- 7*z**4/5 + 8*z**3/15 - 1. Factor n(t).
4*t**2*(t - 1)*(5*t - 2)/5
Let r(p) be the third derivative of -11*p**7/210 + 61*p**6/360 - 8*p**5/45 + p**4/18 - 11*p**2. Suppose r(k) = 0. Calculate k.
0, 2/11, 2/3, 1
Let l be 2 + 0 - (-249)/(-126). Let h(n) be the third derivative of 0*n - 1/735*n**7 - l*n**4 + 0*n**5 + 0 + 1/210*n**6 + n**2 + 1/21*n**3. Factor h(f).
-2*(f - 1)**3*(f + 1)/7
Let r be (-2)/(-3) + (0 - (-6)/(-9)). Suppose -1/4*z**3 + 1/4*z + r*z**2 + 0 = 0. Calculate z.
-1, 0, 1
Let p(b) be the third derivative of 0 + 1/120*b**6 + 2*b**2 + 0*b**3 + 0*b - 1/36*b**4 - 1/180*b**5. Determine o so that p(o) = 0.
-2/3, 0, 1
Solve 29*x**2 + 63*x + 3*x**2 + 13*x**3 + 32*x**3 - 59*x - 81*x**4 = 0.
-2/9, 0, 1
Factor 16/9*x + 4/9*x**5 + 16/9*x**2 + 0 - 8/9*x**4 - 4/3*x**3.
4*x*(x - 2)**2*(x + 1)**2/9
Let o(c) be the second derivative of -c**4/6 + 2*c**3/3 - c**2 + 6*c. What is f in o(f) = 0?
1
Let c(l) = -l**5 + l**4 + l**2 + l + 1. Let p(j) = -14*j**2 + j**3 + 6*j**4 + 21 - 12*j - 5*j**3 - 23. Let g(h) = -2*c(h) + p(h). Solve g(x) = 0.
-1, 2
Let m(f) be the second derivative of -49*f**6/90 - 7*f**5/15 + 5*f**4/4 + 14*f**3/9 + 2*f**2/3 + 5*f. Solve m(u) = 0.
-1, -2/7, 1
Let z(s) = -7*s - 6 + 4 + s**2 + 0*s. Let g be z(10). Solve -21*d**3 + 11*d**2 + 4*d**3 + 8 - g*d + 3*d**4 + 23*d**2 = 0.
2/3, 1, 2
Let y(u) be the first derivative of 10*u**2 + 1 - 2*u**3 - 8*u - 9/4*u**4. Factor y(a).
-(a + 2)*(3*a - 2)**2
Suppose 6/7 + 16/7*p + 10/7*p**2 = 0. What is p?
-1, -3/5
Let s(w) be the third derivative of 4*w**2 + 0*w + 1/150*w**5 + 0 - 1/200*w**6 + 0*w**7 + 0*w**4 + 0*w**3 + 1/1680*w**8. Factor s(k).
k**2*(k - 1)**2*(k + 2)/5
Let p(j) be the third derivative of -j**11/110880 - j**10/50400 - j**5/60 - j**2. Let d(z) be the third derivative of p(z). Suppose d(s) = 0. Calculate s.
-1, 0
Let h(i) be the third derivative of -i**5/120 - i**4/24 - i**3/12 + 9*i**2. Factor h(c).
-(c + 1)**2/2
Let z be (-30)/(-55) + 59/33. Factor z*l**2 + 2/3 + 3*l.
(l + 1)*(7*l + 2)/3
Let p(u) be the first derivative of u**4/24 + u**3/6 + u**2/4 - 2*u - 3. Let s(m) be the first derivative of p(m). Factor s(z).
(z + 1)**2/2
Factor 0*f**2 + 0 + 3/2*f**3 + 0*f.
3*f**3/2
Let x(h) be the third derivative of h**5/240 - h**4/48 + h**3/24 - 7*h**2. Solve x(u) = 0 for u.
1
Let a(o) = -o**3 - 5*o**2 + 5*o + 3. Let r be a(-6). Let p = r - 7. Find t such that 3*t**p + 2*t - 2*t**2 - 1 - 2*t = 0.
-1, 1
Suppose -5*j + 7 + 8 = 0. Find f such that f**5 + 4*f**4 - 2*f - 62*f**3 - f**4 + 63*f**3 - j*f**2 = 0.
-2, -1, 0, 1
Let b = -43 + 133/3. Let u(d) be the first derivative of -b*d**3 - 3 - 5/2*d**2 - d. Factor u(m).
-(m + 1)*(4*m + 1)
Suppose 0 = -8*a + 3*a. Factor a + 0 + v**2.
v**2
Let r(i) be the third derivative of -i**5/240 - 5*i**4/96 - i**3/6 - 20*i**2. Factor r(v).
