Factor h(m).
m*(m - 1)*(m + 6)
Let t(y) = 4*y**5 - 5*y**4 + 9*y**3 + 9*y**2 + 9. Let a(u) = -4*u**3 + 2*u**2 - 2*u**4 + 6*u**3 + u**4 + u**5 + 2. Let q(g) = 9*a(g) - 2*t(g). Factor q(m).
m**4*(m + 1)
Let d = -3817/5365 - -43/435. Let z = 2/37 - d. What is j in 0*j**2 + z*j**4 - 4/3*j - 2/3 + 4/3*j**3 = 0?
-1, 1
Factor -19*s**3 + 6*s**3 + 9*s**3 - 8*s**2.
-4*s**2*(s + 2)
Let y(n) be the third derivative of -n**6/1980 + n**4/132 + n**3/3 + 3*n**2. Let g(o) be the first derivative of y(o). Determine k, given that g(k) = 0.
-1, 1
Let j be (-12)/(-1 + 2) + 0. Let n be (j/15)/((-2)/10). Factor -3*p - 3*p - p**2 + n*p - 1.
-(p + 1)**2
Let j be (-1 + -1)/(8/(-84)). Determine z so that -2*z**3 + 2 + j*z**2 - 2 - 13*z**2 - 8*z = 0.
0, 2
Suppose -2*o - 3*o = -2*o. Factor 2/11*z**4 + 4/11*z + 0 - 6/11*z**2 + o*z**3.
2*z*(z - 1)**2*(z + 2)/11
Let k(m) be the second derivative of m**8/560 - m**6/40 - m**5/20 + m**3 + 6*m. Let s(d) be the second derivative of k(d). Factor s(t).
3*t*(t - 2)*(t + 1)**2
Suppose 0 = -3*z - 0 + 3. Let r be 0 - (z - 7/1). Factor -6*v**3 + 2*v**4 - v - v**5 + 2*v**2 - 6*v**4 - r*v**2.
-v*(v + 1)**4
Let n = 50 - 199/4. Let h(v) be the first derivative of -n*v**4 + 1/3*v**3 + 1/2*v**2 + 2 - v. Suppose h(s) = 0. Calculate s.
-1, 1
Let x(z) be the first derivative of z**4/18 + 2*z**3/9 + z**2/3 + 2*z/9 - 4. Determine k, given that x(k) = 0.
-1
Let x(w) = -w**3 - 4*w**2 - 3*w + 1. Let t be x(-4). Let u = 13 - t. Determine c so that 6/5*c**2 - 8/5*c**3 + u + 2/5*c = 0.
-1/4, 0, 1
Let t(s) = -s**2 - 3*s - 2. Let z(a) = -a + 1. Let f(p) = p**2 + 2*p + 3. Let b(n) = 3*f(n) - 3*z(n). Let l(m) = -3*b(m) - 8*t(m). Suppose l(q) = 0. What is q?
-2, -1
Let h be 2/(30/(-43)) - (-4 + 1). Let o(m) be the first derivative of -3 + 4/5*m + 3/5*m**2 + h*m**3. Factor o(v).
2*(v + 1)*(v + 2)/5
Let r(n) be the first derivative of 3/8*n**4 - 1/3*n**3 - 3/4*n**2 + n + 1. Let r(b) = 0. What is b?
-1, 2/3, 1
Let g = -4 - -7. Factor -m - 3*m**g - m + 0*m + 5*m**3.
2*m*(m - 1)*(m + 1)
Let v(k) be the third derivative of -k**5/20 + 7*k**4/8 - 33*k**2. Factor v(u).
-3*u*(u - 7)
Find x such that 13 + x**2 + 5*x - 26 + 19 = 0.
-3, -2
Determine c so that -16/11 - 2/11*c**3 + 12/11*c + 6/11*c**2 = 0.
-2, 1, 4
Let z be 1*2 - 1 - 72/(-168). Let 0 + z*o**2 - 8/7*o**3 - 2/7*o = 0. What is o?
0, 1/4, 1
Let w(t) = t**2 + 4*t - 2. Let f be w(-5). Let d(o) be the first derivative of -1 + 4*o**2 - 2/3*o**f - 8*o. Factor d(j).
-2*(j - 2)**2
Let g(r) be the first derivative of -1/2*r**3 + 0*r + 9/8*r**4 - 9/4*r**2 - 3 + 3/10*r**5. Factor g(i).
3*i*(i - 1)*(i + 1)*(i + 3)/2
Let l be (-2)/9 + (11 - (-553)/(-63)). Let u be (-12)/(-14) + (-4)/14. Factor 6/7*s**l - u + 2/7*s.
2*(s + 1)*(3*s - 2)/7
Suppose -2*l - 6 = -4*l. Find r such that -l + 7*r**2 - 5*r**2 + 1 = 0.
