13
Let s(m) be the third derivative of m**6/40 - 7*m**5/20 + 7*m**4/4 - 4*m**3 - 278*m**2. Suppose s(z) = 0. Calculate z.
1, 2, 4
Let t(d) be the first derivative of -d**3/3 + 57*d**2 - 3249*d - 3. Factor t(v).
-(v - 57)**2
Let a(h) be the second derivative of -h**6/270 - 2*h**5/45 - 23*h**4/108 - 14*h**3/27 - 2*h**2/3 - 233*h + 2. Determine o, given that a(o) = 0.
-3, -2, -1
Let u(o) be the third derivative of -1/50*o**5 + 0*o + 0 - 5*o**2 + 0*o**4 + 0*o**6 + 1/10*o**3 + 1/350*o**7. Find n, given that u(n) = 0.
-1, 1
Suppose 25/2 - 1/2*b**3 + 23/2*b**2 + 49/2*b = 0. Calculate b.
-1, 25
Let b(z) be the third derivative of 3*z**2 + 0 - 1/7*z**3 - 1/20*z**5 + 0*z - 9/56*z**4. Determine s, given that b(s) = 0.
-1, -2/7
Let a(s) = 9*s**2 + 20*s + 4. Let h(n) be the second derivative of 25*n**4/3 + 110*n**3/3 + 45*n**2/2 + 6*n. Let k(r) = 45*a(r) - 4*h(r). What is l in k(l) = 0?
-4, 0
Let j(f) be the second derivative of f**6/2340 + f**5/390 + f**4/156 - 2*f**3 + 7*f. Let u(r) be the second derivative of j(r). Factor u(d).
2*(d + 1)**2/13
Let m(q) = 5*q**4 - 6*q**3 - 2*q - 5. Let d(x) = 6*x**4 - 7*x**3 - 3*x - 6. Let u be 2*(0 + -3)*4/(-6). Let b(c) = u*d(c) - 5*m(c). Solve b(p) = 0 for p.
-1, 1
Let b be ((-5)/(-15)*0)/1. Let h = 13 - 75/7. Factor h*a + 24/7*a**2 + 12/7*a**3 + b + 2/7*a**4.
2*a*(a + 2)**3/7
Suppose -8 = -m - v, -4*v - 6 = 2*m - 38. Factor m - 5/2*u - 5/2*u**2.
-5*u*(u + 1)/2
Factor -507*c**2 + 0*c + 26*c**3 - 1/3*c**4 + 0.
-c**2*(c - 39)**2/3
Let k(h) be the third derivative of 1/3*h**5 + 0*h - 5*h**3 + 3 + 115/24*h**4 - 7*h**2. Factor k(x).
5*(x + 6)*(4*x - 1)
Suppose 1458*v - 1488*v = -90. What is p in 0*p**2 - 3/4*p**v + 0 + 1/4*p**4 + p = 0?
-1, 0, 2
Let s be 4 - 1 - (0 + 0). Solve -3*q**3 - 7*q**2 + 20*q - 12 - q**s + 9*q**2 - 6*q**2 = 0.
-3, 1
Let b(i) be the first derivative of 3/8*i**2 - 3/4*i**3 - 3/16*i**4 - 8 + 9/4*i. Find f, given that b(f) = 0.
-3, -1, 1
Let h(n) be the third derivative of n**6/160 - 9*n**4/32 + 11*n**2 - 7*n. Factor h(l).
3*l*(l - 3)*(l + 3)/4
Let k be -5 + 37/7 - (-12)/7. Factor -14*d + k*d**2 + 3*d**2 - 191 + 199.
(d - 2)*(5*d - 4)
Let z = -175 + 258. Let q = 85 - z. Find u, given that -6/5 - 19/5*u + 7/5*u**q = 0.
-2/7, 3
Let f(c) = -c**3 - 6*c**2 - c - 6. Let s be f(-6). Let w = s + 3. Factor 6*v**2 - w*v**4 - 7 + 5 - 1.
-3*(v - 1)**2*(v + 1)**2
Let u be (-106)/(-34) + (-4)/34. Factor i**2 - 41*i**4 + i**2 + 42*i**4 + u*i**3.
i**2*(i + 1)*(i + 2)
Let h be 4/7*(-1 + 5 - (-2046)/(-620)). Determine z, given that -12/5*z**2 - 24/5*z - h*z**3 - 16/5 = 0.
-2
Factor 0 + 45*x + 3/2*x**2.
3*x*(x + 30)/2
Let x(h) be the first derivative of -10*h**5/13 + 305*h**4/26 - 76*h**3/3 - 548*h**2/13 - 240*h/13 + 27. Suppose x(a) = 0. What is a?
-2/5, 3, 10
Let f(k) be the first derivative of 1/2*k**6 + 6/5*k**5 + 6*k - 21 - 3/2*k**4 + 3/2*k**2 - 4*k**3. Solve f(y) = 0 for y.