-(v + 1)*(v + 4)/4
Let -4/5*j**4 + j**3 + 1/5*j**5 + 0 - 2/5*j**2 + 0*j = 0. Calculate j.
0, 1, 2
Let i be ((-1)/(-2))/(1/18). Let k = i - 5. Factor 6*x**2 + 4*x - k*x**2 - x**2 + 4.
(x + 2)**2
Suppose 4*z + 5*v + 9 - 32 = 0, -v = -2*z + 1. Factor z*p**4 + 2*p**3 - p**2 - 2*p**2 - 2*p**5 + p**2.
-2*p**2*(p - 1)**2*(p + 1)
Let w(f) be the first derivative of 1/2*f**2 - 1 + 1/48*f**4 - 2*f + 1/6*f**3. Let y(q) be the first derivative of w(q). Factor y(c).
(c + 2)**2/4
Let o(n) = 2*n**4 - 4*n + 7*n**5 + 13*n**4 - 7*n + 8*n**3. Let f = 22 - 44. Let r(l) = -2*l**5 - 4*l**4 - 2*l**3 + 3*l. Let a(w) = f*r(w) - 6*o(w). Factor a(q).
2*q**3*(q - 2)*(q + 1)
Let h(v) be the second derivative of v**4/30 + v. Solve h(l) = 0.
0
Suppose -5*g = -2 - 8. Suppose -t = g*t. Factor t + 4/3*i**5 + 13/3*i**4 + 7/3*i**2 + 1/3*i + 5*i**3.
i*(i + 1)**3*(4*i + 1)/3
Suppose -5*k - 27 - 23 = 0. Let v be 4/20 + (-38)/k. Factor -v*m**2 - 6 - 4*m + 4 + 2*m**2.
-2*(m + 1)**2
Suppose 5*t + 10 = -5. Let h = 5 + t. What is d in -4*d + 4 - 2*d**2 - 4 - h = 0?
-1
Let t(q) be the second derivative of -q**4/36 + 2*q**3/9 - q**2/2 + 6*q. Factor t(i).
-(i - 3)*(i - 1)/3
Suppose d - t - 19 = 5, 0 = -5*d - 5*t + 90. Solve 0 - 16*v**2 + 4*v + d*v**4 + 0 + 10*v**3 - 9*v**3 = 0.
-1, 0, 2/7, 2/3
Let d = 1880/7 - 266. Factor -12/7*h - 2/7*h**2 - d.
-2*(h + 3)**2/7
Let x(j) = -3*j**3 - 4*j**2 + 6*j + 6. Let f(b) = -b**2 + b + 1. Let n(d) = 6*f(d) - x(d). Factor n(i).
i**2*(3*i - 2)
Let i(r) be the first derivative of -r**6/15 + r**4/6 + r + 1. Let n(d) be the first derivative of i(d). What is t in n(t) = 0?
-1, 0, 1
Let f(y) be the third derivative of 0 + 1/30*y**5 + 1/6*y**4 + 0*y + 1/3*y**3 - 2*y**2. Suppose f(t) = 0. Calculate t.
-1
Let n(j) be the first derivative of 0*j**2 + 0*j**3 + 3 + 0*j - 1/16*j**4. Factor n(z).
-z**3/4
Let a(w) = 9*w**2 + 12*w. Let y(r) = -10*r**2 - 12*r. Let u(f) = -6*a(f) - 5*y(f). Factor u(g).
-4*g*(g + 3)
Factor 10*z**3 - 6*z + 4 - 2*z**2 + 4*z**3 - 8*z**3 - 2*z**4.
-2*(z - 2)*(z - 1)**2*(z + 1)
Let s(v) = -v - 3*v + 5*v + 0*v. Let y(q) = 3*q**2 + 9*q - 6 + 6. Let b(m) = -6*s(m) + y(m). Determine c, given that b(c) = 0.
-1, 0
Let b be ((-5)/(-10))/((-5)/10) + 3. Factor 1/5*c**3 + 0 - 1/5*c**b + 0*c.
c**2*(c - 1)/5
Let g(l) = l + 12. Let h be 18/4*6/(-3). Let o be g(h). Determine m so that -4*m**3 + 0*m**2 + 3*m**o - m**2 = 0.
-1, 0
Let b(v) be the second derivative of v**6/45 + v**5/10 + v**4/6 + v**3/9 + 21*v. Factor b(g).
2*g*(g + 1)**3/3
Let b be (-2 - -6) + (-94)/24. Let d = b - -7/12. Determine z, given that 1/3*z - 2/3*z**2 + d - 1/3*z**3 = 0.
-2, -1, 1
Let b(w) = 3*w**3 - 59*w**2 + 128*w. Let j(r) = -2*r**3 + 30*r**2 - 64*r. Let i(u) = -2*b(u) - 5*j(u). Let i(l) = 0. What is l?