-1, 1
Let z(r) be the third derivative of r**7/1155 + r**6/660 + 6*r**2. Factor z(c).
2*c**3*(c + 1)/11
Let 3/2*w**3 + 1/2*w**4 - 1/2*w**2 - 3/2*w + 0 = 0. Calculate w.
-3, -1, 0, 1
Suppose 3*r + o - 10 = 3*o, -5*r + 4*o + 18 = 0. Factor 3/5*s**3 + 0*s**r + 0 - 1/5*s - 2/5*s**4.
-s*(s - 1)**2*(2*s + 1)/5
Let b(j) = 18*j**5 + 12*j**3 - 15*j + 15. Let f(q) = -q**5 - q**3 + q - 1. Let m(w) = -b(w) - 15*f(w). Determine n, given that m(n) = 0.
-1, 0, 1
Factor 0*m + 0 + 2/5*m**3 + 0*m**2.
2*m**3/5
Let h = 3 - 8/3. Let g(f) be the first derivative of 0*f - 1/5*f**5 - 1/4*f**4 + 2 + h*f**3 + 1/2*f**2. Find j such that g(j) = 0.
-1, 0, 1
Let t(y) be the first derivative of -y**6/180 - y**5/30 - y**4/12 - 2*y**3/3 + 4. Let z(x) be the third derivative of t(x). Determine q so that z(q) = 0.
-1
Let z be (-1)/(-9)*8/4. Let l(t) be the first derivative of 2/9*t**3 + z*t**2 + 0*t - 2. Find d, given that l(d) = 0.
-2/3, 0
Let t be 3 - 0/(15/(-5)). Find m such that 2/7 - 2/7*m**2 + 8/7*m**t - 8/7*m = 0.
-1, 1/4, 1
Let w(a) be the third derivative of a**8/168 - 3*a**7/245 - a**6/84 + 3*a**5/70 - a**4/42 - 8*a**2. What is j in w(j) = 0?
-1, 0, 2/7, 1
Let a(i) be the second derivative of -i**6/900 + i**4/60 - i**3/6 - 2*i. Let p(l) be the second derivative of a(l). Factor p(r).
-2*(r - 1)*(r + 1)/5
Suppose 15*z = -2*z + 51. Let d(i) be the second derivative of -1/5*i**6 + 3/10*i**5 + 3*i + 0 + 0*i**2 - 1/6*i**4 + 1/21*i**7 + 0*i**z. Factor d(k).
2*k**2*(k - 1)**3
Let f(q) be the second derivative of q**5/15 - q**4/9 - 2*q**3/9 + 2*q**2/3 + 2*q. Suppose f(i) = 0. Calculate i.
-1, 1
What is j in j**2 + j + 0 + 1/4*j**3 = 0?
-2, 0
Suppose -3*r = -4*g - 4, 2*g - 4*r + 16 = r. Solve 0*t**2 - g*t**2 - 4*t**2 + 4*t**2 = 0.
0
Let i(p) = p + 12. Let z be i(-10). Suppose -5 = -z*n - 3*n, -2*q = 2*n - 2. Factor 3/4*y**3 + q + 1/4*y + 3/4*y**2 + 1/4*y**4.
y*(y + 1)**3/4
Suppose -8 = -2*j - 2*j. Let t be (2 + -1)*j - 0. Determine m so that 4*m**t - m + 3*m - 2*m**2 + 2 - 6*m = 0.
1
Let w = -4 + 7. Find r such that 2*r**2 - w*r + 3*r = 0.
0
Let g(c) be the first derivative of c**6/840 - c**4/42 + 3*c**2/2 + 2. Let b(k) be the second derivative of g(k). Factor b(f).
f*(f - 2)*(f + 2)/7
Let h(m) = 14*m**3 + 61*m**2 - 86*m - 11. Let d(w) = -3*w**3 - 12*w**2 + 17*w + 2. Let g(n) = -11*d(n) - 2*h(n). Let g(f) = 0. What is f?
-3, 0, 1
Let b(r) be the third derivative of r**7/35 - 3*r**6/80 - r**5/40 - 5*r**2. What is v in b(v) = 0?
-1/4, 0, 1
Let b(p) be the second derivative of -1/2*p**3 + 3/8*p**2 + p + 3/8*p**4 - 3/20*p**5 + 1/40*p**6 + 0. Find r, given that b(r) = 0.
1
Let c(i) be the second derivative of 1/20*i**6 + 0 + 0*i**2 - 1/8*i**3 - 1/8*i**4 + 1/56*i**7 + 3*i + 0*i**5. Solve c(j) = 0.