-2, -1, 1
Let q(v) = v + 1. Let j(i) = -i**2 + 9*i + 23 - 16 + 3*i**2. Let u(k) = -j(k) + q(k). What is a in u(a) = 0?
-3, -1
Suppose -19*j = -16*j - 36. Determine g, given that 48*g**3 - 48*g - j*g**2 + 3*g**2 + 4 - 5 - 11 + 21*g**4 = 0.
-2, -1, -2/7, 1
Let n = -6 + 1. Let r be (n/(-20))/(2/24). Factor 0*a**2 + 0*a**2 + 2*a**3 + 1 - 3*a**r - a**2 + a.
-(a - 1)*(a + 1)**2
Let x(f) be the first derivative of f**4 - 4*f**3/3 - 34*f**2 - 60*f - 81. Factor x(r).
4*(r - 5)*(r + 1)*(r + 3)
Let r be 119/68 + (-2)/(-8). Let y be (-1)/(-3) - 2/6. Suppose 1/3*w + 1/6*w**r + y = 0. Calculate w.
-2, 0
Let w(v) be the second derivative of v**6/15 - 7*v**5/10 - v**4/6 + 7*v**3/3 + 5*v + 1. Factor w(x).
2*x*(x - 7)*(x - 1)*(x + 1)
Factor 2/5*r**3 - 4/5 - 8/5*r + 1/5*r**4 - 3/5*r**2.
(r - 2)*(r + 1)**2*(r + 2)/5
Let d be 1 - (4/3 - 1/3). Let m be (1 + -2)*(-8 + 14 + -11). Factor d + 1/3*j**m + 2/3*j**4 - 2/3*j**2 + j - 4/3*j**3.
j*(j - 1)**2*(j + 1)*(j + 3)/3
Let z = 85 + -76. Factor -v**3 - 5*v**2 + v**2 - 13*v**5 + 5*v**3 + z*v**5 + 4*v**4.
-4*v**2*(v - 1)**2*(v + 1)
Let p = -5140/9 + 118238/207. Factor -2/23*u**2 - 6/23*u**4 + 0*u + 0 + p*u**5 + 6/23*u**3.
2*u**2*(u - 1)**3/23
Solve -b**5 + 260*b + 4*b**5 + 50*b**4 + 3 + 9 + 320*b**2 + 2*b**5 + 68 + 185*b**3 = 0 for b.
-4, -2, -1
Let o(a) be the third derivative of -29/150*a**5 + 0*a**3 + 0 + 0*a - 1/75*a**7 - 1/10*a**4 - 1/10*a**6 - 12*a**2. Let o(c) = 0. Calculate c.
-3, -1, -2/7, 0
Suppose -4*k + 1 = -y - 4, -75 = -5*y - 5*k. Find h, given that -6*h - y*h + 6 - 16*h - h**2 + 28*h = 0.
-6, 1
Suppose 8*o + 8*o - 32 = 0. Solve -1470 + f**o + f**3 + 1470 - f**4 - f = 0 for f.
-1, 0, 1
Let n(y) be the second derivative of -y**5/25 - 19*y**4/3 - 556*y**3/15 - 368*y**2/5 + 303*y. Factor n(d).
-4*(d + 1)*(d + 2)*(d + 92)/5
Factor 15/7 + 1/7*x**4 + 2*x - 2*x**3 - 16/7*x**2.
(x - 15)*(x - 1)*(x + 1)**2/7
Let u(m) = -m**2 - m - 1. Let y(f) = 2*f**2 + 6*f - 3. Let a(s) = u(s) + y(s). Let i(o) = 5*o**2 + 20*o - 16. Let w(k) = -18*a(k) + 4*i(k). Factor w(n).
2*(n - 4)*(n - 1)
Let x(i) be the second derivative of -i**4/48 + i**2/8 - 35*i - 1. Factor x(g).
-(g - 1)*(g + 1)/4
Let a = -23/12 - -9/4. Let l be ((0/4)/(-4))/1. Let 0*k + 0*k**3 + 1/3*k**4 + l + a*k**5 + 0*k**2 = 0. What is k?
-1, 0
Solve -2015*q**5 - 5*q**3 - 2*q**2 + 2030*q**5 + 14*q**4 + 2*q**3 = 0 for q.
-1, -1/3, 0, 2/5
Suppose -2*p = 3*p + 10, 4*m - 60 = -2*p. Factor -4*c**3 - 3 + 6 + 4*c**2 + 5 - m*c**2 + 4*c + 4*c**4.
4*(c - 2)*(c - 1)*(c + 1)**2
Let d(z) be the third derivative of -2*z**2 + 1/36*z**4 + 1/60*z**5 - 1/18*z**3 + 0*z + 0. What is g in d(g) = 0?