0, 4
Let j(k) be the first derivative of k**6/45 + k**5/30 - 2*k + 1. Let t(l) be the first derivative of j(l). Let t(b) = 0. What is b?
-1, 0
Let g(i) be the third derivative of -i**8/378 + i**7/945 + i**6/27 - i**5/54 - 4*i**4/27 + 4*i**3/27 + 39*i**2. Solve g(b) = 0 for b.
-2, -1, 1/4, 1, 2
Let f be (-4)/4*(-5)/90. Let r(c) be the third derivative of 1/36*c**4 + 0*c + 0 + c**2 + 1/180*c**5 + f*c**3. Determine i so that r(i) = 0.
-1
Find m, given that -3*m**4 - 3*m**3 - 8*m**2 + 12*m**3 + 5*m**2 + 6 - 9*m = 0.
-1, 1, 2
Let y be (-40)/32*6/25. Let z = y + 11/20. Factor 0 + 1/4*k**5 + 0*k + 1/4*k**2 - z*k**3 - 1/4*k**4.
k**2*(k - 1)**2*(k + 1)/4
Suppose 3*n + 3*o = -3, -n - 9*o = -4*o + 17. Factor 1/6 - 3/2*y**n - 7/6*y + 5/2*y**2.
-(y - 1)*(3*y - 1)**2/6
Let m(g) be the third derivative of g**6/60 + 2*g**5/15 + g**4/3 - 4*g**2. Solve m(z) = 0 for z.
-2, 0
Suppose 4*l - 5*l + b + 3 = 0, -2*l - 1 = 5*b. Find v such that -v**l + v**2 + 6*v - 4 + 1 - 3*v**2 = 0.
1
Factor 14*c + 10*c**5 - 69*c + 25 - 35*c**4 + 8*c**2 + 50*c**3 + 2*c**2 - 5*c**5.
5*(c - 5)*(c - 1)**3*(c + 1)
Let k(c) be the second derivative of -7/15*c**6 + 4*c + 1/5*c**5 + 4/3*c**4 - 4/21*c**7 + 2/3*c**3 + 0 - c**2. Suppose k(w) = 0. Calculate w.
-1, 1/4, 1
Suppose -2*s + 5*s - 24 = 0. Let d(p) be the first derivative of 38/3*p**3 + 2 + 91*p**4 - 20*p**2 + 294/5*p**5 - s*p. Find a, given that d(a) = 0.
-1, -2/7, 1/3
Suppose h - 4*h = 0. Factor 2*m**3 - 6*m + 0*m + h*m + 4*m.
2*m*(m - 1)*(m + 1)
Let h(p) be the first derivative of p**6/9 + 4*p**5/15 - 4*p**3/9 - p**2/3 - 1. Let h(v) = 0. Calculate v.
-1, 0, 1
Factor -2*q**4 + 48*q**2 - 88*q**2 + 38*q**2 - 4*q**3.
-2*q**2*(q + 1)**2
Determine n so that 4*n - 2*n**5 - 4*n - 16*n**3 - 28*n**4 - 6*n**5 + 16*n**2 = 0.
-2, 0, 1/2
Let m be (2/(-3))/(4/(-30)). Factor j**3 + 4*j**3 - j - j**m + 0*j**3 - 3*j**3.
-j*(j - 1)**2*(j + 1)**2
Let a = 17 + 12. Let t = a - 144/5. Factor -1/5*r**2 + t*r + 0.
-r*(r - 1)/5
Let u(p) = -8*p**3 + p**2 + 8*p - 8. Let g be (-1)/1*(-2 - 5). Let b(o) = -7*o**3 + o**2 + 7*o - 7. Let y(a) = g*b(a) - 6*u(a). Solve y(z) = 0.
-1, 1
Let t(y) be the second derivative of -1/60*y**5 + 0 + 0*y**2 - 1/126*y**7 + 0*y**3 - 1/45*y**6 - y + 0*y**4. Determine m, given that t(m) = 0.
-1, 0
Let i(j) = j**3 + 6*j**2 - 8*j - 3. Let c be i(-7). Suppose l + 6 = 4*w, -3*w - 1 = -4*l + 1. Factor 3*h**4 - 1 + 0*h - w*h**c - 2*h**3 + 2*h.
(h - 1)**3*(h + 1)
Let w(h) = -h**2 + 3*h. Let z be 1/4 + 9/(-4). Let f(k) = -k + 1. Let j = -2 - -1. Let l(m) = j*w(m) + z*f(m). Factor l(o).
(o - 2)*(o + 1)
Suppose -25 = -2*b - 5*d, 3*d + 35 + 12 = 5*b. Let a be (-4)/b*3/(-3). What is o in 8/5*o + 26/5*o**3 + 0 + 12/5*o**4 + 24/5*o**2 + a*o**5 = 0?
-2, -1, 0
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