3/4
Let d(s) = 3*s. Let v(r) = -r**2 - 2*r. Let o(t) = -2*d(t) - 3*v(t). Factor o(m).
3*m**2
Suppose -6/13*x**3 - 6/13*x**4 - 2/13*x**2 - 2/13*x**5 + 0*x + 0 = 0. Calculate x.
-1, 0
Let u(c) = 10*c**4 - 20*c**3 - 10*c**2 + 20*c - 7. Let s(h) = 5*h**4 - 10*h**3 - 5*h**2 + 10*h - 3. Let r(w) = -7*s(w) + 3*u(w). Solve r(g) = 0 for g.
-1, 0, 1, 2
Let a(m) be the first derivative of 2 - 15/2*m**2 + 3*m**5 - 15/2*m**4 - 1/2*m**6 + 10*m**3 + 3*m. Find v such that a(v) = 0.
1
Let i = -2 - -4. Suppose 0 = 2*o + 3*o + 4*k + i, 2*k + 10 = 2*o. Factor 4*s**3 - 2*s**3 - 2*s**o - 4*s**3.
-2*s**2*(s + 1)
Factor -15*d**3 + 2*d**4 - 4*d**4 - 3*d**4.
-5*d**3*(d + 3)
Let b(c) be the third derivative of 1/8*c**4 + 0*c**3 + 1/10*c**5 + 1/40*c**6 - 3*c**2 + 0*c + 0. Factor b(a).
3*a*(a + 1)**2
Let g be (-2 + 6/48*52)/2. Factor -g - 1/4*t**2 + 3/2*t.
-(t - 3)**2/4
Let m(w) = -w + 3. Let x = 8 - 5. Let k be m(x). Factor 0 + 2/9*c**5 + 0*c**4 - 2/9*c**3 + 0*c**2 + k*c.
2*c**3*(c - 1)*(c + 1)/9
Let f(j) be the first derivative of -3*j**4/32 + j**3/24 + 3*j**2/16 - j/8 + 26. Factor f(m).
-(m - 1)*(m + 1)*(3*m - 1)/8
Let v(u) be the third derivative of u**6/420 - u**5/210 - 5*u**4/84 - u**3/7 + 4*u**2. Factor v(z).
2*(z - 3)*(z + 1)**2/7
Let y = -46 - -139/3. Let t be ((-1)/3)/((-1)/2). Factor y*p**3 + 0 - 1/3*p**2 - t*p.
p*(p - 2)*(p + 1)/3
Let c(b) be the second derivative of 4*b**5/5 - 7*b**4/3 - 4*b**3/3 + 9*b. Find x, given that c(x) = 0.
-1/4, 0, 2
Let n(p) be the third derivative of p**7/945 + p**6/270 + p**5/270 + 7*p**2. Factor n(u).
2*u**2*(u + 1)**2/9
Let x be 24/6*(1 - 0). Suppose -x*t - 12 = 0, 2*t - 9 = 2*v + 7*t. Solve -2/7 + 2/7*d + 2/7*d**5 - 2/7*d**4 - 4/7*d**v + 4/7*d**2 = 0 for d.
-1, 1
Let u(w) = 8*w**2 - 23*w - 12. Let k(i) = 8*i - 3*i**2 - i**2 + 4 + i**2. Let n(h) = -11*k(h) - 4*u(h). Determine c, given that n(c) = 0.
-2
Let s = 413 - 2879/7. Factor -8/7 - s*x**2 - 4*x.
-4*(x + 2)*(3*x + 1)/7
Let n(o) = o**3 + 21*o**2 + o + 23. Let d be n(-21). Factor -8/7 + 2/7*s**3 - 10/7*s**d + 16/7*s.
2*(s - 2)**2*(s - 1)/7
Let q = -156 - -5. Let i = q - -458/3. Let -i*a**4 + 10/3*a**3 - 10/3*a**2 - 1/3 + 5/3*a + 1/3*a**5 = 0. What is a?
1
Let l(k) be the second derivative of -k**4/4 + 5*k**3/3 - 3*k**2/2 - 22*k. What is z in l(z) = 0?
1/3, 3
Suppose -2*n - g + 2 = 0, -1 = -g - 3. Let l(v) be the second derivative of 0*v**n + 1/45*v**6 + 1/9*v**3 + 1/6*v**4 - 2*v + 0 + 1/10*v**5. Factor l(x).
2*x*(x + 1)**3/3
Let p be ((-51)/(-17)*(-2)/(-3))/3. Let f(l) be the first derivative of l**4 - 3 + 0*l - p*l**3 + 2/5*l**5 - 2*l**2. Find m such that f(m) = 0.
-2, -1, 0, 1
Let h be 57/4*(-3)/(-9). Let b = 5 - h. Solve -t**2 + 0 - 3/4*t**3 - b*t = 0.