-1, 0, 1
Let p(m) = 2*m**2 + m - 3. Let z be p(-2). Let v(h) be the first derivative of 5/9*h**z - 3 - 2/3*h**2 - 1/6*h**4 + 1/3*h. Suppose v(s) = 0. Calculate s.
1/2, 1
Factor -6/7*t**2 - 2/7*t**4 + 0 + 6/7*t**3 + 2/7*t.
-2*t*(t - 1)**3/7
Let t(y) = -y**2 + 8*y - 5. Let k be t(7). Suppose k*x = 5*x. Factor -37*d**4 + 16*d**5 - 2*d + 38*d**3 - 4*d**5 + x - 2 + 3 - 12*d**2.
(d - 1)**3*(3*d - 1)*(4*d + 1)
Let 0*v + 0 + 2/5*v**3 - 2/5*v**2 = 0. Calculate v.
0, 1
Let q(i) be the first derivative of -i**5/40 + i**4/24 + 5*i**3/12 + 3*i**2/4 + 5*i - 2. Let s(k) be the first derivative of q(k). Factor s(r).
-(r - 3)*(r + 1)**2/2
Let f = -6 + 6. Let 38 - p**3 - 3*p - 4*p + 5*p**2 + f*p - 35 = 0. Calculate p.
1, 3
Let x be 12*(-4)/(-6)*1. Let d be 26/x - (-1 + 4). Factor 0*r**3 + 1/4*r**2 + 0 + 0*r - d*r**4.
-r**2*(r - 1)*(r + 1)/4
Suppose -2*q - 141 = -51. Let g be -4 - (-3 - (-85)/q). Factor 0 + 2/9*v - g*v**3 + 2/3*v**2.
-2*v*(v - 1)*(4*v + 1)/9
Let m(p) = -8*p - 24. Let j be m(-10). Find k, given that -51*k**3 + k**5 - 19*k**5 - j*k**2 - 84*k**4 - 8*k - 71*k**3 = 0.
-2, -1/3, 0
Let w = -520 - -522. Factor 0*j + 0 + 2/3*j**w.
2*j**2/3
Let y(r) be the second derivative of 0 + 2/5*r**5 + 12*r**3 - 27*r**2 - r - 1/45*r**6 - 3*r**4. Factor y(q).
-2*(q - 3)**4/3
Let x(k) = k + 10. Let a be x(-12). Let f be 0*a/8*1. Factor f*g**2 + 2/9*g**3 + 0 - 2/9*g.
2*g*(g - 1)*(g + 1)/9
Let l be (-2)/4*(-3 + 3). Suppose 3*h - 1 - 5 = l. Factor 3 - 5*v**2 + v**3 + 0*v**3 + 2*v**3 - 3*v + 2*v**h.
3*(v - 1)**2*(v + 1)
Let f(y) be the first derivative of y**3/18 - 3*y/2 + 35. Suppose f(v) = 0. Calculate v.
-3, 3
Let p(m) be the first derivative of 4*m**3/15 + 12*m**2/5 + 36*m/5 - 8. Suppose p(g) = 0. Calculate g.
-3
Let c(v) = 5*v**4 + 26*v**3 + 63*v**2 + 54*v - 2. Let n(t) = -t**4 - t**3 + 1. Let m(a) = c(a) + 2*n(a). Solve m(f) = 0.
-3, -2, 0
Let t(f) be the third derivative of -1/120*f**5 + 0 - 1/48*f**4 + 1/12*f**3 + 1/240*f**6 + 0*f - 2*f**2. Factor t(q).
(q - 1)**2*(q + 1)/2
Let t(h) = -6*h**4 + 4*h**3 + 12*h**2 + 6*h - 2. Let q(u) = -11*u**4 + 7*u**3 + 23*u**2 + 11*u - 4. Let f(m) = 3*q(m) - 5*t(m). Suppose f(o) = 0. What is o?
-1, 1/3, 2
Let o(n) be the second derivative of -n**9/7560 - n**8/3360 + n**7/1260 + n**6/360 - n**4/6 + n. Let s(m) be the third derivative of o(m). Factor s(c).
-2*c*(c - 1)*(c + 1)**2
Let w be (5 - 26)*8/(-6). Let r = -111/4 + w. Factor -1/4*u - 1/2 + r*u**2.
(u - 2)*(u + 1)/4
Let j(b) be the first derivative of -2*b**4 - 22*b**3/3 - 5*b**2 + 4*b - 14. Factor j(h).
-2*(h + 1)*(h + 2)*(4*h - 1)
Solve 0*t**2 - 6/7*t + 2/7*t**3 - 4/7 = 0.
-1, 2
Let n = -346/65 + 90/13. Let i(s) be the first derivative of -2*s**2 + 7/2*s**4 - s + s**3 + n*s**5 + 3. Determine h