-1, 1/3
Let c(o) = 9 - 13 - 2*o**2 + 3*o**2 + 5*o + 8. Let f be c(-5). Factor -18*i**2 + 8*i**2 + f*i + 12*i**2.
2*i*(i + 2)
Suppose 5380*d - 5377*d = 12. Let o(g) = 2*g**3 - 4*g**2 - 4*g. Let w(a) = 2*a + 5*a**2 + 4*a - a - 2*a**3. Let y(j) = d*w(j) + 5*o(j). Factor y(l).
2*l**3
Suppose -27/4*i + 27/4*i**3 + 1/4*i**4 + 49/4*i**2 - 25/2 = 0. What is i?
-25, -2, -1, 1
Let d(m) be the second derivative of -m**4/84 - 3*m**3/7 - 81*m**2/14 + 90*m. Determine o so that d(o) = 0.
-9
Let p(n) be the second derivative of n**7/840 + n**6/360 - n**5/30 - n**4/6 - 3*n**3 + 18*n. Let x(d) be the second derivative of p(d). Let x(t) = 0. What is t?
-2, -1, 2
Let c be ((-7)/4)/((-273)/312). Let g(d) be the second derivative of 0 + 0*d**3 + 2/5*d**c - 1/20*d**4 + 10*d + 1/100*d**5. Suppose g(w) = 0. What is w?
-1, 2
Let b(a) = -a**4 - 137*a**3 + 247*a**2 - 129*a. Let s(h) = -68*h**3 + 124*h**2 - 64*h. Let j(r) = 4*b(r) - 10*s(r). Solve j(l) = 0 for l.
0, 1, 31
Let g(a) be the third derivative of -a**6/600 - a**5/30 + 11*a**4/120 + 7*a**2 + 15*a. Find i such that g(i) = 0.
-11, 0, 1
Let h(f) = -8 + 4*f - 4*f**3 + 0 - 7*f**2 + 11*f**2. Let x(a) = -a**4 - 11*a**3 + 13*a**2 + 11*a - 23. Let g(m) = -11*h(m) + 4*x(m). Factor g(v).
-4*(v - 1)**2*(v + 1)**2
Let i(t) be the second derivative of 28*t**6/45 - 5*t**5/3 + 13*t**4/9 - 4*t**3/9 + 80*t - 2. Suppose i(m) = 0. What is m?
0, 2/7, 1/2, 1
Let n = 3/44 - -101/132. Let i(x) be the first derivative of n*x**3 - 3 - 10*x + 5/8*x**4 - 5*x**2. What is v in i(v) = 0?
-2, -1, 2
Let l be (-2)/(-8) + (-203)/28. Let w = l + 9. Factor 6*t**3 - t**2 + 0*t**3 + 2*t**w + t**4 - 8*t**3.
t**2*(t - 1)**2
Let i(v) be the first derivative of -v**4 - 4*v**3/3 + 2*v**2 + 4*v - 4. Let z(q) = 0 + q**2 + q**3 + 2*q - 3*q - 1. Let a(y) = 2*i(y) + 6*z(y). Factor a(k).
-2*(k - 1)*(k + 1)**2
Let o(s) = s**2 + 10*s - 5. Let p be o(-11). Factor 4*k**2 + 0 - 2*k**2 - p + 4*k.
2*(k - 1)*(k + 3)
Let a(n) be the third derivative of -n**5/15 - 21*n**4/2 + 260*n**3/3 - 46*n**2 + 3. Factor a(q).
-4*(q - 2)*(q + 65)
Let l(n) = -6*n**2 + 11*n + 6. Let i be l(6). Let h be (-6)/(-5)*(-540)/i. Factor 6*b + 3/2*b**2 + h.
3*(b + 1)*(b + 3)/2
Let u(v) be the third derivative of 5*v**5/18 + 15*v**4/2 + 81*v**3 - 111*v**2. Factor u(k).
2*(5*k + 27)**2/3
Suppose -5 = 5*y - 5*r, 3*y - 7 = -7*r + 8*r. Let x(f) be the first derivative of -3/5*f**2 - 4 + 3/10*f**y + 4/15*f**3 - 4/5*f. Suppose x(p) = 0. What is p?
-1, -2/3, 1
Let g(o) = 15*o**4 + 127*o**3 + 74*o**2 - 232*o - 16. Let k(p) = -5*p**4 - 42*p**3 - 24*p**2 + 77*p + 6. Let a(w) = 3*g(w) + 8*k(w). Let a(n) = 0. Calculate n.
-8, -2, 0, 1
Suppose 0 = 2*u - 3 - 3. Suppose 8*i**u - 18*i**2 - i**5 - 28*i**3 + 27*i - i**3 - 9*i**4 - 5*i**3 + 27 = 0. Calculate i.
-3,