-1, -1/3, 0
Suppose -5*x = 47 - 67. Let t(o) be the third derivative of -1/6*o**3 - 3*o**2 - 1/120*o**5 - 1/16*o**x + 0*o + 0. Find h, given that t(h) = 0.
-2, -1
Let h(u) = -9*u - 3*u**2 + u**3 - u**2 + 5 + 7 - 3*u**2. Let x be h(8). Factor 6*p**2 - 10*p + 8 + 0*p**2 - x.
2*(p - 1)*(3*p - 2)
Let b(w) = -3*w - 1. Let j be b(-1). Suppose j = q + g - 1, g = 5*q - 9. Determine x, given that 6*x - q*x**2 - 3*x - x = 0.
0, 1
Let v(k) be the third derivative of k**8/1176 + k**7/735 - k**6/210 - 9*k**2. Determine d so that v(d) = 0.
-2, 0, 1
Let u(n) be the first derivative of -n**7/840 - n**6/480 + n**5/240 + n**4/96 - 5*n**2/2 + 6. Let g(f) be the second derivative of u(f). Factor g(p).
-p*(p - 1)*(p + 1)**2/4
Suppose 0 = -2*a + 4*a - 4. Let f = -3 - -6. Let 0*o - 5/4*o**4 - 7/4*o**f + 0 - 1/2*o**a = 0. What is o?
-1, -2/5, 0
Let q(x) = -4*x**3 - 2*x + 6. Let d(u) = 3*u**3 + u**2 + u - 5. Let f(v) = -7*d(v) - 6*q(v). Factor f(z).
(z - 1)**2*(3*z - 1)
Let o = -31 - -63/2. Let -o*l**4 + 0 - 1/2*l - 3/2*l**3 - 3/2*l**2 = 0. Calculate l.
-1, 0
Suppose 4*j = -40 + 8. Let s be (j/(-10))/(4/10). Factor q**2 - 6*q**3 - s + q**2 - 2*q**3 + 8*q.
-2*(q - 1)*(q + 1)*(4*q - 1)
Let f(l) be the second derivative of -l**6/120 - 3*l**5/80 - l**4/16 - l**3/24 + 5*l. Let f(s) = 0. What is s?
-1, 0
Let j(k) be the first derivative of 4*k**5/5 + 3*k**4 - 4*k**3/3 - 6*k**2 + 18. Factor j(h).
4*h*(h - 1)*(h + 1)*(h + 3)
Let k(h) be the first derivative of -h**6/4 + 3*h**5/5 + 3*h**4/4 - 4*h**3 + 21*h**2/4 - 3*h + 17. Factor k(l).
-3*(l - 1)**4*(l + 2)/2
Let s(c) = -c**5 - c**2 - 1. Let b(o) = -2*o**5 + 4*o**4 + 32*o**3 + 26*o**2 + 10. Let l(g) = b(g) + 10*s(g). Solve l(n) = 0.
-1, -2/3, 0, 2
Let s(z) be the second derivative of z**5/30 - z**3/9 - 3*z. Factor s(i).
2*i*(i - 1)*(i + 1)/3
Let i be (-3)/(-2)*112/24. Let k = i - 2. Find l such that 4*l**5 + l**4 + l - k*l**5 - 2*l**2 + l**4 + 0*l**5 = 0.
-1, 0, 1
Let o(f) be the third derivative of f**5/30 + f**4 + 11*f**3/3 - 3*f**2. Let o(j) = 0. What is j?
-11, -1
Let k(a) be the second derivative of a**7/252 - 7*a**6/180 + 13*a**5/120 + a**4/24 - a**3/2 - a - 40. Determine i so that k(i) = 0.
-1, 0, 2, 3
Let g(f) = -2*f**5 + 10*f**4 - 5*f**3 + 15*f**2 + 9. Let i(j) = j**5 - 5*j**4 + 3*j**3 - 7*j**2 - 4. Let q(z) = -4*g(z) - 9*i(z). Factor q(r).
-r**2*(r - 3)*(r - 1)**2
Let b(i) = -3*i - 15. Let q be b(-5). Suppose 0*y**2 + 0*y + 0 + q*y**4 + 1/2*y**5 + 0*y**3 = 0. What is y?
0
Suppose 2*n = -2*n + 8. Let k be -2 - (-2 + 0 - n). What is d in d**3 + 51*d**2 - 2*d - 3*d**3 - 47*d**k = 0?
0, 1
Let v(l) be the first derivative of -2*l**3/27 + l**2/3 - 4*l/9 - 32. Solve v(a) = 0.
1, 2
Suppose -4*m + 3*i + 15 + 22 = 0, -2*i - 6 = 0. Suppose -6*l + m*l - 2 = 0. Suppose -1/3 - 4/3*u - 4/3*u**3 - 1/3*u**4 - 2*u**l = 0. What is u?
