*o**3 - 14*o**a.
-2*o**2*(o + 1)**2*(4*o - 1)
Let a(c) be the second derivative of c**6/12 - 3*c**5/8 + 5*c**4/8 - 5*c**3/12 - 6*c. Factor a(d).
5*d*(d - 1)**3/2
Let r(s) be the first derivative of -s**6/33 + 6*s**5/55 - 3*s**4/22 + 2*s**3/33 + 1. Factor r(b).
-2*b**2*(b - 1)**3/11
Let o(a) = 7*a**2 - 3*a - 4. Let r be o(-2). Let l be (r/(-75))/((-6)/10). Suppose -l*b**2 - 8/3*b - 8/3 = 0. What is b?
-2
Let i be 93/35 + -1 - 236/295. Factor i*o**3 + 0 - 1/7*o + 3/7*o**5 + 0*o**2 + 8/7*o**4.
o*(o + 1)**3*(3*o - 1)/7
Let r(i) be the first derivative of i**3 - 9*i**2/2 - 7*i - 2. Let s(o) = -14*o + 0*o**2 + 5*o**2 - 9 - 2. Let n(a) = 8*r(a) - 5*s(a). Factor n(w).
-(w + 1)**2
Let w(a) be the second derivative of -a**4/102 - 2*a**3/51 + 3*a**2/17 + 13*a. Suppose w(f) = 0. Calculate f.
-3, 1
Let s(y) be the third derivative of y**5/60 - 11*y**4/24 - 2*y**3 + 17*y**2 + 2*y. Factor s(r).
(r - 12)*(r + 1)
Determine z, given that 0*z - 2/17*z**2 + 0 = 0.
0
Factor 3*g**3 - 48*g**2 - 25*g - 32 + 13*g**3 - 2*g**4 + 89*g.
-2*(g - 2)**4
Let t = 34 - 16. Let n be (-4)/t + (-114)/(-27). Factor n - 2 + 0*p**2 + 0 - 2*p**2.
-2*(p - 1)*(p + 1)
Let a(g) = g**2 + 3*g. Let s(t) = 4*t**2 + 16*t. Let y(o) = 16*a(o) - 3*s(o). What is w in y(w) = 0?
0
Let a = -14819/78 - -190. Let p = a - -58/39. Suppose 9/4*y**2 + p*y + 1/4 = 0. Wha