-1
Let c(l) = 18*l**3 + l**2 - 2*l - 2. Let x(h) = h + 1. Let s(y) = c(y) + 2*x(y). Let b be s(1). Factor 3*p - 11 + 3 - b*p - 6*p**2.
-2*(p + 2)*(3*p + 2)
Suppose s + 0 + 16 = 2*n, 0 = -5*s. Find d such that -n*d**4 - 10/3*d**3 + 10/3*d + 28/3*d**2 - 4/3 = 0.
-1, -2/3, 1/4, 1
Factor 2*n**2 + 104 + 24*n + 0*n**2 - 32.
2*(n + 6)**2
Suppose -5*c + 4 = -1. Let t be 1/(-2) - c/(-1). Suppose -1/2*p + t*p**3 - 1/2 + 1/2*p**2 = 0. What is p?
-1, 1
Let b(x) be the second derivative of -2/75*x**6 + 0 + 3/50*x**5 - 3*x + 1/210*x**7 - 1/15*x**4 + 1/30*x**3 + 0*x**2. Solve b(d) = 0.
0, 1
Let r be 160/70 + (1 + -3)/1. Find c, given that -r*c**2 + 2/7 + 0*c = 0.
-1, 1
Factor 0*q**3 + 0*q + 1/3*q**2 - 1/3*q**4 + 0.
-q**2*(q - 1)*(q + 1)/3
Let l be -6*((-6)/45 + (-4)/20). What is w in w + 1/2*w**l + 1/2 = 0?
-1
Let b(y) be the second derivative of -y**7/14 - 2*y**6/5 - 9*y**5/10 - y**4 - y**3/2 - y. Let b(o) = 0. Calculate o.
-1, 0
Let v(f) be the third derivative of f**6/120 + f**5/30 - f**4/6 - 4*f**3/3 + 3*f**2. Solve v(w) = 0 for w.
-2, 2
Let w(n) be the third derivative of n**8/5040 + n**7/2520 - n**6/1080 - n**5/360 - n**3/6 - n**2. Let l(k) be the first derivative of w(k). Factor l(s).
s*(s - 1)*(s + 1)**2/3
Let q be (-1)/(-2)*-4 + -368. Let t = q + 2594/7. Let 2/7*v**4 + 2/7*v**2 + 0 + t*v**3 + 0*v = 0. Calculate v.
-1, 0
Suppose 4*z + 20 = -s, -3*s = -4*z + 2*z + 4. Let r(g) = -g**2 + g - 1. Let t(v) = 3*v**2 - 4*v + 4. Let m(h) = s*r(h) - t(h). Factor m(o).
o**2
Suppose -5 = -k - 3*d, -5*k - d + 2*d + 25 = 0. Factor -6*o**2 + 3*o**5 + 3*o**4 + 6*o**3 - 9*o + 0 - 3 + o**4 + k*o**4.
3*(o - 1)*(o + 1)**4
Let m be (10/25)/((-26)/20). Let r = m + 21/26. Factor 3/2*c**2 + 7/4*c + r.
(2*c + 1)*(3*c + 2)/4
Let g(w) = -15*w**4 - 207*w**3 - 417*w**2 - 192*w + 33. Let q(p) = -p**4 - 13*p**3 - 26*p**2 - 12*p + 2. Let t(x) = 2*g(x) - 33*q(x). Let t(y) = 0. What is y?
-2, -1, 0
Let l(q) = q. Let c(y) = 2*y**2 - 3*y + 6. Let b(n) = c(n) - 5*l(n). Factor b(o).
2*(o - 3)*(o - 1)
Let y(z) be the first derivative of -5*z**6/6 - 4*z**5 - 15*z**4/2 - 20*z**3/3 - 5*z**2/2 - 3. What is u in y(u) = 0?
-1, 0
Solve 0 + k + 3/2*k**2 - 3/2*k**4 - k**3 = 0 for k.
-1, -2/3, 0, 1
Suppose 2*l - 4*l = -4. Let y(z) = -z**3 - z**2 - 3*z - 2. Let t be y(-2). Factor -2/3 - t*v**2 - l*v**4 + 20/3*v**3 + 4*v.
-2*(v - 1)**3*(3*v - 1)/3
Let m(l) be the second derivative of 5*l**7/14 + l**6/3 + 31*l. Determine a, given that m(a) = 0.
-2/3, 0
Let s = -203 + 206. Factor 0 + 0*u + 3/2*u**s - 3/2*u**2.
3*u**2*(u - 1)/2
Let f(d) be the first derivative of -6*d**5 + 59*d**4/2 - 26*d**3 - 11*d**2 + 12*d - 33. Solve f(z) = 0.
-2/5, 1/3, 1, 3
Factor -20*g + 5*g**3 + 91*g**2 - 35*g**2 - 46*g**2 - 40.
5*(g - 2)*(g + 2)**2
Determine u so tha